REVIEW ARTICLE

Subsonic jet aeroacoustics: associating experiment, modellingand simulation

Peter Jordan Æ Yves Gervais

Received: 18 December 2006 / Revised: 12 September 2007 / Accepted: 12 September 2007 / Published online: 17 October 2007

� Springer-Verlag 2007

Abstract An overview of jet noise research is presented

wherein the principal movements in the field are traced

since its beginnings. Particular attention is paid to the

evolution of our understanding of what we call a ‘‘source

mechanism’’ in free shear flows; to the theoretical, experi-

mental and numerical studies which have nurtured this

understanding; and to the currently unresolved conceptual

difficulties which render analysis of experimental and

numerical data so difficult. As it is clear that accelerated

progress in this field of research can be made possible by a

more effective synergy between the theoretical, experi-

mental and numerical disciplines—one which draws in

particular on the impressive recent progress in experi-

mental and numerical techniques—we endeavour to

elucidate the various ‘‘source’’ characteristics identified by

these different means of study; the points on which the

studies agree or disagree, and the significance of such

accord or discord; and, the new analysis possibilities which

can now be realised by effectively associating experiment,

modelling and simulation.

1 Introduction

The science of aeroacoustics is now over fifty years old,

and the considerable range of analysis strategies which

have evolved during this time have seen much progress.

Experimental diagnostics have become more sophisticated,

as a result of improvements in measurement technology,

and the more ambitious and innovative data extraction and

analysis techniques which these improvements have

encouraged. The numerical simulation constitutes a rela-

tively recent aid to our understanding of the most

fundamental aspects of the physics of sound production: as

this discipline matures more light is shed on the subtleties

which comprise the source mechanisms in jets, and guid-

ance is provided, both for jet-noise modelling strategies,

and for the implementation of perspicacious experimental

measurement and analysis. As a result of this enhanced

measurement and analysis capability, our understanding of

the mechanisms underlying the production of sound by un-

bounded turbulence has improved, old ideas have been

revisited, and new challenges identified.

In this paper we present an overview of this progress,

with an emphasis on the association of experiment, mod-

elling and simulation. The paper is organised as follows. In

Sect. 2 we endeavour to clearly identify where we cur-

rently stand in terms of our understanding of the sound

production mechanisms in jets, and to outline the road by

which we have arrived at this point. This overview is fol-

lowed in Sect. 3 by a review of the more pertinant

experimental studies which have appeared in recent years,

and as some of the more interesting results have been

produced as a result of progress in measurement technol-

ogy, we pay particular attention to the new measurement

strategies which this progress has made possible. We out-

line and discuss the novel analysis procedures which have

accompanied these, and the impact that the results have had

on the way we attempt to model aerodynamically generated

sound. In Sect. 4 we look briefly at contributions from

numerical aeroacoustics, in terms of the physical insights

which these have provided, and finally a resume of some

current ideas regarding the dominant source mechanisms in

jets is provided in Sect. 5.

P. Jordan (&) � Y. Gervais

Laboratoire d’Etudes Aerodynamiques, UMR CNRS 6609,

Universite de Poitiers, Poitiers Cedex, France

e-mail: peter.jordan@lea.univ-poitiers.fr

123

Exp Fluids (2008) 44:1–21

DOI 10.1007/s00348-007-0395-y

To close the paper we discuss the implications of the

most recent analysis strategies for future aeroacoustic

research, highlighting in particular the weak points, where

additional energy needs to be focused, but also indicating

the possible directions in which the stronger points can

now be steered in order to further untangle our under-

standing of the noise-producing jet.

2 Where do we currently stand, and how did we get

here?

In order to put recent developments in their proper context

we here provide a brief history of aeroacoustics with regard

to the unbounded turbulent jet. While such a summary

cannot hope to be exhaustive in such a small number of

pages, we hope nonetheless to provide a relatively com-

prehensive outline of the main movements in this field

since its beginnings in the early 1950s.

2.1 Early ideas of the sound-producing jet

To begin it is worth pointing out that in fact, contemporary

with Lighthill (1952), other researchers were also beginning

to touch on the theoretical aspects of aerodynamically

generated sound: Moyal (1952) for example, in a study

focused on the spectra of turbulence in compressible fluid

media, had demonstrated how spectral components of the

turbulent velocity field lying normal to the wavenumber

vector (turbulent eddies) would excite velocity, pressure

and temperature components lying parallel to the wave-

number vector (acoustic perturbations) by means of non-

linear inertia terms. However, there is no question that the

real birth of aeroacoustics as we know it today is due to

Lighthill, whose more specific focus on the problem of

aerodynamically generated sound led to the observation that

the exact equations of fluid motion can be recast in the form

of an inhomogeneous wave equation, whose inhomogeneity

comprises all the non-linearities of the Navier–Stokes

equations. Such an equation describes freely propagating

linear disturbances (an acoustic field) which are driven by

the dynamics described by a non-linear term on the right-

hand-side. Lighthill recognised that this form is particularly

well-suited to the problem of the noise-producing jet, as

such a flow system comprises precisely this: a freely prop-

agating sound field, which is driven by a confined region of

intense rotational motion, where non-linearity reigns.

As this kind of differential equation had been familiar to

scientists for some time, mathematical tools were readily

available for its manipulation, and so a solution was forth-

coming whence it was possible to establish a number of

facts, which subsequently came to constitute our first ideas

on the mechanisms underlying the production of sound by

turbulence. The jet was known to comprise random turbulent

fluctuations, correlated over a spatiotemporal extent defined

by the integral scales of the turbulence. The double spatial

derivative in Lighthill’s source term implied a quadrupole

behaviour, and so the sources of jet noise came to be

understood as quadrupole elemental deformations associ-

ated with these correlated turbulent eddies. The spatial

extent of the eddies was supposed considerably less than the

wavelength of the sound waves transmitted from the flow,

implying that the quadrupole ‘‘sources’’ are acoustically

compact: this means that the source can be recrafted in such

a way that cancellations due to time differences between

sound waves radiated from different regions of a given eddy

can be ignored. The sources were thought to be convected by

the flow, and Lighthill stressed that it was therefore impor-

tant to consider the Lagrangian dynamics of the turbulence

in order to understand, or predict, the spectral content of the

effective source and its sound field. There are two further

important consequences of a convected source field: more

efficient radiation in the downstream direction, and a

Doppler shift in the frequency of the radiated sound field.

2.2 Flow–acoustic interaction

The next important development where this vision of the

sound producing jet is concerned arose as a result of the

need to deal with the effect of flow–acoustic interaction,

and in particular refraction of sound away from the jet

axis—which would lead to the cone of relative silence

which is known to exist at small angles, an effect attributed

by Lighthill to a preferred orientation of the quadrupole

sources. Because all of the non-linearities of the flow

equations are lumped into the right-hand-side of Lighthill’s

equation, all flow–acoustic interaction terms are effectively

hidden in the source. Ribner (1962) first discussed this, it

was experimentally observed by Atvars et al. (1965), and

Lilley (1974) derived a modified wave equation whereby

flow–acoustic interaction effects were effectively separated

from the ‘‘production’’ mechanisms and incorporated into a

third order Pridmore–Brown wave operator. This consti-

tuted the next evolution in our vision of the mechanism by

which the free jet produces sound. The aeroacoustic system

was now considered to comprise compact, convected

sources, whose sound fields are modified by the sheared

mean-flow into which they radiate.

2.3 Temperature effects

An additional source term related to temperature fluctua-

tions was also believed to exist, and its form was assumed

2 Exp Fluids (2008) 44:1–21

123

to be dipolar (see for example Fisher et al. 1973). An

extensive analysis of this source component was performed

by Tester and Morfey (1976) and Morfey et al. (1978). The

authors considered a Lilley-like description of the problem,

obtained low and high frequency solutions analytically, and

proceeded to examine the characteristics of a source term

which they considered to be due to scattering of the tur-

bulent pressure field by temperature-induced density

inhomogeneities. Their solution for the farfield sound led to

the proposition of master-spectra for the basic quadrupole,

and additional temperature-induced dipole contributions.

Put together these master-spectra gave shapes similar to

those observed experimentally for radiation in sideline

directions. Furthermore, they argued that the dipole con-

tribution would scale with velocity raised to the sixth

power.

The above description of the effects of heating were

globally accepted for the best part of 30 years. However,

recently Viswanathan (2004) has raised some serious

questions about the validity of these interpretations, and

the reliability of the experimental data which was used to

support both the existence of a dipole master spectrum

and the sixth power velocity dependence. By means of an

exhaustive study, wherein the specific effects of Reynolds

number, jet temperature, and both jet-dynamic and

acoustic Mach numbers1 were investigated, Viswanathan

(2004) was able to demonstrate quite convincingly how

the characteristic ‘‘hump’’ in the farfield spectra, tradi-

tionally attributed to the effect of the dipole master

spectrum, is in fact due to a Reynolds number effect

(heating a jet at constant Mach number leads to a

reduction in the Reynolds number). Viswanathan shows

how the effect of heat alone does not change the spectral

character of the noise radiated in sideline directions. On

the other hand the effect of heating on the sound field

radiated at small angles to the jet is shown to involve a

narrowing of the spectrum. A final important effect of

heating, observed in early experiments (Tanna et al. 1975;

Tanna 1977) and which has been confirmed by the

experiments of Viswanathan (2004), is the respective

increase and decrease in sound power radiated by the

flow which occurs when low and high velocity jets are

heated: at a critical acoustic Mach number of 0.7 the

effects of heating are reversed. Both this tendency, and

the spectral narrowing which occurs for sound radiated at

small angles to the jet axis are currently not clearly

understood and warrant further attention.

2.4 Vortex-noise analogies

Before going on to discuss the generalities of what con-

stitutes an acoustic analogy, three further important

contributions must first be cited. These are due to Powell

(1964), Howe (1975) and Mohring (1978) and comprise

acoustic analogies where the source term is formulated in

terms of the vorticity of the flow. The appeal of this kind of

analogy is largely constituted by the more intuitive feel

which it provides where the mechanisms underlying the

sound production are concerned—vortical motion is more

intuitively understood than the double divergence of a

second order stress tensor! However, in addition to this

feature of the vortex-noise analogies, there is some evi-

dence to suggest that sources so defined bring us closer to

the true physics underlying the production of sound by

unbounded turbulence (Ewert and Schroeder 2003; Cabana

et al. 2006), and, that as a result, this kind of analogy is

more robust when it comes to source modelling and its

associated inaccuracies (Schram and Hirschberg 2003;

Schram et al. 2005).

In the foregoing we have tried only to give a broad

outline of the early development of the acoustic analogy,

the interested reader can refer to the review article of

Ribner (1981) for a more exhaustive treatment of the

subject.

2.5 On the generalities of an acoustic analogy

At this point it is worth considering what precisely con-

stitutes an acoustic analogy, in order to better understand

the different forms which such a construct can take. In the

case of any of the analogies discussed above there is an

implicit linearisation about some base flow. In the case of

Lighthill-like analogies the base flow is homogeneous,

uniform, while for Lilley-like analogies the base-flow is

parallel and sheared. In each case the residual system—i.e.

the difference between the base-flow and the full com-

pressible Navier–Stokes equations—is used to define the

source, which is then considered to drive, or excite the

base-flow system. The appeal of the Lighthill-like analo-

gies is that it is relatively straightforward to compute the

response of the base-flow to such excitation; we thus see

how the trick is to define a base-flow which is described by

a partial differential equation to which either known ana-

lytical solutions exist, or which is amenable to relatively

straightforward numerical solution. The inconvenience is

that the ‘‘source’’ term must be known in full—and of

course the simpler the base-flow, the greater the complexity

of the source term if the equation is to remain exact. This

reveals an interesting situation, which is at the heart of

much controversy in aeroacoustics today: depending on the

1 Jet dynamic Mach is defined as U/cj where U is the jet exit velocity,

and cj the sound speed based on the jet temperature, acoustic Mach

number is defined as U/co, where co is the ambient temperature.

Exp Fluids (2008) 44:1–21 3

123

particularities of the linearisation procedure, and the

resultant base-flow, the source definition will be different;

and so, this raises the philosophical question as to what

precisely constitutes a source mechanism. If nothing has

been discarded then the acoustic analogy is exact, the

physics of sound production is therefore described in all its

detail, and yet the space–time dynamics of what has been

called a source can vary considerably depending on the

particular analogy which has been proposed! In effect, this

situation demonstrates that in most cases there is a con-

siderable degree of redundancy (where sound ‘‘production’’

per se is concerned) in source terms so defined. In the case

of Lighthill-like analogies the redundancy of the source

term is largely manifest in the flow/acoustic effects which

are an inherent part of the source definition. A Lilley-like

analogy removes some of this redundancy by including

mean-flow/acoustic effects as part of the base flow

response; however, a certain degree of redundancy does

remain: much of the remaining source dynamic is inef-

fective in the excitation of progressive pressure modes

(perturbations which will be transmitted to the farfield):

only those source components which are acoustically

matched will couple with the farfield (Ffowcs-Williams

1963; Crighton 1975). Needless to say the Lighthill-like

analogy contains this redundancy in addition to the afore-

said flow/acoustic effects. In both Lighthill- and Lilley-like

analogies the solution procedure for the base-flow response

involves an inherent ‘‘sorting-out’’ of the source redun-

dancies: in both systems the Greens function solution for

the base-flow response translates a filtering operation

which only passes acoustically matched source compo-

nents. This filtering amounts to the radiation criterion

x = jc (Ffowcs-Williams 1963; Crighton 1975).

The implication here is that none of the aforementioned

analogies are optimal—the job of describing the physics of

sound production is essentially shared between the source

term (the excitation) and the response of the differential

equation which describes the base-flow. This is one of the

reasons for the considerable controversy which surrounds

the question of what constitutes a meaningful source defi-

nition. Recognising this, Goldstein (2003) endeavoured to

put the acoustic analogy on a more general footing, and

demonstrated indeed how the procedure can be generalised

such that a linearisation can be performed about any given

base-flow. He demonstrates how Lighthill- and Lilley-like

analogies are just special cases in a more general frame-

work, and how in fact the base-flow can comprise an

unsteady system, e.g. a URANS-type solution to the

Navier–Stokes equations, or an incompressible Navier–

Stokes solution. Indeed, in a later paper Goldstein (2005)

proposes an acoustic analogy, which, were it possible to

achieve, might constitute an optimal description of the

problem, whence the source definition would comprise no

redundancy and would thus provide a true source defini-

tion. Unfortunately, in all but a periodic, homogeneous

unsteady flow system (such as homogeneous, isotropic

turbulence in a periodic cube), such a procedure will vio-

late locality constraints, and so in the case of flows of

practical interest it is unlikely that this procedure can be

applied. Furthermore, the proposed method involves a fil-

tering operation based on the criterion x = jc, which is

simply a spectral expression of the radiation criterion for

small amplitude fluctuations propagating in an irrotational

medium at rest or in uniform motion; it is uncertain that

such a filtering operation will isolate acoustic disturbances

in a more complex rotational flow system.

We will later see how these questions are finally

becoming, and indeed must be made the primary focus of

the experimental approach. The experimentalist must

understand how to relate what is measured to something

which can be meaningfully considered to describe the

sound production mechanism. As we will see, even if we

manage to measure or compute the entire space–time

structure of the Lighthill stress tensor, or other so-called

‘‘source’’ quantity, the problem is far from solved.

An alternative means by which the physics of aerody-

namically generated sound can be described involves the

use of rapid distortion theory; however, in a 1984 review

article Goldstein (1984) provides an excellent account of

this kind of approach and so we will here omit any detailed

description of the subject.

2.6 Coherent structures

As we have seen, our early ideas of the sound production

mechanisms in jets were based on a system of randomly

distributed eddies, convected with and radiating into a

given mean-flow. This view was to change radically over

the course the 1960s and 1970s when the turbulence

community began to recognise the existence of a more

organised underlying structure in free shear-flows.

Needless to say the aeroacoustics community was quick

to realise that this could have significant implications

where the corresponding sound production mechanisms

are concerned. A few researchers were to address this

issue in the 1960s. Bradshaw et al. (1964a, b) observed

large, organised eddies in the near-nozzle region of the

round jet, and Mollo-Christensen (1967) discussed the

possibility that such structures might play an important

role in the production of sound. However, it was in the

early 1970s, with the work of Crow and Champagne

(1971), Lau et al. (1972), Fuchs (1972) and Brown and

Roshko (1974) that the aeroacoustics community really

began to focus on the implications for sound production

by free jets.

4 Exp Fluids (2008) 44:1–21

123

Michalke and Fuchs (1975), in an analytical develop-

ment based on Lighthill’s theory re-cast in cylindrical

coordinates, represented the source in terms of its azi-

muthal Fourier modes, and showed thence that the lowest

order modes would be the most efficient producers of

sound, this efficiency depending strongly on the axial

coherence of the source. The existence of strong azimuthal

coherence in the sound field radiated by the round jet

(Michalke and Fuchs 1975; Maestrello 1977; Fuchs and

Michel 1978; Juve et al. 1979) provided evidence that the

source mechanisms might indeed comprise such azimuth-

ally coherent vortex-ring-like structures; and while Bonnet

and Fisher (1979) were to warn against such overhasty

inferences regarding the source structure based purely on

the far sound field—they demonstrated that the coherence

of the sound field radiated by a ring-like structure, coherent

or otherwise, depends largely on the Helmholtz number,

and how an azimuthally incoherent ring-source could in

fact produce an azimuthally coherent sound field for cer-

tain frequencies—Fuchs (1972) and Armstrong et al.

(1977) demonstrated that in fact the flow does comprise

such azimuthally coherent structures, these observations

being based on two-point pressure and velocity measure-

ments in the rotational region of the jet. Where the axial

coherence of the jet structure is concerned Chan (1974)

showed that the growth and decay of pressure disturbances

is similar to that predicted by linear hydrodynamic stability

theory (Michalke 1964, 1965).

The identification of such a deterministic underlying

structure triggered considerable interest in alternative

means of modelling source mechanisms. The likeness of

the coherent flow dynamics of moderate-to-high Reynolds

number jets to the linear instabilities observed in laminar

flows led to attempts to use linear instability theory to

predict jet noise. Tam (1972) first presented such an

approach for supersonic jets in 1972 by considering the

linear instability of an infinitely thin shear-layer in a par-

allel mean-flow. Liu (1974) attempted to better integrate

the effects of a spreading mean-flow and a fine-grained

background turbulence, which would respectively sustain

and dissipate the large-scale instability.2 The near pressure

field thus predicted showed good qualitative agreement

with experimental measurements. Ffowcs-Williams and

Kempton (1978) studied the sound production capability of

both a wavy-wall type instability and a vortex-merger

event using an ad hoc description of the said mechanisms

and a Lighthill source formulation. For both cases the rapid

amplification, saturation and decay of the fluctuations

associated with such mechanisms were shown to be

important in the production of sound. Moore (1977) pro-

vided experimental evidence for the importance of

coherent structures in the production of jet noise, while

Dahan et al. (1978) subsequently demonstrated, experi-

mentally, for a hot jet, that 50% of the sound energy

radiated to the farfield could be attributed to the dynamics

of coherent flow structures. An early attempt to address the

question numerically was made by Gatski (1979).

By the end of the 1970s, both the existence and the

importance of coherent source structures had been estab-

lished, experimentally and theoretically. It is worth

mentioning that this identification of the importance of

coherent structures in the production of sound was to

produce a divide in the aeroacoustics community, as the

existence of such structures cast some doubt on the validity

of the earlier vision of a random distribution of compact,

convected quadrupoles. While there was no question of

entirely eliminating the possibility of such source mecha-

nisms, it was clear that this picture was not complete. An

interesting exchange between Fuchs (1978) and Ribner

(1978) provides a nice resume of some of the contentious

issues.

Subsequent developments in the modelling of source

mechanisms associated with the coherent component of the

free jet have been largely tied to the supersonic scenario

(e.g. Morris 1977; Tam and Morris 1980; Tam and Burton

1984; Tam and Chen 1994), and indeed linear stability

theory can be used to provide a reasonable quantitative

prediction of the sound field radiated, via Mach wave

mechanisms, by the most amplified linear modes in

supersonic jets, as shown by Tam and Burton (1984), Tam

et al. (1992), and Tam and Chen (1994). However,

Mohseni et al. (2002) have shown, by means of numerical

simulations comprising both linear and non-linear Navier–

Stokes solutions, that for off-peak frequencies discrepan-

cies between the linear and non-linear solutions are

considerable, indicating that the linear theory is not suffi-

cient to account for all of the subtleties of Mach wave

radiation. For subsonic jets, similar theoretical work has

been performed by Mankbadi and Liu (1981, 1984),

wherein instabilities computed using a combination of

linear and non-linear theory—the shape function is derived

from local inviscid linear theory while an axial amplitude

function is obtained from non-linear theory—are used to

construct source terms using a reworking, by Michalke and

Fuchs (1975), of the Lighthill (1952) theory. Predictions of

the spectral and directive character of the acoustic field

radiated by spatially stationary, coherent source mecha-

nisms were found to reproduce many of the observed

subsonic jet noise characteristics. Axisymmetric and

2 This was based on a three-way split of flow quantities into time

averaged, phase-averaged and random components (associated,

respectively, with the mean flow, the large-scale instability and the

fine-scaled, random turbulence) which was first used by the turbu-

lence community in order to understanding the dynamics of coherent

structures in free shear flows (see Hussain and Reynolds 1970 for

example).

Exp Fluids (2008) 44:1–21 5

123

helical source modes were found to resemble longitudinal

and lateral quadrupoles; peak radiation was found to occur

at small angles to the jet axis, at Strouhal numbers of the

order of 0.3, and the linear, ‘‘shear-noise’’ mechanism, was

found to dominate. A particularly attractive feature of their

approach is that energy transfers between the mean-flow,

the large-scale instability, and the fine-scale turbulence are

accounted for, and in this the model is physically more

complete than the models which are typically used for

supersonic predictions, even if the authors neglected the

finescale turbulence in the source integral. Discrepancies

between predictions and experimental results were attrib-

uted to this neglect of the fine-scale component, however it

is likely that the observations of Mohseni et al. (2002) may

also be applicable here.

The possibility of the existence of both a large-scale

coherent component and a more random small-scale com-

ponent was further investigated by Tam et al. (1996) for a

perfectly expanded supersonic jet, and this led Tam (1998)

to propose two similarity spectra, related to each of the two

mechanisms. These were shown to agree well with data

taken from a large number of supersonic jet noise experi-

ments, and Viswanathan (2002) has shown how subsonic

jet noise spectra also fit these shapes. However, the

essential features of the physics underlying the two kinds

of mechanism in the subsonic jet remain unclear to this

day, and thus in terms of source modelling this small-scale-

random/large-scale-coherent source duality remains a

central problem. An interesting interpretation of this source

duality has recently been provided by Goldstein and Leib

(2005), who show that the Greens function solution for a

Lilley-like acoustic anology comprises two distinct terms,

each of which filters the source dynamic in a different way;

again the conceptual difficulty alluded to earlier, wherein

the physics of the sound production problem is shared

between the ‘‘source’’ and the base-flow ‘‘response’’, arises

here: the authors argue that the base-flow responds in two

different ways to the turbulence dynamic: a low frequency

response which is greatest at shallow angles to the jet axis,

and a high frequency response which dominates at larger

angles. The former component corresponds to linear

instabilities associated with the homogeneous solution for

the base-flow equation, and so is argued to be synonymous

with large-scale flow instabilities, although the authors do

make the further comment that the said instabilities ‘‘may

not actually correspond to any physical flow structure’’—

an apposite remark in view of the aforesaid conceptual

difficulties which arise when it comes to ‘‘speaking of’’

source mechanisms.

Where the small-scale-random component is concerned

the traditional Lilley or Lighthill approaches, which

involve assumptions of convected, compact quadrupoles,

may be well adapted. However it is unclear how individual

contributions from the coherent and random turbulence

components to the moving-frame two-point space–time

velocity correlation tensors (see Sects. 2.1, 3.1 for related

discussion) can be separately identified experimentally.

Indeed the form of the correlation tensor is quite likely

dominated by the large-scale, coherent flow dynamics. This

problem presents a challenge for the future. On the other

hand, where the coherent component is concerned there is

no real consensus as to the essential mechanisms involved.

The early candidates were vortex-pairing and/or wavy-wall

type instabilities; Coiffet et al. (2006) give experimental

evidence supporting the existence of this kind of mecha-

nism in the region upstream of the end of the potential core,

and demonstrate that the production mechanism is a linear

one. On the other hand, Kopiev and Chernyshev (1997)

have provided an analytical demonstration of how the ei-

gen-oscillations of a single vortex structure can constitute

an efficient octupole sound production mechanism, which

presents a directivity similar to that produced by a jet

(Kopiev et al. (1999, 2006). There is also a considerable

body of experimental and numerical evidence suggesting

that a particularly violent event associated with the collapse

of the annular mixing-layer at the end of the potential core

may constitute the dominant sound production mechanism.

The early causality methods (discussed in Sect. 3.2.1)

identified this region of the flow as the dominant source

region, and an experimental study undertaken by Juve et al.

(1980) showed how sound producing events in this region

are characterised by high levels of intermittency: sudden

decelerations near the end of the potential core, thought to

be related to fluid entrainment on the upstream side of ring-

like coherent structures, were postulated as a possible

mechanism. More recently Guj et al. (2003) and Hileman

et al. (2005) have provided further experimental evidence

for intermittent noise producing events in this region of the

flow. Numerical simulations which further support the

existence of such a source mechanism have been per-

formed by Bogey et al. (2003) and Viswanathan et al.

(2006). The former work shows how large amplitude sound

waves are generated by the intrusion of structures into the

potential core region, while in the latter work a strong,

inherently directive, spatially stationary sound source is

again identified just downstream of the end of the potential

core.

2.7 Summary

The foregoing gives an overview of the different ideas

which currently exist regarding the sound production

mechanisms in free jets. Jets are believed to comprise two

kinds of mechanism: one related to the small-scale, random

flow eddies, which are compact, convected, and behave as

6 Exp Fluids (2008) 44:1–21

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quadrupole sound sources; and another related to the

coherent flow dynamic, which is variously considered to

produce sound via vortex-pairing, vortex eigen-oscilla-

tions, quasi-irrotational instability or wavy-wall-like

mechanisms, and a violent intermittent flow dynamic in the

transition region of the flow. However, as discussed in the

introduction, it remains unclear whether this hypothesis of

two distinct mechanisms is justified. Goldstein’s perspec-

tive suggests that one and the same ‘‘source’’ mechanism

may simply be coupling with the farfield in a highly

directive fashion, and such that an angle-dependent fre-

quency selection occurs. Furthermore, the idea that the

mechanisms might be associated with disparate scales is

not so clear, as there is a considerable degree of overlap

between the spectral shapes associated with each of these

mechanisms (i.e. those observed at 90� and 30� to the jet

axis).

We defer further discussion on this to the next section,

where we will look more closely at the various measure-

ment and analysis strategies which have been used to

extract pertinent information concerning the various sound

production mechanisms believed to exist in the unbounded

round jet.

3 Experimental methodologies and source modelling

Despite impressive recent progress in our capacity to solve

the flow equations numerically, such approaches remain

seriously limited in terms of the kinds of Reynolds num-

bers which can be achieved, and the precision with which

the turbulent motion of a heat-conducting, viscous, com-

pressible fluid can be resolved. Where jets are concerned

the extremely thin boundary layers (upstream of the exit

plane) and initial shear-layers require prohibitively large

numbers of mesh points. This leads to severe restrictions in

terms of the run-times which can be obtained, and so it is

generally difficult to obtain fully converged statistics. The

experimental approach, where the flow equations are per-

fectly solved by the flow, is therefore presently essential if

we are to arrive at an integral understanding of the sound

production problem for the kinds of flows which are of

practical interest.

In this section we wish to provide an account of the

evolution of the different experimental approaches which

has accompanied the developments outlined above. Such

evolution is driven both by improvements in measurement

technology, and, possibly more importantly, by the evo-

lution of our understanding of the mechanisms which

underlie the production of sound by a jet. As the various

visions of the sound-producing jet appeared, experiments

were designed in order to access the pertinent information

where sound production is concerned. Needless to say this

process is ongoing, and recent developments are bringing

us ever closer to directly accessing the ever elusive jetnoise

‘‘source’’ dynamic.

3.1 Two-point statistics

Within the framework of the original acoustic analogies,

the sound power radiated from a jet comprising randomly

distributed, compact, convected quadrupole sources is

related to the fourth order, spatiotemporal velocity corre-

lation tensor. By means of a Reynolds decomposition of the

velocity field, this can be shown to comprise second, third

and fourth order terms. The third order terms are generally

neglected as they integrate to zero in homogeneous, iso-

tropic turbulence.3 The second and fourth order terms are

related to linear and quadratic pressure production mech-

anisms, respectively,4 the so-called ‘‘shear-’’ and ‘‘self-

noise’’ mechanisms (Lighthill 1954; Ribner 1969) (or fast

and slow pressure terms in the turbulence community).

With an assumption of quasi-normal joint probability of the

turbulence statistics [this assumption has been shown to be

justified, experimentally by Seiner et al. (1999), and

numerically by Freund (2003) using DNS] the fourth-order

quantity can be expressed in terms of the second order

velocity correlation tensor, and so early experiments

designed to extract information related to the source

mechanisms via direct turbulence measurements targeted

the two-point velocity correlation (e.g. Davies et al. 1963;

Fisher and Davies 1964; Chu 1966). Due to limited mea-

surement capabilities, such experiments were generally

limited to a study of only one of the nine components of the

correlation tensor (the axial component); assumptions of

isotropy and homogeneity were then invoked in order to

model the remaining terms. The three quantities of interest

are the integral space scale, the Lagrangian integral time

scale and the convection velocity. Armed with these and an

isotropic, homogeneous turbulence model—taken for

example from Batchelor (1953)—it is possible to make jet

noise predictions, and indeed this kind of approach is still

at the heart of many current noise-prediction procedures.

Progress where this kind of approach is concerned has

involved a more complete measurement of the said two-

point tensor by means of PIV and LDV (e.g. Bridges 2002;

Chatellier and Fitzpatrick 2006; Kerherve et al. 2004,

2006). And in terms of improvements in subsequent

modelling the focus has generally been on the inclusion of

3 It should be noted that the turbulence in a round jet is neither

isotropic nor homogeneous, and so neglect of the third order term may

constitute a dangerous oversimplification.4 By pressure production terms we mean terms such as are found on

the right-hand side of a Poisson’s equation for the pressure field in an

incompressible turbulence field.

Exp Fluids (2008) 44:1–21 7

123

more flow physics. Models are frequently based on

assumptions of isotropic, homogeneous turbulence. As the

jet is clearly neither, a certain effort has gone into devel-

oping more realistic models which include more of the

observed flow physics. Goldstein and Rosenbaum (1973)

examined the role of anisotropy by means of models based

on the theory of axisymmetric turbulence of Chandrasekhar

(1950). Later work on the same lines includes the use, by

Khavaran (1999), of the axisymmetric turbulence model to

deal with anisotropy and to predict the sound radiated from

a jet using data obtained from a RANS computation. Jordan

and Gervais (2005) combined a similar turbulence model

with a technique developed by Devenport et al. (2001) in

order to deal with the inhomogeneity of the jet structure,

and a direction-dependent length-scale was proposed in

order to deal with the anisotropy of the turbulence; jet noise

predictions were then made using data obtained from two-

point LDV measurements.

Other progress in this kind of statistical modelling

includes the use of frequency-dependent space–time scales

(Self 2004; Kerherve et al. 2006). Khavaran and Bridges

(2005) have shown how the shape of the temporal part of

the two-point velocity correlation can play an important

role in the accuracy of predictions, exponential forms being

more appropriate than the traditionally used Gaussian

forms, while Jordan et al. (2004) suggest that it is also

important to model the curvature of the correlation function

close to zero. In order to do so, without losing the expo-

nential global decay, they proposed a function obtained via

convolution of exponential and Gaussian forms, charac-

terised, respectively, by the integral and Taylor scales of

the flow: again emphasis is here laid on the inclusion of

physical flow quantities, rather than the use of empirical

constants to get the right answer.

3.2 Simultaneous flow–acoustic measurements

As discussed earlier, there exists a degree of uncertainty

when it comes to defining the sound production mecha-

nisms in unbounded turbulence. This means that there is a

corresponding uncertainty when it comes to designing

experiments aimed at understanding the dynamics of such

mechanisms in a given turbulent flow.

An experimental approach which can help shed some

light in this matter involves the synchronous recording of

fluctuations in both the near field of the flow—which may

include both rotational and irrotational regions—to which

the source mechanisms are confined but largely swamped

by acoustically un-important hydrodynamic fluctuations,

and in the far acoustic field, where only the source signa-

ture remains. By means of such a measurement the causal

relationship between the flow/source dynamic and its

acoustic effect (the sound field) can be assessed by corre-

lation or other appropriate signal processing techniques.

While there is little doubt that the appropriate farfield

quantity to target is the fluctuating pressure, the pertinant

flow/source quantity is not so obvious. Experiments can

either be guided by an acoustic analogy, or causal rela-

tionships can be sought using whatever flow information it

is possible to obtain: indeed this is often the decisive factor

when it comes to performing such an experiment: we

cannot access the full space–time dynamics of the flow; we

have different tools, each permitting of partial access to

different flow quantities.

3.2.1 The causality method

Early experiments were guided by the Lighthill analogy,

and in particular by the identification of linear and qua-

dratic (‘‘shear-’’ and ‘‘self-noise’’) quadrupole source

mechanisms on one hand, and the simple pressure source

mechanisms proposed both by Ribner (1962) and Powell

(1963) on the other. Two variants of the causality method

thus appeared in the early 1970s as a result of these dif-

ferent source descriptions. The first can be attributed to

Siddon and Rackl (1972) and was based on cross-correla-

tions between in-flow pressure fluctuations and those

radiated to the farfield. The second approach, first pre-

sented by Lee and Ribner (1972), was based on correlating

Reynolds stress fluctuations with the farfield pressure.

Before going on to discuss the principal results, a few

words are appropriate concerning the importance of this

particular approach.

The appeal of the causality method derives from the fact

that the farfield pressure autocorrelation—which consti-

tutes a measure of the sound energy radiated from the

flow—can be formally related to the source–farfield cor-

relation, which can in turn be formally related to the

source-source correlation which comprises the integrand in

the farfield solution of Lighthill’s wave equation. Such

causality-correlations are thus more than a mere ad-hoc

test for a cause–effect relationship. Indeed, within the

framework of Lighthill’s acoustic analogy, a two-point

source–farfield correlation, hS(x,t)p(y, t + s)i, amounts to a

quantitative measure of the local contribution from source

activity at a point x in the jet, to the farfield sound intensity

measured at y. By integrating the source–farfield correla-

tions over the entire jet volume, taking care to correctly

account for negative source contributions, the total sound

power radiated by the jet is retrieved. The causality method

is thus seen to be no less than a high-precision source

localisation technique, which identifies the structure of the

coupling mechanism via which the largely acoustically

ineffective jet dynamics drive the farfield pressure. This is

8 Exp Fluids (2008) 44:1–21

123

an extremely important point in view of the earlier dis-

cussion related to the difficulty of identifying something

which can be meaningfully referred to as a ‘‘radiating’’

source: because of the formal identity between the source–

farfield correlation and the integral solution of Lighthill’s

equation, the filtering operation by which the said solution

sorts and extracts acoustically matched source activity is

inherently present in the source–farfield correlations.

As different researchers implemented the causality

method a number of important improvements were made,

and some interesting findings reported. The first experi-

ments availed of hot-wire, hot-film, and in-flow pressure

probes to sample fluctuations in the flow field. Lee and

Ribner (1972) used a hot film to correlate the square of the

fluctuating velocity with the farfield pressure of a Mach 0.3

jet. This was done using only the velocity component in the

direction of a farfield microphone (which was located at

40� to the jet axis), in accordance with a formulation of the

Lighthill equation proposed by Proudman (1952). Scharton

and White (1972) alternatively studied correlations

between pressure measurements effected in the rotational

region of a sonic jet and in the farfield at 30� to the jet axis.

Seiner (1974) and Seiner and Reethof (1974) performed a

similar experiment to that of Lee and Ribner (1972), in a jet

at Mach 0.32 using a hot-wire, but where both the linear

and quadratic velocity fluctuations were considered. In this

way it was possible to assess contributions from the so-

called ‘‘shear-’’ and ‘‘self-noise’’ mechanisms. Again fil-

tered correlations were computed, whence it was shown

that the frequency of the sound radiated from the jet is a

function of axial position: high frequencies were found to

be radiated from upstream positions, lower-frequencies

from downstream positions. The linear (‘‘shear-noise’’)

mechanism was shown to dominate the quadratic (‘‘self-

noise’’) mechanism by 13 dB, and the transition region of

the jet (downstream of the end of the potential core) was

shown to be dominant in the production of sound.

A difficulty with this kind of approach arises due to the

strong possibility that the in-flow probe is generating more

sound than the sources it is designed to measure.

Researchers thus took to designing experiments where

probe contamination was minimised. Schaffar (1979) used

LDV to measure the axial component of the velocity

fluctuations in a high Mach number jet (M = 0.97), and by

correlating the linear source component with the farfield

pressure was able to conclude, in agreement with Seiner,

that ‘‘nearly all of the far field noise measured at 20� and

30� to the jet axis’’ is produced by linear, ‘‘shear-noise’’

mechanisms present in the transition region of the flow,

between 5 and 10 diameters downstream.

Juve et al. (1980) also performed an experiment where

efforts were made to minimise probe contamination. A hot-

wire probe was designed such that the hotwire support

structure exposed to the turbulent flow comprised only four

100 lm diameter support wires. Acoustic measurements

were made using microphones located at 30� to the jet axis.

In addition to time-averaged correlations, the authors

studied instantaneous correlations, and they emphasised

that the exact time-delay associated with transmission from

source to observer must be appropriately accounted for if

cancellation effects are to be correctly captured. These

correlations provide a means of assessing the instantaneous

sound emission associated with the ‘‘shear-noise’’ source

term, and led to a number of important observations

regarding the nature and localisation of the sound pro-

duction mechanisms. The dominant source was again

shown to be localised in the transition region, downstream

of the end of the potential core; it was found to be non-

compact and related to the coherent dynamic of the jet;

and, finally, it was shown to be highly intermittent, with

50% of the sound being generated in 10–20% of the time.

This last point is an extremely important one where source

models are concerned. In addition to a confirmation of the

non-compactness of the source mechanism which had been

suggested by earlier research, as discussed in Sect. 6, the

observed intermittency of the source suggests that the

statistical source models, which are based on the existence

of compact turbulent eddies in an isotropic, homogeneous

field (where source terms associated with the third order

statistical moments are considered negligible), are insuffi-

cient for an accurate description of the full source dynamic.

Schaffar and Hancy (1982), following the earlier work

of Schaffar (1979), used an LDV system to measure

velocity components in the direction of farfield micro-

phones at 30�, 45� and 60� to the jet axis. It was thereby

possible to better understand the directivity of the ‘‘source’’

mechanisms. Both the linear and the quadratic components

were found to be active in the transition region of the flow,

between 4 and 11 diameters downstream of the exit. The

linear term was found to dominate considerably, with over

70% of the radiated energy being emitted at angles smaller

than 45� to the jet axis; the quadratic term was found to

contribute of the order of 15%; for sound emitted at angles

greater than 60�, the linear term was found to be ineffec-

tive, while the quadratic term only contributed a few

percent of the radiated energy. The authors again evoked

the importance of using the exact time-delay when per-

forming source–farfield correlations, such that source

cancellation effects are correctly taken into account.

Panda et al. (2005) have more recently performed a

similar experiment using a novel technique, based on

molecular Rayleigh scattering, which permits simultaneous

measurement of both unsteady density and velocity. Such a

measurement allows the Lighthill stresses to be measured

in full, without the incompressibility assumption. The work

of Cabana et al. (2006) and George et al. (2007) suggests

Exp Fluids (2008) 44:1–21 9

123

that terms associated with the unsteady density may com-

prise the most fundamental event where the source

mechanisms are concerned, and so direct experimental

access to such quantities is of considerable interest. In-flow

measurements of quu, qvv, q, u and v were performed in

subsonic and supersonic jets, synchronously with farfield

pressure measurements at 30� and 90� to the jet axes by

Panda et al. (2005). Correlation levels in the subsonic flows

were of the order of 1–2% (considerably lower than in the

supersonic flows). The highest correlations were obtained

from the quu, q and u measurements. As the measurements

were performed on the jet axis, the failure of the v com-

ponents to correlate led to the conclusion that axisymmetric

instability waves/coherent structures were the primary

sound producers in the supersonic jets. The highest corre-

lations were observed for in-flow measurements performed

just downstream of the end of the potential core, consistent

with many previous experiments. For in-flow measure-

ments in the mixing-layer region, at r/D = 0.45,

correlations were found to be negligible in the subsonic

flows. It should be pointed out that this may be partly due

to the masking effect of the more random turbulence—the

random component of the turbulence may be sufficiently

energetic to swamp the part of the coherent dynamic which

is correlated with the farfield—we will see later how there

is a strong coherent dynamic in this region of the subsonic

jet, which does generate sound, but whose signature is

strongest on the low and high speed sides of the mixing-

layer, where the masking effect of the random turbulence is

less severe.

3.2.2 Flows dominated by coherent structures

In the previous subsection techniques which were strongly

rooted in the acoustic analogy were considered, and while

the associated physical picture was frequently that of a

convected field of compact quadrupoles, many of the

conclusions pointed to non-compact source mechanisms

associated with the coherent dynamics of the flow. Rec-

ognising this, researchers began to address the question of

how to study the underlying mechanisms in more detail.

Experimentalists thus took to contriving flow systems

which were dominated by deterministic coherent motion.

One approach is to use an acoustic excitation to lock a low

Mach number round jet into a regular flow pattern. By

forcing at the most unstable frequency of the flow, a system

of coherent vortex structures can be produced, where the

roll-up and pairing phases are fixed in space. Moore

(1977), Kibens (1980), Laufer and Yen (1983), Arbey and

Ffowcs-Williams (1984), Bridges and Hussain (1992),

Ghosh et al. (1995) and Fleury et al. (2005) have all

studied such coherent-structure-dominated flows.

In addition, Laufer and Yen (1983) performed syn-

chronous flow–acoustic measurements in both excited and

un-excited flows with a view to relating the flow dynamics

to the radiated sound. However, their work differed from

the causality approaches described above in that they did

not place themselves within the framework of any under-

lying aeroacoustic theory; they simply observed the

simultaneous behaviour of the flow and its radiated pres-

sure field. From measurements restricted to the first

diameter of the flow, they found that the turbulent velocity

and the nearfield pressure—measured in the irrotational

entrainment region—are linearly related, while a quadratic

relationship exists between nearfield and farfield pressures.

They observed that for both the excited and unexcited

flows ‘‘the acoustic sources are not convected even though

they are being generated by moving disturbances in the

jet’’, and the quadratic relationship between the nearfield

and farfield measurements led to the conclusion that the

source mechanism could be associated with the non-linear

saturation of unstable wave amplitudes occurring near the

vortex-pairing locations. Clearly the observed phenomena

violate some of the assumptions on which the original

source models were based: if the source is not convected

there can be no convective amplification and no Doppler

shift, and yet they observed a superdirective radiation

pattern! Non-linear mechanisms associated with vortex

pairing mechanisms were also argued by Stromberg et al.

(1980) to be dominant in the production of sound by low

Reynolds number round jets. They used a novel experi-

mental approach, pioneered by Morrison and McLaughlin

(1979) for the study of supersonic flows, which involves

exhausting high speed jets into an anechoic vacuum

chamber. By virtue of the low Reynolds number thus

obtained, coherent flow patterns in high Mach number, un-

excited flows, could be studied.

The apparent contradiction, between these observations

of a non-linear relationship between the nearfield dynamics

and the farfield sound, and the conclusions from the cau-

sality approach which indicate that the linear source term is

dominant, may be an indication that such vortex-pairing (or

non-linear instability wave interactions) do not constitute

the dominant mechanism in unexcited, high Reynolds

number flows. It is possible that in an unexcited jet the

coherent dynamic is not coherent enough to produce such

‘‘clean’’ quadratic interactions. Further investigation of this

point would be useful.

3.2.3 Conditional averaging

We have seen how synchronous flow–acoustic measure-

ments led to a number of important observations with

regard to the sound production mechanisms in free jets:

10 Exp Fluids (2008) 44:1–21

123

the dominant sound producing region of the flow, where

both linear and quadratic mechanisms are concerned, was

found to be the transition region downstream of the col-

lapse of the potential core, and at least some component of

the source mechanism was found to be non-compact,

spatially stationary—and therefore inherently directive—

and strongly intermittent. One important implication of an

intermittent source is that second order averaging tech-

niques may be missing the essential character of the sound

production event. With this in mind Guj et al. (2003)

performed synchronous flow–acoustic measurements with

a view to analysing the relationship between the dynamics

of the unsteady intermittent structures in the transition

region of the jet and the sound they radiate. Conditional

ensemble averaging was implemented, peak events in the

acoustic signature being used as a conditional trigger.

Intermittent source activity was identified between seven

and nine diameters downstream, and the characteristic

sound production event found to be characterised by a

cusp-like signature, as previously observed by Juve et al.

(1980) (cf. Sect. 3.2.1) and later by Hileman et al. (2005).

The methodology implemented by Hileman et al. (2005) is

very similar to that of Juve et al. (1980) and Guj et al.

(2003), but in the place of single-point flow measure-

ments, high-speed flow visualisations were performed

using a PIV system. In similar fashion to the work of Guj

et al. (2003), the farfield acoustic signal was used to sort

the flow images into noisy and quiet ensembles. The signal

processing tool used in this case was proper orthogonal

decomposition, which was applied to both ensembles, and

thus used to understand the characteristic features com-

prised by the images associated with periods of high noise

production and with periods of relative quiet. The transi-

tion region was once again identified as dominant in the

production of sound, and a cusp-like signature again

shown to characterise the intermittent sound production

events.

3.2.4 Summary

The evolution of synchronous flow–acoustic measurements

has primarily involved improvements in measurement

technology, and has been marked by a movement away

from the theoretical groundings which typified the early

causality methods. As discussed in Sect. 2.5, the concep-

tion of an acoustic analogy has seen some evolution and the

new formulations which will now be possible should be

conducive to a return to more theoretical groundings.

Indeed, the experiment will be an interesting testing ground

for evaluation of the different source definitions which the

new approaches provide. And of course, the new source

definitions will constitute a continued challenge to the

experimentalist to extract the associated pertinent infor-

mation. We will return to this point a little later.

3.3 Nearfield pressure measurements

Another means of investigating the dynamics of a free

jet—which was first implemented in the early 1950s—

involves the use of microphones located in the irrotational

region just outside the jet periphery. Although this kind of

measurement presents numerous advantages, it also raises

considerable interpretational difficulties. On one hand

pressure is a scalar quantity, the measurement is non-

intrusive, and as the smaller turbulence scales are ineffi-

cient in driving the pressure field in this region of the flow,

such measurements involve a natural filtering of these, and

are thus conducive to a study of the large-scale, coherent

dynamics of the jet. On the other hand, as discussed in

Tinney et al. (2006b), interpretation of the measured fluc-

tuation in terms of the underlying turbulence and its sound

source mechanisms is far from straightforward. There is

always an uncertainty as to precisely how much informa-

tion has been filtered out with respect to the pressure

signatures at the heart of the turbulent flow. A further

difficulty arises related to the fact that the measurement

comprises contributions from both ‘‘hydrodynamic’’ and

‘‘acoustic’’ pressure fields. If these issues are not appro-

priately dealt with, such measurements can be easily

misinterpreted.

Early theoretical work in this field was undertaken by

Franz (1959) and Ollerhead (1967), both of whom made

detailed studies of the nearfield solution to Lighthill’s wave

equation. This solution comprises rapidly decaying terms

related to the highly energetic reactive pressure field which

exists close to an acoustic source, but which does not reach

the farfield due to its non-progressive nature. The irrota-

tional nearfield of an unbounded jet is dominated by such

pressure fluctuations, which, on account of their rapid

spatial decay, present a relatively local information where

the large-scales of the underlying turbulence are concerned.

An alternative analytical approach, used for example by

Howes (1960), involves treating the pressure fluctuations

as entirely incompressible. The characteristics of the

nearfield pressure are then described by a Poisson equation,

whence Howes derived expressions for the evolution of the

nearfield pressure rms and found reasonable agreement

with experimental measurements.

Early experiments by Mayes et al. (1959), Howes

(1960), Mollo-Christensen (1963) and Keast and Maidanik

(1966) involved one and two-point measurements from

which the axial evolution of the first and second order

moments, and the two-point pressure correlations were

obtained. Howes (1960) appears to have been the first to

Exp Fluids (2008) 44:1–21 11

123

consider the subsonic jet, the near pressure field of which

was found to comprise an amplification, saturation and

decay of the fluctuation amplitudes, as predicted by the

theoretical approach, mentioned above, which was based

on incompressible pressure fluctuations and jet similarity

relations. Mollo-Christensen (1963) performed two-point

pressure correlations, using probes separated both axially

and in azimuth. The shape of the space–time correlations

thus obtained suggested a harmonic travelling wave,

weighted by a Gaussian envelope and an exponential axial

decay. A striking feature identified by these early experi-

ments, and in particular that of Mollo-Christensen (1963),

was the coherent nature of the near pressure field: as dis-

cussed above it presents a natural filter, which extracts the

coherent flow dynamics from a background of more ran-

dom turbulence. Despite the fact that this filter is presently

poorly understood, such measurements are nonetheless

attractive where the small-scale/large-scale source duality

discussed earlier is concerned, and this kind of experiment

may constitute a valuable means for understanding these

source mechanisms.

A problem evoked earlier with respect to source defi-

nitions is the redundancy present in many of these, and in

particular with respect to the non-radiating components. In

a subsonic jet much of the flow dynamic is non-radiating,

and so some care is required when the nearfield signatures

are considered in terms of the underlying, radiating

source. Keast and Maidanik (1966) provide a nice

description of this difficulty where the near pressure field

is concerned. However, until recently (Tinney et al.

2006b) this point, as well as the question of the compo-

sition of the nearfield in terms of ‘‘hydrodynamic’’ and

‘‘acoustic’’ components (e.g. Arndt et al. 1997; Millet and

Casalis 2004; Coiffet et al. 2006), have been largely

overlooked in nearfield studies.

In an analytical development based on the unsteady

Bernoulli equation and a quadrupole solution to the wave

equation, Arndt et al. (1997) obtained predictions for the

spectral character of nearfield pressure fluctuations of a

subsonic jet, and the ‘‘hydrodynamic’’ and ‘‘acoustic’’

spectral regimes thus predicted agreed well with mea-

surements. A Helmholtz number of kr = 2 was found to

mark the passage from ‘‘hydrodynamic’’ to ‘‘acoustic’’

dominance. Harper-Bourne (2004) and Coiffet et al. (2006)

found values of kr = 1 and kr = 1.3, respectively, while

Guitton et al. (2007) have more recently derived an

empirical relationship which accounts for the velocity

dependence of the ‘‘hydrodynamic’’–‘‘acoustic’’ demarca-

tion: this empirical law accounts for the different velocity

dependence of the hydrodynamic and the acoustic com-

ponents of the nearfield pressure intensity, which scale,

respectively, as U4 and U7. In terms of the relationship

between the ‘‘hydrodynamic’’ and ‘‘acoustic’’ components

of the near pressure field, further light has been shed on the

matter by Coiffet et al. (2006), who by means of an axially

aligned linear nearfield array, demonstrated a causal link

between the two fluctuating fields, manifest in the form of

interference nodes which occur when the energy and phase

of the component fluctuations are appropriately matched.

This result shows how the dynamic of the flow driving the

‘‘hydrodynamic’’ part of the nearfield signature generates

sound by a linear process. It furthermore shows that the

nearfield can be considered to comprise a superposition of

convective, ‘‘hydrodynamic’’ and propagative, ‘‘acoustic’’

components.

Progress in data acquisition technology has permitted

progressively larger numbers of microphones to be used

in the nearfield, and this has led to the application of

more sophisticated signal processing techniques. Large

azimuthal nearfield arrays have been used by Ricaud

(2003), Harper-Bourne (2004), Coiffet et al. (2006),

Jordan et al. (2005), Tinney et al. (2006b, 2007), Reba

et al. (2006), Suzuki and Colonius (2006) and Tinney

et al. (2006a). Such measurements have been used to

study the structure of the nearfield in terms of its Fourier-

azimuthal modes: for both single and co-axial subsonic

jets the first 3 Fourier azimuthal modes were found by

Guerin and Michel (2006) and Jordan et al. (2005) to

dominate the near pressure field. Extension of the

microphone distribution in the axial direction has allowed

further information to be obtained regarding the axial

coherence of the Fourier azimuthal modes (Guerin and

Michel 2006; Jordan et al. 2005). In the latter work the

axisymmetric and helical modes were found to have

similarly extensive axial coherence, while for the higher

order modes this coherence is considerably reduced. In the

context of Michalke’s formulation of Lighthill’s aeroa-

coustic theory this suggest that the first two modes will

dominate in the production of sound.

Examples of more ambitious signal processing are typ-

ified by the work of Suzuki and Colonius (2006), who avail

of multiple azimuthal arrays located in the nearfield to

implement a beamforming algorithm for the identification

of instability wave amplitudes; Reba et al. (2006) used

similar nearfield pressure measurements to construct a

wave-packet ansatz for the solution of a boundary value

problem giving the radiated sound field; and Tinney et al.

(2006b) applied a filtering operation in order to separate the

‘‘hydrodynamic’’ and ‘‘acoustic’’ components of the near-

field of heated co-axial jets.

This kind of measurement currently presents a promis-

ing means of studying the role played by the large-scale

coherent flow dynamics in the production of sound. How-

ever, there are a number of difficulties, one of these being

the uncertainty as to the amount of information which is

lost due to the radial distance of the measurement from the

12 Exp Fluids (2008) 44:1–21

123

source region. Techniques such as developed by Suzuki

and Colonius (2006) can provide a means of partially

overcoming this difficulty; however, their identification

tool does involve an assumption that the large-scale

dynamics are well-described by linear stability theory. An

attractive means of further reducing this uncertainty is to

perform synchronous measurement of both the near pres-

sure field and the turbulence. This is discussed in the next

section.

3.4 Simultaneous flow/nearfield-pressure

measurements

The mechanisms by which the near irrotational pressure

field is driven by the underlying non-linear rotational flow

dynamics in a subsonic flow are difficult to ascertain

theoretically, for in moving across the short distance

which separates the rotational heart of the flow from its

irrotational near- and mid-fields we pass from a dynamic

in which the pressure field is predominantly elliptic, to

one in which the behaviour is predominantly hyperbolic.

The near pressure field thus constitutes a transition region

where the predominant physics are a strong function of

the radial position. Thus, as mentioned above, interpre-

tation of nearfield pressure measurements is difficult when

a link with the underlying turbulence is sought. By cou-

pling nearfield pressure measurements with velocity

measurements effected in the mixing-layer of the flow

however, some light can be shed on the matter. Laufer

and Yen (1983) show that the fluctuating velocity and

nearfield pressure amplitudes are linearly related over the

first diameter of an acoustically excited jet, while in

Picard (2001) and Picard and Delville (2000) significant

pressure–velocity correlations are demonstrated in an

unexcited jet (M = 0.15, Re = 1.5 · 10–5) using a 16

microphone array and a rake of 12 X-wire probes. Ricaud

(2003) showed similar results at (M = 0.3, Re = 3 · 10–5)

using an 18 microphone axial array synchronously with an

LDV system, as did Tinney et al. (2006b, 2007) at

(M = 0.6, Re = 6 · 10–5) and (M = 0.85, Re = 1 · 10–6)

using azimuthal pressure transducer arrays synchronous

with both LDV and PIV. These studies all show that the

turbulence mechanisms predominant in driving the near-

field pressure are the linear, fast pressures. Tinney et al.

(2006b, 2007) have recently reported correlations between

the nearfield pressure and both the linear and quadratic

mixing-layer velocity terms, and again the predominance

of the linear term is demonstrated; the work of Coiffet

et al. (2006) shows furthermore how sound pressures are

also produced via a linear process, in agreement with

conclusions drawn from the causality methods applied in

the 1970s and 1980s.

3.4.1 Signal processing tools/low order analysis

Progress in measurement technology has led to the use of

progressively larger numbers of microphones, and more

spatiotemporally extensive turbulence measurements via

two-point, three-component LDV and two-point, stereo-

scopic, time-resolved PIV. Such simultaneous sampling of

pressure and velocity can lead to the generation of enor-

mous databases, and in particular when PIV is used to

measure velocity: on account of the temporal limitation of

PIV, large numbers of samples are required in order to

build up the pressure–velocity correlation. Creative post-

processing of the data is thus not simply a possibility, but a

necessity if the huge datasets are to be useful. Tools are

required which can compress the data, both in order to

optimise storage and manipulation, but also from the point

of view of analysis of the underlying physics. It is clear that

some means is necessary by which to make sense of the

thousands of cross-correlations—or other products of syn-

chronous measurement—which can result from such

measurements. Two such means, both based on the second-

order, two-point statistics of a given field or set of fields,

are proper orthogonal decomposition (Lumley 1967) and

linear stochastic estimation (Adrian 1977). From the two-

point statistics of a field quantity (pressure, velocity,

etc…), the flow can be represented in terms of a sum of

empirical eigenmodes, and in many cases a small number

of these suffices to capture the majority of the fluctuation

energy. In such cases a low-order representation of the flow

dynamic is possible. The eigenmodes comprise both spatial

and temporal components. The spatial component trans-

lates some characteristic, spatial flow feature, while the

temporal component dictates how the amplitude of the

spatial component fluctuates in unison with the other

modes in order to reproduce the full flow dynamic. A

particularly attractive feature of POD is that time-resolved

measurements are not necessarily required to obtain the

temporal POD coefficients. This means that time-resolved

flow representations can be obtained from measurements

which are temporally limited. A further attractive feature of

POD is that the temporal POD coefficients represent the

dynamics of a spatially extensive information, which of

course means that its correlation with a time varying

quantity of another measurement will translate a consid-

erably richer information than simple two-point

correlations between two flow quantities [such correlation

leads to what Boree (2003) has described as Extended POD

modes]. As the relationship between the farfield pressure

and its source is governed by a volume integral, this

capacity of POD presents considerable possiblities: some

interesting preliminary results using such an approach have

been obtained by Jordan et al. (2007), who by means of an

acoustically-optimised modal decomposition of a low-

Exp Fluids (2008) 44:1–21 13

123

Reynolds number jet (computed by Groschel et al. 2005)

were able to make a quantitative estimate of the sound

produced by: a wavy-wall-like mechanism; a more ener-

getic event in the transition region; and by the less-

organised smaller flow-scales.

The second tool which has proved indispensable in

dealing with extensive synchronous pressure–velocity

measurements is linear stochastic estimation (Adrian 1977)

and its improved spectral-based sucessor, as proposed by

Ewing and Citriniti (1997) and later by Tinney et al.

(2006a).5 These techniques are again based on multi-point

correlations between two fields of interest (e.g. nearfield

pressure and velocity), and they lead essentially to the

identification of a transfer function which relates the fields.

Once this transfer function has been identified—and again

for this to be achieved time-resolved measurement of both

fields is not a necessary condition—an extremely valuable

information has been obtained with respect to the physics

underlying the causal link between the two. Indeed, the

transfer function can be used both to understand the

dynamics of one field which were responsible in driving

the other (e.g. the velocity dynamic which was essential in

producing the dynamic of the pressure field in the near and/

or far fields), but also to produce a real-time estimate of

one field using data acquired from the other. Nice examples

of this are the reconstruction of velocity fields using

pressure measurements made in the nearfield (e.g. Picard

and Delville 2000; Ricaud 2003; Coiffet 2006; Tinney et

al. 2006b, 2007).

Natural extensions of these techniques include com-

bined use of LSE and POD (Bonnet et al. 1994), which

involves correlating single point field measurements with

POD coefficients obtained from multi-point measurements

in another field of interest, in order to build a transfer

function which can then be the basis for a subsequent

stochastic estimation. And, finally, a further compression

can be obtained by correlating the temporal coefficients of

POD modes obtained in two fields. Each time it is possible

to correlate two quantities (i.e. whenever a linear rela-

tionship exists), a stochastic estimation is possible.

The capacity of these tools to provide physical insight

which takes us beyond what was possible with simple

point-to-point correlations is considerable, and their future

in the field of aeroacoustics promises to be an exciting one.

Recent examples of where they may be headed can be

found in the work of Picard and Delville (2000), Ricaud

(2003), Coiffet (2006), Tinney et al. (2006b, 2007) and

Jordan et al. (2007). However, there are a number of

important issues, and potential stumbling blocks, which

must be addressed. Take for example the work of Tinney

et al. (2006b, 2007). In this work pressure measurements

taken in the nearfield of a round jet (0.6, 6 · 10–5) are

correlated with velocity signals obtained from LDV mea-

surements in the mixing-layer region. Spectral LSE is then

used to perform a 3D reconstruction of the velocity field

using the near pressure field, whence an aeroacoustic

source term is computed according to Lighthill’s definition.

The source estimate thus obtained, being based on the

mechanisms which were central in driving the near pres-

sure field, corresponds to the low-order, coherent flow

dynamic. However, the Lighthill formulation has been

shown by Freund et al. (2005) to be particularly sensitive

to errors which may arise from such an incomplete repre-

sentation of the source. And so this brings us back to the

question of what constitutes an appropriate source defini-

tion. It is clear that where the experimental approach is

concerned, in addition to questions of what constitutes a

meaningful source definition, a further question arises as to

what constitutes a robust source definition. An interesting

development where this question is concerned is the con-

servative form of the vortex sound theory proposed by

Schram and Hirschberg (2003), who demonstrate how a

reiteration of the momentum and kinetic energy conser-

vation laws leads to a formulation of the vortex sound

theory which is less sensitive to experimental error, and

indeed they used PIV measurements in an acoustically

excited jet to construct a source quantity which leads to

farfield predictions in good agreement with measurements.

As the techniques described above target the low-order,

coherent flow/source dynamic, source definitions derived

from vortex sound theories are probably quite apt, and so

the conservative formulation of Schram and Hirschberg

may constitute a very important tool for such source

analysis and modelling. This constitutes another exciting

prospect for future research: as discussed in Sect. 2.5 there

is considerable redundancy in most source definitions; the

Goldstein framework presents a possibility for the removal,

or at least the reduction of this redundancy; however, this

must not be to the detriment of the robustness of the

resultant source term. These two aspects should be con-

sidered together where experimental source analysis and

modelling is concerned.

4 Contributions from computational aeroacoustics

The advent of high precision direct numerical simulation

(DNS) in the 1990s consituted a major advance for

aeroacoustic research, as it provided a means of exploring

complexities of the sound production mechanisms which

are beyond the reach of current experimental diagnostics. A

comprehensive survey of progress in this specialised

5 The stochastic estimation is in fact exactly equivalent to the

Extended POD, in that the EPOD amounts to the solution of the linear

problem.

14 Exp Fluids (2008) 44:1–21

123

branch of aeroacoustics would not be appropriate in this

review paper (the interested reader can refer to papers by

Colonius and Lele (2004) and Wang et al. (2006)), and so

we will simply focus on some of the more pertinent find-

ings where the physics of sound production is concerned

and, in particular where these findings can be compared

with experimental results.

Early simulations were limited to low Reynolds number,

2D flows, entirely dominated by coherent vortex dynamics.

However, this kind of simulation is qualitatively similar to

the excited jet studies undertaken in the 1970s (discussed in

Sect. 3.2.2), and so experimental-numerical comparison is

possible. Mitchell et al. (1995) studied the sound generated

by compact and non-compact co-rotating vortex pairs,

showing the nearfield to comprise quadrupole dilatation

patterns while the farfield was found to be cylindrical: no

inherent directivity was observed. Colonius et al. (1997)

simulated a 2D mixing-layer forced at its most unstable

frequency. This flow is dominated by a vortex pairing

event, and consitutes a spatially stationary, non-compact

source best modelled by a wavepacket structure, but which

produces a strongly directive sound field. We have already

seen how there is a considerable body of evidence sug-

gesting that at least some component of the large-scale

production mechanism in a real jet is spatially stationary,

non-compact and behaves in many ways like a wavy-wall.

These numerical observations lend further support to the

hypothesis that the directive nature of a jet is not related to

convective amplification, but rather to the inherently

directive character of a source structure which is fixed in

space, though generated by moving disturbances, as poin-

ted out by Laufer and Yen (1983). Of course, such 2D, low

Mach number simulations are a long way from the high

Reynolds number jets whose production mechanisms we

seek to understand and model. Freund (2001) was to take

the direct aeroacoustic numerical simulation a step closer

to the real jet by computing a 3D jet (M = 0.9, Re =

3.6 · 10–3). Analysis of the Lighthill source term, and in

particular its radiating structure, revealed two important

features: the regions of radiating source activity did not

correspond to either the peak turbulence levels or the peak

Lighthill source levels, showing very clearly the danger in

interpreting source activity in a flow based on a source

definition which comprises large redundancy; Freund fur-

thermore demonstrated how the radiating source structure

in the low Reynolds number jet resembled a wavy-wall-

like mechanism. This simulation can be compared with: the

low Reynolds number experiments of Stromberg et al.

(1980), where non-linearities associated with wavelike

instabilities were postulated as a possible source mecha-

nism; and the higher Reynolds number flow studied by

Coiffet et al. (2006), in which the existence of a linear

wavy-wall source mechanism was demonstrated. A study

by Sandham et al. (2005) has further demonstrated how

weak non-linearities associated with the linear instability

waves of a 2D mixing-layer produce a sound field very

similar to that computed by DNS, while the sound field

linearly generated by the instability waves was a good deal

weaker; this result can be compared with the experimental

observations of Laufer and Yen (1983) and Stromberg et

al. (1980); however, as we have seen, it may not be an

accurate depiction of the coherent source mechanisms in

high Reynolds number, unexcited flows. Wei and Freund

(2006) used an adjoint based optimisation procedure to

control the flow dynamics of a 2D mixing-layer. This

resulted in reductions of between 5 and 11 dB, depending

on the type of control which was implemented. The neg-

ligible differences observed between the controlled and

uncontrolled flows—despite enormous differences in the

sound power radiated from the flows—is a testament to the

subtlety of the sound producing dynamics of free shear

flows, its closeness to a quiet ‘‘state’’, and the difficulty of

understanding the true ‘‘source’’ structure; a recent study

by Eschricht et al. (2007) has shown how the effect of the

controller involves very slight modifications to the space–

time flow structure, which are sufficient to significantly

degenerate the two-point, two-time source correlations, in

the retarded-time reference-frame. Cabana et al. (2006)

used a DNS of a temporal mixing-layer to understand how

some of the aforesaid redundancies can be removed from a

given source description. A decomposition of the Lighthill

source led to the identification of source mechanisms

associated with the Lamb vector divergence, i.e. the source

term identified by vortex sound theories, and the Laplacian

of the turbulent kinetic energy; the former was found to

dominate sound production in the flow considered. A closer

study of these terms showed how compressibility plays an

essential role in the production of progressive pressure

modes, in agreement with a theoretical description of the

aeroacoustic problem by George et al. (2007). Cabana et

al. (2006) subsequently performed a filtering operation in

wavenumber space (similar to that of Freund 2001) which

led to the identification of the radiating source structure of

the flow.

The simulation of more industrially relevant, high

Reynolds number jets, where the nozzle geometry can be

included, is currently beyond the capability of DNS, and to

this end a powerful surrogate simulation which is becom-

ing increasingly popular is large eddy simulation (hereafter

LES). This kind of simulation uses a coarser space–time

grid, and so only directly computes the larger turbulence

scales, the subgrid scales being either modelled, or ignored

and left to the caprice of numerical dissipation. As the

large-scales appear to play an important role in the pro-

duction of sound however, and as such simulations can

now achieve Reynolds numbers of the same order as flows

Exp Fluids (2008) 44:1–21 15

123

of practical interest (e.g. Bogey et al. 2003; Andersson

et al. 2005; Viswanathan et al. 2006), this kind of tool

provides a powerful means for the prediction and study of

jet noise. Some pertinent results which can be compared

with experiment include the causality correlations of

Bogey and Bailly (2005) which again identify the region at

the end of the potential core as an important, intermittent

producer of sound, in agreement with the experiments of

Juve et al. (1980), Guj et al. (2003), Hileman et al. (2005)

and Panda et al. (2005); the two-point space–time corre-

lations of Andersson et al. (2005) were validated by the

experiments of Jordan and Gervais (2005); the co-axial

computations of Viswanathan et al. (2006) identified

important sound sources both at the nozzle exit, and

towards the end of the potential core, both of which were

observed in the experiments of Tinney et al. (2006b) by

means of a nearfield microphone array. Other interesting

results obtained by means of LES include the identification

by Groschel et al. (2005) of the Lamb vector as a dominant

source mechanism in a high Mach number, high Reynolds

number flow, in agreement with the observations of Cabana

et al. (2006); the identification of strong correlations

between entropy and momentum sources by Bodony and

Lele (2006); and the study of the effect of Reynolds

number by Bogey and Bailly (2004).

5 Current candidate source mechanisms

In the foregoing sections we have presented an outline of

the main movements in subsonic jet aeroacoustics over the

past 50 years. We have seen how, in this time, considerable

progress has been made where our understanding of the

mechanisms underlying the production of sound by

unbounded turbulent jets is concerned. And, even if a

general consensus on the matter stubbornly continues to

elude us, there exist nonetheless a number of candidate

source mechanisms, for which a considerable body of

experimental and numerical support can be found.

It seems clear that there are a number of different

mechanisms at work in the production of sound by a jet. In

some respects this is not surprising as a jet presents a

number of well-defined regions, between which the tur-

bulence characteristics vary considerably. The initial

mixing-layer region, just downstream of the nozzle exit, is

characterised by a highly sheared, inflexional mean-flow.

Instabilities in this region of the flow can be rendered more

efficient in the production of sound by the presence of the

nozzle. The experimental results of Bridges and Hussain

(1995) for an excited jet, and Tinney et al. (2006b) for a

high Reynolds, high Mach number co-axial jet, identify an

important source in this region, as do the numerical results

of Viswanathan et al. (2006). The fact that such a strong

source is not observed when the nozzle is not included in

simulations (see for example the results of Bogey and

Bailly 2004) constitutes further evidence for a source

related to the presence of the nozzle.

The region between the nozzle exit and the end of the

potential core has been shown by a number of experimental

studies to be characterised by wavelike instabilities, or

coherent structures (see for example Fuchs 1972; Lau et al.

1972; Chan 1974; Armstrong et al. 1977). Analytical,

experimental and numerical work has shown how such

wavy-wall mechanisms can present spatially stationary,

inherently directive sound sources (see for example the work

of Ffowcs-Williams and Kempton (1978), Laufer and Yen

(1983), Mankbadi and Liu (1984), Crighton and Huerre

(1990) and Colonius et al. (1997)). And, in excited and low

Reynolds number flows, where the flow dynamic is highly

coherent, the sound production mechanism has been argued

to be non-linear (for example Stromberg et al. 1980; Laufer

and Yen 1983; Sandham et al. 2005). However, the exper-

imental observations of Coiffet et al. (2006), and the

numerical results of Jordan et al. (2007) suggest that in

unexcited flows, such instabilities radiate sound via a linear

mechanism. The results of the causality techniques (Lee and

Ribner 1972; Siddon and Rackl 1972; Scharton and White

1972; Seiner 1974; Juve et al. 1980; Schaffar and Hancy

1982) also show the linear component of the Lighthill source

quantity to correlate best with the farfield, in regions both

upstream and downstream of the end of the potential core.

The transition region has long been considered a dom-

inant region where the production of sound is concerned.

The beginning of this region is marked by the annular

mixing-layer at the end of the potential core, where the

wavelike instabilities/coherent structures of the upstream

region undergo a violent transition. Jung et al. (2004)

describe an intermittent ‘‘volcano’’ effect associated with

the collapse of low order azimuthally coherent ring-like

structures. The early causality methods (Lee and Ribner

1972; Siddon and Rackl 1972; Scharton and White 1972;

Seiner 1974; Juve et al. 1980; Schaffar and Hancy 1982)

all identified this region as a dominant source of sound, and

as mentioned, showed the relationship between the turbu-

lent velocity fluctuations and the farfield pressure to be

predominantly linear. Again this contradicts results from

excited flows Laufer and Yen (1983), and indicates that the

source mechanisms in unexcited jets may be fundamentally

different. Events at the end of the potential core have

furthermore been shown to be stationary—and therefore

inherently directive—non-compact, intermittent, powerful

generators of sound (Juve et al. 1980; Guj et al. 2003;

Bogey and Bailly 2004; Hileman et al. 2005; Viswanathan

et al. 2006).

It is important to note that the characteristics of the

source mechanisms described above preclude the use of

16 Exp Fluids (2008) 44:1–21

123

statistical modelling approaches involving RANS compu-

tations coupled with an acoustic analogy (cf. Sects. 2.1,

3.1). Even if the non-compactness can be dealt with, the

intermittency cannot, as the RANS computation cannot

provide information regarding the third order velocity

moments. Also, as there can be neither Doppler shift nor

convective amplification associated with a spatially sta-

tionary source, the physical basis of such models must be

seriously questioned. However, in high Reynolds number

flows a further source mechanism may exist related to the

fine-scale, random turbulence. The two similarity spectra

proposed by Tam (1998) and shown to fit subsonic jet noise

data by Viswanathan (2002) support this conjecture, as do

both the acoustically filtered nearfield measurements of

Tinney et al. (2006b), and the differences which have been

identified between high Reynolds number and low Rey-

nolds number flows by Bogey and Bailly (2004) for

example. For this source component statistical models may

be well adapted; however, clarification is first necessary

regarding the associated underlying physics. This presents

a considerable and important challenge for the future.

Analytical decompositions such as performed by Mankbadi

and Liu (1981, 1984), and the recent work of Goldstein

(2005) and Goldstein and Leib (2005) may provide means

by which an integral framework can be obtained for the

experimental/numerical identification and study of this

source component and its relative importance where the

farfield sound is concerned.

6 Concluding remarks

We have tried in the foregoing to give a reasonably com-

prehensive overview of jet noise research since 1952. In

tracing out the various phases which have marked the

evolution of both our understanding of, and the means by

which we endeavour to probe the underlying physics,

something which becomes clear, and, incidentally, which

was evoked by Lighthill (1952) at the outset, is the extre-

mely subtle character of the mechanisms by which a

compressible, turbulent fluid excites a progressive pressure

field. It is on account of this that there remains today a

good deal of controversy and lack of consensus as to what

constitutes a source mechanism in an unbounded shear-

flow. The experimental approach suffers badly at the hands

of this subtlety—the fluctuating levels which characterise

the very-small portion of the jet dynamic implicated in the

production of sound are completely swamped by largely

acoustically ineffective hydrodynamic fluctuations, and are

therefore practically unmeasureable—and is thus obliged

to rely heavily on theoretical frameworks which remain

contentious. Furthermore, and despite our best hopes, even

the recent progress in high-precision numerical simulation

has not been entirely successful in alleviating this apparent

impasse.

There have however been some encouraging recent, and

not-so-recent, theoretical developments, respectively, by

Goldstein (2003, 2005) and Goldstein and Leib (2005), and

by Mankbadi and Liu (1981, 1984). The experimental

approach has become considerably more powerful in its

capacity to access, in a spatiotemporally extensive manner,

the various fields of interest (e.g. Hileman et al. 2005;

Jordan et al. 2005; Suzuki and Colonius 2006; Reba et al.

2006; Tinney et al. 2006b, 2007; Chatellier and Fitzpatrick

2006). And the numerical approach has the capacity to

provide what the experiment cannot (e.g. Freund 2001;

Bogey et al. 2003; Wei and Freund 2006; Cabana et al.

2006). It is clear that what is necessary for the future

development of perspicacious analysis methodologies is a

better synergy between these three disciplines. The theo-

retical frameworks provided by Mankbadi and Liu (1984),

and Goldstein and Leib (2005) warrant further attention,

and most importantly, experimental and numerical analysis

strategies need to be contrived in concert with directives

derived from these theories.

A point which is worth evoking with regard to this is the

following: we seek to identify the space–time signature of

the mechanisms by which the jet couples with the farfield.

This signature is contained in the farfield. In fact, this

signature is the farfield. And while it is well known that it

is not possible to obtain a unique solution for source dis-

tributions from farfield information alone (by inverse

techniques for example), coupled sampling of farfield

pressure with extensive flow data can lead to an improved

conditioning of such inversion techniques. The causality

methods used in the 1970s constituted an early attempt at

such identification (Lee and Ribner 1972; Siddon and

Rackl 1972; Scharton and White 1972; Seiner 1974; Juve

et al. 1980; Schaffar and Hancy 1982), and both Guj et al.

(2003) and Hileman et al. (2005) have more recently made

similar good use of such nearfield–farfield coupling.

However, we now have the capacity, both in terms of

measurement technology and signal-processing, to take

these approaches much farther. In addition, numerical

simulations are well situated to help understand the limits

of such techniques. The simulation can be used to help

optimise the experiment. The adjoint-based approaches

which are now beginning to be applied numerically (Wei

and Freund 2006) constitute an upper limit in terms of

what’s possible, and these need to be exploited to help

understand how much can be achieved experimentally.

Ambitious research programmes are required which com-

prise three indispenable phases: a first in which a thorough

theoretical treatment and definition of the problem is

considered; a second phase involving a numerical investi-

gation which pushes the theory to its limits; and a third

Exp Fluids (2008) 44:1–21 17

123

experimental phase which is optimised by virtue of lessons

learned during the numerical phase. High-powered signal

processing will be central to effective mining of the

numerical and experimental databases, and in this regard

an integration of techniques from other research fields

should be encouraged. In particular, research fields where

pattern-recognition and structure-identification are central

could constitute a source of new ideas: fields where tech-

niques are developed in order to understand the

relationship between different kinds of N-dimensional

signature, and whose extrapolation to the field of jet

aeroacoustics could help answer the question: what was the

space–time flow pattern which generated this signal (the

farfield)? Such an approach is currently being developed by

Jordan et al. (2007).

It seems clear that, despite some formidable obstacles

the future of aeroacoustic is set to be an exciting one,

where genuinely new analysis strategies can be made

possible by an efficient synergy between theoretical,

experimental and numerical disciplines, one which takes

good advantage of the impressive recent progress in

numerical and experimental tools; however, we would like

to close this paper by suggesting that there is a further

essential element, and this is: a keen sense of adventure!

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