density current down a slope - civil.ist.utl.pt€¦ · 3 what is a gravity current a gravity...

GRAVITY CURRENTS

Claudia Adduce

University of Rome “Roma Tre”

Department of Civil Engineering

[email protected]

SUMMARY

• INTRODUCTION

• MIXING IN GRAVITYCURRENTS FLOWING DOWN A SLOPE IN A ROTATING FLUID

• GRAVITY CURRENTS PRODUCED BY LOCK EXCHANGES

3

WHAT IS A GRAVITY CURRENT

A gravity current is the flow of a fluid into another fluid (ambient fluid), due to a density difference.

This density difference may be due to a difference in:

- salinity

- temperature

- presence of suspended sediments

Examples of gravity currents:

- Mediterranean outflow

- Avalanches

- Pyroclastic flows

- Turbidity currents

GRAVITY CURRENT CONFIGURATIONS

a) bottom current of more dense (heavy) fluid; b) top (surface) current of less dense (light) fluid; c) intrusion of mixed fluid in a sharply stratified ambient; d) intrusion of mixed fluid in a linearly-stratified ambient.

Ungarish (2009)

CLASSIFICATIONS OF GRAVITY CURRENTS

1) COSTANT/NON-CONSTANT VOLUME The volume may decrease due to drainage into a porous

horizontal boundary, or may increase due to a source at the origin.

Volume variations of the current may be due to entrainment and to particle settling in particle-driven currents.

2) BOUSSINESQ/NON-BOUSSINESQ A current system is of Boussinesq type when the density

differences between the current (1) and the ambient (2)

are relatively small. In a two-fluid case:


3) INVISCID/VISCOUS A current is inviscid (inertial) when Re>>1 and viscous

when Re is not large with An initially inviscid gravity current may become viscous or

a current starting in the viscous regime, after some propagation can become inertial

INVISCID VISCOUS VISCOUS INVISCID


4) ROTATING/NON-ROTATING FRAMES Suppose that the system in which the current propagates

is rotating with about the vertical axis z. This introduces a new effect: the Coriolis acceleration. An observer attached to the channel may say that the current is deflected toward a side-wall by a Coriolis force.

5) COMPOSITIONAL/PARTICLE DRIVEN Compositional current when the density difference is a

result of different concentrations of a dissolved material like salt, or of different temperatures.

Particle driven current when the density difference is a result of a suspension of non-neutrally buoyant particles.

STRUCTURE OF A GRAVITY CURRENT

MIXING IN GRAVITY CURRENTS

FLOWING DOWN A SLOPE IN A

ROTATING FLUID

MIXING IN GRAVITY CURRENTS

Models that do not resolve entrainment processes use a supercritcal (Fr>1) Froude number parameterization

(Turner, 1986).

1.252

Frfor 0

1.252 Frfor 52Fr

0.120.08Fr

E

11

EXPERIMENTAL APPARATUS

Glass tank, mounted on a rotating turntable with a vertical axis of rotation (GFD laboratory of WHOI, USA)

1 density of the ambient fluid

2 density of the gravity current

SIDE VIEW TOP VIEW

EXPERIMENTAL PARAMETERS

FLOW RATE OF THE DENSITY CURRENT: Q

(2.5 – 8.3 cm3 s-1)

CORIOLIS PARAMETER: f = 2Ω

(1 – 1.75 s-1)

BOTTOM SLOPE: s = tan θ

(0.45 – 8.6)

REDUCED GRAVITY:

(0.7 – 99.8 cm s-2)

FLOW REGIMES

LAMINAR-TURBULENT

LAMINAR – WAVES – WAVES BREAKING

TURBULENT

Cenedese & Adduce, JFM, 2008

MIXING DEPENDENCE ON Re

1

1'

'

0

b

mg

gQ

AWe


MIXING DEPENDENCE ON Fr


MIXING DEPENDENCE ON BOTH Fr AND Re


MIXING DEPENDENCE ON Fr: OBSERVATIONAL AND LABORATORY DATA


NEW ENTRAINMENT PARAMETRIZATION

Cenedese & Adduce, JPO, 2010

)(1 0inf FrFrCA

FrAMinE

Re

1inf

B

MaxC

5.0

52.243

1

18.7

51.0

104.3

104

0

3

5

B

Max

Fr

A

Min

Nonlinear regression function using least squares estimation

GRAVITY CURRENTS PRODUCED BY

A LOCK EXCHANGE RELEASE:

EXPERIMENTS AND SHALLOW

WATER MODELING

THE LOCK EXCHANGE RELEASE EXPERIMENT

SLUMPING PHASE

I

II

III

SELF SIMILAR PHASE

VISCOUS PHASE

t2/3

t1/5

EXPERIMENTAL SET UP

ρ2

3 m

0.3 m

h0

gate

y ρ1

x

x0

ϑ

Hydraulics Laboratory of University of Rome “Roma Tre”

•CCD camera • 25 Hz • 768 x 576 pixels

Measurements of: • Interface between the dense and the light fluid • Density • Velocity (PIV)

PHASES IN A GRAVITY CURRENT

0

00

0 '*

hg

xt

t

tT

0

*

x

xx

f

f

DENSITY FIELDS

As the current advances, the front motion is characterized by repeated cycles of stretching/rupture, being observed mass detachment from the head towards

upstream, into the current body.

The head length Lf was defined taking the position of the first local minimum of function w near the front

t,xht,x)t,x(w v

DEFINITION OF CURRENT HEAD

TWO-LAYER SHALLOW WATER MODEL

22

212

2

221

2

11

121

2

1

1

22111

222222

211111

2cossin

2cossin

)()(

)()(

h

Vghh

xg

t

V

h

Vg

hh

xg

t

V

Vx

hV

t

h

Vx

hV

t

h

b

b

E

E

B

hVVB

BhVV

b

b

222

222

111

111

2

8

2

8

i

iii

h

Re

81

2

713

4

1

i

i

h.log

i

ii

i

hVRe

82

1212211212

VVVV

θ

y

x ρ1, h1

ρ2, h2

La Rocca et al. (2008)

unknownsVVhh 2121 ,,,b = bottom

1 = dense fluid

2 = ambient fluid

Supino (1981)

TWO-LAYER SHALLOW WATER MODEL

22

212

2

221

2

11

121

2

1

1

22111

222222

211111

2cossin

2cossin

)()(

)()(

h

Vghh

xg

t

V

h

Vg

hh

xg

t

V

Vx

hV

t

h

Vx

hV

t

h

b

b

E

E

52

2

1

Fr

Frk

V

VE

θ

y

x ρ1, h1

ρ2, h2

unknownsVVhh 2121 ,,,b = bottom

1 = dense fluid

2 = ambient fluid

Turner (1986)

25.10

25.15

1.008.0

2

1

2

12

1

2

1

1Fr

FrFr

Fr

V

VE

Adduce et al. (2012)

θgρ

ρρh

VFr

cos1

211

1

1

ENTRAINMENT

Adduce et al., JHE, 2012

LABORATORY ENTRAINMENT EVALUTATION:

Runs 1–9 1.6 × 10-2 ≤ E≤ 2 × 10-2 Run 10 E ≅ 2.5 × 10-3

Run 11 E ≅ 8 × 10-3

ENTRAINMENT EFFECT


NUMERICAL SIMULATIONS


PIV MEASUREMENTS IN A GRAVITY CURRENT

Problem: the index of refraction changes with the local value of density


Refraction Index Method Alahyari and Longmire (1994)


1.15 m

y

x

0

0.37 m

0.18 m

0.78

m

ρ01

ρ2

ϑ

ρ2

Gate

h0 ρ1

x0

ρ1 [Kg/m3] 1038

ρ2 [Kg/m3] 1011

h0 [m] 0.25

x0 [m] 0.10

ϑ [°] 1.41

KH2PO4

6%

Water

Glycerol

6%

Water

0.78 m 1.15 m


NUMERICAL SIMULATIONS

0.3

m

y x

L = 1.175 m

B = 1.35 m d

ρ1 ρ2

Gate

L = 1.175 m

x

z Gate

ρ1

ρ2

h0

3D GRAVITY CURRENTS

REFERENCES

• Nogueira H. I. S., Adduce C., Alves E. and Franca M. J., 2012, Analysis of lock-exchange gravity currents over smooth and rough

beds, Journal of Hydraulic Research (submitted).

• Adduce C., Sciortino G. & Proietti S., 2012, Gravity currents produced by lock-exchanges: experiments and simulations with a two

layer shallow-water model with entrainment, Journal of Hydraulic Engineering, 138 (2).

• La Rocca M., Adduce C., Lombardi V., Sciortino G., Hinkermann R., 2012, Development of a lattice Boltzmann method for two-

layered shallow-water flow, International Journal for Numerical Methods in Fluids, (accepted).

• La Rocca M., Adduce C., Sciortino G., Bateman Pinzon A. and M. A. Boniforti, 2012, A two-layer shallow water model for 3D

gravity currents, Journal of Hydraulic Research, 50 (2), 208-217.

• Cenedese C. and Adduce C., 2010, A new entrainment parameterization for mixing in overflows, Journal of Physical Oceanography,

40, 8, 1835-1850.

• La Rocca M., Adduce C., Sciortino G. and Bateman Pinzon A., 2008, Experimental and numerical simulation of three-dimensional

gravity currents on smooth and rough bed, Physics of Fluids, 20, 106603.

• Cenedese C. and Adduce C., 2008, Mixing in a density driven current flowing down a slope in a rotating fluid, Journal of Fluid

Mechanics, 604, 369-388.

COOPERATIONS

• Maria Antonietta Boniforti, University of Rome “La Sapienza”

• Michele La Rocca, University of Rome “Roma Tre”, Italy

• Valentina Lombardi, University of Rome “Roma Tre”, Italy

• Giampiero Sciortino, University of Rome “Roma Tre”, Italy

• Elsa Alves, LNEC, Portugal

• Allen Bateman, UPC, Spain

• Claudia Cenedese, Woods Hole Oceanographic Institution, USA

• Mario Franca, New University of Lisbon, Portugal

• Reinard Hinkelmann, Technical university of Berlin, Germany

• Helena Nogueira, University of Coimbra, Portugal

density current down a slope - civil.ist.utl.pt€¦ · 3 what is a gravity current a gravity...

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