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

adduce@uniroma3.it

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:

CLASSIFICATIONS OF GRAVITY CURRENTS

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

CLASSIFICATIONS OF GRAVITY CURRENTS

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

Cenedese & Adduce, JFM, 2008

MIXING DEPENDENCE ON Fr

Cenedese & Adduce, JFM, 2008

MIXING DEPENDENCE ON BOTH Fr AND Re

Cenedese & Adduce, JFM, 2008

MIXING DEPENDENCE ON Fr: OBSERVATIONAL AND LABORATORY DATA

Cenedese & Adduce, JFM, 2008

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

Adduce et al., JHE, 2012

ENTRAINMENT EFFECT

Adduce et al., JHE, 2012

NUMERICAL SIMULATIONS

Adduce et al., JHE, 2012

NUMERICAL SIMULATIONS

Adduce et al., JHE, 2012

PIV MEASUREMENTS IN A GRAVITY CURRENT

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

PIV MEASUREMENTS IN A GRAVITY CURRENT

Refraction Index Method Alahyari and Longmire (1994)

PIV MEASUREMENTS IN A GRAVITY CURRENT

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

PIV MEASUREMENTS IN A GRAVITY CURRENT

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