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GRAVITY CURRENTS
Claudia Adduce
University of Rome “Roma Tre”
Department of Civil Engineering
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SUMMARY
• INTRODUCTION
• MIXING IN GRAVITYCURRENTS FLOWING DOWN A SLOPE IN A ROTATING FLUID
• GRAVITY CURRENTS PRODUCED BY LOCK EXCHANGES
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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
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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)
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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:
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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
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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.
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STRUCTURE OF A GRAVITY CURRENT
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MIXING IN GRAVITY CURRENTS
FLOWING DOWN A SLOPE IN A
ROTATING FLUID
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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
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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
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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)
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FLOW REGIMES
LAMINAR-TURBULENT
LAMINAR – WAVES – WAVES BREAKING
TURBULENT
Cenedese & Adduce, JFM, 2008
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MIXING DEPENDENCE ON Re
1
1'
'
0
b
mg
gQ
AWe
Cenedese & Adduce, JFM, 2008
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MIXING DEPENDENCE ON Fr
Cenedese & Adduce, JFM, 2008
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MIXING DEPENDENCE ON BOTH Fr AND Re
Cenedese & Adduce, JFM, 2008
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MIXING DEPENDENCE ON Fr: OBSERVATIONAL AND LABORATORY DATA
Cenedese & Adduce, JFM, 2008
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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
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GRAVITY CURRENTS PRODUCED BY
A LOCK EXCHANGE RELEASE:
EXPERIMENTS AND SHALLOW
WATER MODELING
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THE LOCK EXCHANGE RELEASE EXPERIMENT
SLUMPING PHASE
I
II
III
SELF SIMILAR PHASE
VISCOUS PHASE
t2/3
t1/5
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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)
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PHASES IN A GRAVITY CURRENT
0
00
0 '*
hg
xt
t
tT
0
*
x
xx
f
f
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DENSITY FIELDS
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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
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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)
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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
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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
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ENTRAINMENT EFFECT
Adduce et al., JHE, 2012
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ENTRAINMENT EFFECT
Adduce et al., JHE, 2012
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NUMERICAL SIMULATIONS
Adduce et al., JHE, 2012
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NUMERICAL SIMULATIONS
Adduce et al., JHE, 2012
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PIV MEASUREMENTS IN A GRAVITY CURRENT
Problem: the index of refraction changes with the local value of density
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PIV MEASUREMENTS IN A GRAVITY CURRENT
Refraction Index Method Alahyari and Longmire (1994)
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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
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0.78 m 1.15 m
PIV MEASUREMENTS IN A GRAVITY CURRENT
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NUMERICAL SIMULATIONS
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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
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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