density current down a slope - civil.ist.utl.pt€¦ · 3 what is a gravity current a gravity...
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GRAVITY CURRENTS
Claudia Adduce
University of Rome “Roma Tre”
Department of Civil Engineering
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