The governing equations of two-dimensional steady density currents are solved numerically using a finite volume method. The v2¯f turbulence model, based on standard kε model, is used for the turbulence closure. In this method, all Reynolds stress equations are replaced with both a transport equation for v2¯ and an elliptic relaxation equation for f, a parameter closely related to the pressure strain redistribution term. The Simple-C procedure is used for pressure-velocity coupling. In addition, Boussinesq’s approximation is used to obtain the momentum equation. The computed height of the progressive density current is compared to the measured data in the literature, resulting in good agreement. The present results show that the flow rate is the most dominant parameter among those affecting the density currents hydrodynamics. The results also show that the v2¯f turbulence model is able to predict and simulate the characteristics of the low Reynolds turbulent density currents successfully, although it is based on a high Reynolds number turbulence model, i.e., the standard kε model. The use of boundary layer convention, saying that the density current’s height is a height at which the concentration is 1% of the inlet concentration, seems to yield reasonable results.

1.
Buckee
,
C.
,
Kneller
,
B.
, and
Peakall
,
J.
, 2001, “
Turbulence Structure in Steady, Solute-Driven Gravity Currents
,”
Spec. Publs. Int. Assn. Sediment.
,
31
, pp.
173
187
.
2.
Alavian
,
V.
,
Jirka
,
G. H.
,
Denton
,
R. A.
,
Johnson
,
M. C.
, and
Stefan
,
H. G.
, 1992, “
Density Currents Entering Lakes and Reservoirs
,”
J. Hydraul. Eng.
0733-9429,
118
(
11
), pp.
1464
1489
.
3.
Alavian
,
V.
, 1986, “
Behavior of Density Currents on an Incline
,”
J. Hydraul. Eng.
0733-9429,
112
(
1
), pp.
27
42
.
4.
Garcia
,
M.
, 1990, “
Depositing and Eroding Turbidity Sediment Driven Flows: Turbidity Currents
,” Project Report No. 306, St. Anthony Falls Hydraulic Lab., Univ. of Minnesota, Minneapolis.
5.
Altinakar
,
M. S.
,
Graft
,
W. H.
, and
Hopfinger
,
E. J.
, 1996, “
Flow Structure in Turbidity Current
,”
J. Hydraul. Res.
0022-1686,
34
(
5
), pp.
713
718
.
6.
Kneller
,
B. C.
,
Bennett
,
S. J.
, and
McCaffrey
,
W. D.
, 1997, “
Velocity and Turbulence Structure of Gravity Currents and Internal Solitary Waves
,”
J. Sediment Geol.
,
122
, pp.
235
250
.
7.
Firoozabadi
,
B.
,
Farhanieh
,
B.
, and
Rad
,
M.
, 2000, “
The Propagation of Turbulent Density Currents on Sloping Bed
,”
J. Sci. Iran.
,
8
(
2
), pp.
223
235
.
8.
Best
,
J. L.
,
Kirkbride
,
A. D.
, and
Peakall
,
J.
, 2001, “
Mean Flow and Turbulence Structure of Sediment-Laden Gravity Currents: New Insights Using Ultrasonic Doppler Velocity Profiling
,”
Spec. Publs. Int. Assn. Sediment.
,
31
, pp.
159
172
.
9.
de Rooji
,
F.
, and
Dalziel
,
B.
, 2001, “
Time- and Space-Resolved Measurements of Deposition Under Turbidity Currents
,”
Spec. Publs. Int. Assn. Sediment.
,
31
, pp.
207
215
.
10.
Alexander
,
J.
, and
Mulder
,
T.
, 2002, “
Experimental Quasi-Steady Currents
,”
J. Marine Geol.
,
186
, pp.
195
210
.
11.
Luthi
,
S.
, 1980, “
Some New Aspects of Two-Dimensional Turbidity Currents
,”
J. Sedimentology
,
28
, pp.
97
105
.
12.
Akiyama
,
J.
, and
Stefan
,
H. G.
, 1984, “
Plunging Flow Into Reservoir: Theory
,”
J. Hydraul. Eng.
0733-9429,
110
(
4
), pp.
484
499
.
13.
Akiyama
,
J.
, and
Stefan
,
H. G.
, 1985, “
Turbidity Current With Erosion and Deposition
,”
J. Hydraul. Eng.
0733-9429,
111
(
12
), pp.
1473
1495
.
14.
Parker
,
G.
,
Fukushima
,
Y.
, and
Pantin
,
H. M.
, 1986. “
Self Accelerating Turbidity Currents
,”
J. Fluid Mech.
0022-1120,
171
, pp.
145
181
.
15.
Akiyama
,
J.
, and
Stefan
,
H. G.
, 1988, “
Turbidity Current Simulation in a Diverging Channel
,”
Water Resour. Res.
0043-1397,
24
(
4
), pp.
579
587
.
16.
Fukushima
,
Y.
, and
Watanabe
,
M.
, 1990, “
Numerical Simulation of Density Underflow by the k−ε Turbulence Model
,”
J. Hydrosci. Hydr. Eng.
0912-2508,
8
, pp.
31
40
.
17.
Garcia
,
M.
, 1993, “
Hydraulic Jumps in Sediment-Driven Bottom Current
,”
J. Hydraul. Eng.
0733-9429,
119
(
10
), pp.
1094
1117
.
18.
Akiyama
,
J.
,
Ura
,
M.
, and
Wang
,
W.
, 1994, ”
Physical-Based Numerical Model of Inclined Starting Plumes
,”
J. Hydraul. Eng.
0733-9429,
120
(
10
), pp.
1139
1157
.
19.
Bradford
,
S. F.
, and
Katapodes
,
N.
, 1999, “
Hydrodynamics of Turbid Underflows. II: Aggradation, Avulsion, and Channelization
,”
J. Hydraul. Eng.
0733-9429,
125
(
10
), pp.
1016
1028
.
20.
Salaheldin
,
T. M.
,
Imran
,
J.
,
Chaudhry
,
M. H.
, and
Reed
,
C.
, 2000, “
Role of Fine-Grained Sediment in Turbidity Current Flow Dynamics and Resulting Deposits
,”
J. Marine Geol.
,
171
, pp.
21
38
.
21.
Stacey
,
M. W.
, and
Bowen
,
A. J.
, 1988, “
The Vertical Structure of Turbidity Currents and a Necessary Condition for Self-Maintenance
,”
J. Geophys. Res.
0148-0227,
93
(
C4
), pp.
3543
3553
.
22.
Eidsvik
,
K. J.
, and
BrØrs
,
B.
, 1989, “
Self-Accelerated Turbidity Current Prediction Based Upon k−ε Model Turbulence
,”
Cont. Shelf Res.
0278-4343,
9
(
7
), pp.
617
627
.
23.
Farrell
,
G. J.
, and
Stefan
,
H. G.
, 1988, “
Mathematical Modeling of Plunging Reservoir Flows
,”
J. Hydraul. Res.
0022-1686,
26
(
5
), pp.
525
537
.
24.
Bournet
,
P. E.
,
Dartus
,
D.
,
Tassin
,
B.
, and
Vincon-Leite
,
B.
, 1999, “
Numerical Investigation of Plunging Density Current
,”
J. Hydraul. Eng.
0733-9429,
125
(
6
), pp.
584
594
.
25.
de Cesare
,
G.
,
Schleiss
,
A.
, and
Hermann
,
F.
, 2001, “
Impact of Turbidity Currents on Reservoir Sedimentation
,”
J. Hydraul. Eng.
0733-9429,
127
(
1
), pp.
6
16
.
26.
Firoozabadi
,
B.
,
Farhanieh
,
B.
, and
Rad
,
M.
, 1998, “
Numerical Investigation of the Structure of Density Currents in a Two Dimensional Channel
,”
J. Esteghlal
,
2
, pp.
155
169
(in Farsi).
27.
Choi
,
S.
, and
Garcia
,
M.
, 2002, “
k−ε Turbulence Modeling of Density Currents Developing Two Dimensionally on a Slope
,”
J. Hydraul. Eng.
0733-9429,
128
(
1
), pp.
55
63
.
28.
Huang
,
H.
,
Imran
,
J.
, and
Pirmez
,
C.
, 2005, “
Numerical Model of Turbidity Currents With a Deforming Bottom Boundary
,”
J. Hydraul. Eng.
0733-9429,
131
(
4
), pp.
283
293
.
29.
Imran
,
J.
,
Kassem
,
A.
, and
Khan
,
S. M.
, 2004, “
Three Dimensional Modeling of Density Current. I. Flow in Straight Confined and Unconfined Channels
,”
J. Hydraul. Res.
0022-1686,
42
(
6
), pp.
578
590
.
30.
Kassem
,
A.
, and
Imran
,
J.
, 2004, “
Three-Dimensional Modeling of Density Current. I. Flow in Straight Confined and Unconfined Channels
,”
J. Hydraul. Res.
0022-1686,
42
(
6
), pp.
591
602
.
31.
BrØrs
,
B.
, and
Eidsvik
,
K. J.
, 1992, “
Dynamic Reynolds Stress Modeling of Turbidity Currents
,”
J. Geophys. Res.
0148-0227,
97
(
c6
), pp.
9645
9652
.
32.
Taulbee
,
D. B.
,
Mashayek
,
F.
, and
Barré
,
C.
, 1999, “
Simulation and Reynolds Stress Modeling of Particle-Laden Turbulent Shear Flows
,”
Int. J. Heat Fluid Flow
0142-727X,
20
, pp.
368
373
.
33.
Felix
,
M.
, 2001, “
A Two-Dimensional Numerical Model for Turbidity Current
,”
Spec. Publs. int. Assn. Sediment.
,
31
, pp.
71
81
.
34.
Drago
,
M.
, 2002, “
A Coupled Debris Flow-Turbidity Current Model
,”
Ocean Eng.
0029-8018,
29
, pp.
1769
1780
.
35.
Durbin
,
P.
, 1991, “
Near-Wall Turbulence Closure Modeling Without ‘Damping Functions’
,”
Theor. Comput. Fluid Dyn.
0935-4964,
3
, pp.
1
13
.
36.
Parneix
,
S.
,
Durbin
,
P.
, and
Behnia
,
M.
, 1998, “
Computation of 3-D Turbulent Boundary Layer Using the ν2¯−f Model
,”
Flow, Turbul. Combust.
1386-6184,
60
, pp.
19
46
.
37.
Sveningsson
,
A.
, and
Davidson
,
L.
, 2004, “
Assessment of Realizability Constraints in v2¯−f Turbulence Models
,”
Int. J. Heat Fluid Flow
0142-727X,
25
, pp.
785
794
.
38.
Davidson
,
L.
, and
Farhanieh
,
B.
,1991, “
A Finite Volume Code Employing Collocated Variable Arrangement and Cartesian Velocity Components for Computation of Fluid Flow and Heat Transfer in Complex Three-Dimensional Geometries
,” Chalmers Univ. of Tech., Sweden.
39.
Heschl
,
Ch.
,
Sanz
,
W.
, and
Klanatsky
,
P.
, 2005, “
Implementation and Comparison of Different Turbulence Models for Three Dimensional Wall Jets With FLUENT
,” CFD Forum, Bad Nauheim, Deutschland.
40.
Peakall
,
J.
,
McCaffrey
,
W. D.
, and
Kneller
,
B. C.
, 2000, “
A Process Model for the Evolution, Morphology and Architecture of Sinuous Submarine Channels
,”
J. Sediment Res.
1073-130X,
70
, pp.
434
448
.
41.
Ellison
,
T. H.
, and
Turner
,
J. S.
, 1959, “
Turbulent Entrainment in a Stratified Fluid
,”
J. Fluid Mech.
0022-1120,
6
, pp.
423
449
.
You do not currently have access to this content.