The collapse of a heavy fluid column in a lighter environment is studied by direct numerical simulation of the Navier-Stokes equations using the Boussinesq approximation for small density difference. Such phenomenon occurs in many engineering and environmental problems resulting in a density current spreading over a no-slip boundary. In this work, density currents corresponding to two Grashof (Gr) numbers are investigated ($105$ and $1.5×106$) for two very different geometrical configurations, namely, planar and cylindrical, with the goal of identifying differences and similarities in the flow structure and dynamics. The numerical model is capable of reproducing most of the two- and three-dimensional flow structures previously observed in the laboratory and in the field. Soon after the release of the heavier fluid into the quiescent environment, a density current forms exhibiting a well-defined head with a hanging nose followed by a shallower body and tail. In the case of large Gr, the flow evolves in a three-dimensional fashion featuring a pattern of lobes and clefts in the intruding front and substantial three-dimensionality in the trailing body. For the case of the lower Gr, the flow is completely two dimensional. The dynamics of the current is visualized and explained in terms of the mean flow for different phases of spreading. The initial phase, known as slumping phase, is characterized by a nearly constant spreading velocity and strong vortex shedding from the front of the current. Our numerical results show that this spreading velocity is influenced by Gr as well as the geometrical configuration. The slumping phase is followed by a decelerating phase in which the vortices move into the body of the current, pair, stretch and decay as viscous effects become important. The simulated dynamics of the flow during this phase is in very good agreement with previously reported experiments.

1.
Simpson
,
J.
, 1997,
Gravity Currents
,
2nd ed.
,
Cambridge University Press
.
2.
Allen
,
J.
, 1985,
Principles of Physical Sedimentology
,
George Allen and Unwin Ltd.
.
3.
García
,
M.
, and
Parker
,
G.
, 1989, “
Experiments on Hydraulic Jumps in Turbidity Currents Near a Canyon-Fan Transition
,”
Science
0036-8075,
245
, pp.
393
396
.
4.
García
,
M.
, 1994, “
Depositional Turbidity Currents Laden With Poorly Sorted Sediment
,”
J. Hydraul. Eng.
0733-9429,
120
(
11
), pp.
1240
1263
.
5.
von Kármán
,
T.
, 1940, “
The Engineer Grapples With Nonlinear Problems
,”
Bull. Am. Math. Soc.
0002-9904,
46
, pp.
615
683
.
6.
Benjamin
,
T.
, 1968, “
Gravity Currents and Related Phenomena
,”
J. Fluid Mech.
0022-1120,
31
, pp.
209
248
.
7.
Rottman
,
J.
, and
Simpson
,
J.
, 1983, “
Gravity Currents Produced by Instantaneous Releases of a Heavy Fluid in a Rectangular Channel
,”
J. Fluid Mech.
0022-1120,
135
, pp.
95
110
.
8.
Bonnecaze
,
R.
,
Huppert
,
H.
, and
Lister
,
J.
, 1993, “
Particle-Driven Gravity Currents
,”
J. Fluid Mech.
0022-1120,
250
, pp.
339
369
.
9.
Choi
,
S.-U.
, and
García
,
M.
, 1995, “
Modeling of One-Dimensional Turbidity Currents With a Dissipative-Galerkin Finite Element Method
,”
J. Hydraul. Res.
0022-1686,
33
(
5
), pp.
623
648
.
10.
Hallworth
,
M.
,
Huppert
,
H.
,
Phillips
,
J.
, and
Sparks
,
R.
, 1996, “
Entrainment Into Two-Dimensional and Axisymmetric Turbulent Gravity Currents
,”
J. Fluid Mech.
0022-1120,
308
, pp.
289
311
.
11.
Hallworth
,
M.
,
Huppert
,
H.
, and
Ungarish
,
M.
, 2001, “
Axisymmetric Gravity Currents in a Rotating System: Experimental and Numerical Investigations
,”
J. Fluid Mech.
0022-1120,
447
, pp.
1
29
.
12.
Huppert
,
H.
, and
Simpson
,
J.
, 1980, “
The Slumping of Gravity Currents
,”
J. Fluid Mech.
0022-1120,
99
, pp.
785
799
.
13.
Allen
,
J.
, 1971, “
Mixing at Turbidity Current Heads, and its Geological Implications
,”
J. Sediment. Petrol.
0022-4472,
41
(
1
), pp.
97
113
.
14.
Simpson
,
J.
, 1972, “
Effects of the Lower Boundary on the Head of a Gravity Current
,”
J. Fluid Mech.
0022-1120,
53
(
4
), pp.
759
768
.
15.
McElwaine
,
J.
, and
Patterson
,
M.
, 2004, “
Lobe and Cleft Formation at the Head of a Gravity Current
,”
Proceedings of the XXI International Congress of Theoretical and Applied Mechanics
,
Warsaw
, August 15–21.
16.
García
,
M.
, and
Parsons
,
J.
, 1996, “
Mixing at the Front of Gravity Currents
,”
Dyn. Atmos. Oceans
0377-0265,
24
, pp.
197
205
.
17.
Parsons
,
J.
, and
García
,
M.
, 1998, “
Similarity of Gravity Current Fronts
,”
Phys. Fluids
1070-6631,
10
(
12
), pp.
3209
3213
.
18.
García
,
C.
,
Manríquez
,
C.
,
Oberg
,
K.
, and
García
,
M.
, 2005, “
Density Currents in the Chicago River, Illinois
,”
Proceedings of the 4th IAHR Symposium on River, Coastal and Estuarine Morphodynamics
,
G.
Parker
and
M.
García
, eds., Urbana, IL, October 4–7, Vol.
1
, pp.
191
201
.
19.
Droegemeier
,
K.
, and
Wilhelmson
,
R.
, 1987, “
Numerical Simulation of Thunderstorm Outflows Dynamics. Part I: Outflow Sensitivity Experiments and Turbulence Dynamics
,”
J. Atmos. Sci.
0022-4928,
44
(
8
), pp.
1180
1210
.
20.
Terez
,
D.
, and
Knio
,
O.
, 1998, “
Numerical Study of the Collapse of an Axisymmetric Mixed Region in a Pycnoclyne
,”
Phys. Fluids
1070-6631,
10
(
6
), pp.
1438
1448
.
21.
Terez
,
D.
, and
Knio
,
O.
, 1998, “
Numerical Simulation of Large-Amplitude Internal Solitary Waves
,”
J. Fluid Mech.
0022-1120,
362
, pp.
53
82
.
22.
Härtel
,
C.
,
Meiburg
,
E.
, and
Necker
,
F.
, 2000, “
Analysis and Direct Numerical Simulation of the Flow at a Gravity-Current Head. Part 1. Flow Topology and Front Speed for Slip and No-Slip Boundaries
,”
J. Fluid Mech.
0022-1120,
418
, pp.
189
212
.
23.
Necker
,
F.
,
Härtel
,
C.
,
Kleiser
,
L.
, and
Meiburg
,
E.
, 2002, “
High-Resolution Simulations of Particle-Driven Gravity Currents
,”
Int. J. Multiphase Flow
0301-9322,
28
, pp.
279
300
.
24.
Alahyari
,
A.
, and
Longmire
,
E.
, 1996, “
Development and Structure of a Gravity Current Head
,”
Exp. Fluids
0723-4864,
20
, pp.
410
416
.
25.
Canuto
,
C.
,
Hussaini
,
M.
,
Quarteroni
,
A.
, and
Zang
,
T.
, 1988,
Spectral Methods in Fluid Dynamics
,
Springer-Verlag
.
26.
Cortese
,
T.
, and
Balachandar
,
S.
, 1995, “
High Performance Spectral Simulation of Turbulent Flows in Massively Parallel Machines With Distributed Memory
,”
Int. J. Supercomput. Appl.
0890-2720,
9
(
3
), pp.
187
204
.
27.
Härtel
,
C.
,
Michaud
,
L. K. M.
, and
Stein
,
C.
, 1997, “
A Direct Numerical Simulation Approach to the Study of Intrusion Fronts
,”
J. Eng. Math.
0022-0833,
32
, pp.
103
120
.
28.
Härtel
,
C.
,
Carlsson
,
F.
, and
Thunblom
,
M.
, 2000, “
Analysis and Direct Numerical Simulation of the Flow at a Gravity-Current Head. Part 2. The Lobe-and-Cleft Instability
,”
J. Fluid Mech.
0022-1120,
418
, pp.
213
229
.
29.
Spicer
,
T.
, and
Havens
,
J.
, 1987, “
Gravity Flow and Entrainment by Dense Gases Released Instantaneously Into Calm Air
,”
Proceedings of the Third International Symposium on Stratified Flows
,
E.
List
and
G.
Jirka
, eds., Pasadena, CA, February 3–5, pp.
642
651
.
30.
Cantero
,
M.
,
García
,
M.
,
Buscaglia
,
G.
,
Bombardelli
,
F.
, and
Dari
,
E.
, 2003, “
Multidimensional CFD Simulation of a Discontinuous Density Current
,”
Proceedings of the XXX IAHR International Congress
, Thessaloniki, Greece, August 24–29.
31.
Simpson
,
J.
, and
Britter
,
R.
, 1979, “
The Dynamics of the Head of a Gravity Current Advancing Over a Horizontal Surface
,”
J. Fluid Mech.
0022-1120,
94
, pp.
477
495
.