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 ( and ) 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.
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e-mail: mcantero@uiuc.edu
e-mail: s-bala@uiuc.edu
e-mail: mhgarcia@uiuc.edu
e-mail: jferry@uiuc.edu
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November 2006
Technical Papers
Direct Numerical Simulations of Planar and Cylindrical Density Currents
Mariano I. Cantero,
Mariano I. Cantero
Department of Civil and Environmental Engineering,
e-mail: mcantero@uiuc.edu
University of Illinois at Urbana-Champaign
, Urbana, IL 61801
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S. Balachandar,
S. Balachandar
Department of Theoretical and Applied Mechanics,
e-mail: s-bala@uiuc.edu
University of Illinois at Urbana-Champaign
, Urbana, IL 61801
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Marcelo H. García,
Marcelo H. García
Department of Civil and Environmental Engineering,
e-mail: mhgarcia@uiuc.edu
University of Illinois at Urbana-Champaign
, Urbana, IL 61801
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James P. Ferry
James P. Ferry
Center for the Simulation of Advanced Rockets,
e-mail: jferry@uiuc.edu
University of Illinois at Urbana-Champaign
, Urbana, IL 61801
Search for other works by this author on:
Mariano I. Cantero
Department of Civil and Environmental Engineering,
University of Illinois at Urbana-Champaign
, Urbana, IL 61801e-mail: mcantero@uiuc.edu
S. Balachandar
Department of Theoretical and Applied Mechanics,
University of Illinois at Urbana-Champaign
, Urbana, IL 61801e-mail: s-bala@uiuc.edu
Marcelo H. García
Department of Civil and Environmental Engineering,
University of Illinois at Urbana-Champaign
, Urbana, IL 61801e-mail: mhgarcia@uiuc.edu
James P. Ferry
Center for the Simulation of Advanced Rockets,
University of Illinois at Urbana-Champaign
, Urbana, IL 61801e-mail: jferry@uiuc.edu
J. Appl. Mech. Nov 2006, 73(6): 923-930 (8 pages)
Published Online: December 19, 2005
Article history
Received:
May 24, 2005
Revised:
December 19, 2005
Citation
Cantero, M. I., Balachandar, S., García, M. H., and Ferry, J. P. (December 19, 2005). "Direct Numerical Simulations of Planar and Cylindrical Density Currents." ASME. J. Appl. Mech. November 2006; 73(6): 923–930. https://doi.org/10.1115/1.2173671
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