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Gravity currents propagating into two-layer stratified fluids: vorticity-based models

  • M. A. Khodkar (a1), M. M. Nasr-Azadani (a1) and E. Meiburg (a1)


The vorticity-based modelling approach originally introduced by Borden & Meiburg (J. Fluid Mech., vol. 726, 2013b, R1) is extended to gravity currents propagating into two-layer stratified ambients. Vorticity models are developed for three different flow configurations: no upstream-propagating wave, an upstream-propagating expansion wave only and an upstream-propagating expansion wave and a bore. For a given gravity current height and stratification strength, along with ambient inflow layer thicknesses and velocities, the models yield the gravity current velocity, the bore and expansion wave properties and the ambient outflow layer thicknesses and velocities. We furthermore establish which of the three configurations will occur in a given parameter regime. Since energy-related closure assumptions are not required for any of the configurations, we can determine the dissipation as a function of the gravity current height, for a given set of flow parameters. To investigate which gravity current height is selected in real flows, we carry out two-dimensional Navier–Stokes simulations for comparison. These yield gravity current heights close to the vorticity model solutions for energy-conserving flows. Hence we adopt these energy-conserving solutions as the vorticity model predictions. We subsequently discuss these predictions in the context of earlier models by other authors, and of two-layer stratified flows over obstacles.


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Baines, P. G. 1984 A unified description of two-layer flow over a topography. J. Fluid Mech. 146, 127167.10.1017/S0022112084001798
Baines, P. G. & Davies, P. A. 1980 Laboratory studies of topographic effects in rotating and/or stratified fluids. In Orographic Effects in Stratified Fluids, pp. 233299. GARP Publ. no. 23.
Benjamin, T. B. 1968 Gravity currents and related phenomena. J. Fluid Mech. 31 (2), 209248.10.1017/S0022112068000133
Borden, Z. & Meiburg, E. 2013a Circulation-based models for Boussinesq gravity currents. Phys. Fluids 25 (10), 101301.10.1063/1.4825035
Borden, Z. & Meiburg, E. 2013b Circulation-based models for Boussinesq internal bores. J. Fluid Mech. 726, R1.10.1017/jfm.2013.239
Crook, N. A. 1983 The formation of the Morning Glory. In Mesoscale Meteorology: Theories, Observations and Models (ed. Lilly, D. K. & Gal-Chen, T.), pp. 349353. D. Reidel.10.1007/978-94-017-2241-4_19
Crook, N. A.1984 A numerical and analytical study of atmospheric undular bores. PhD thesis, University of London.
Crook, N. A. & Miller, M. J. 1985 A numerical and analytical study of atmospheric undular bores. Q. J. R. Meteorol. Soc 111, 225242.10.1002/qj.49711146710
Flynn, M. R., Ungarish, M. & Tan, A. W. 2012 Gravity currents in a two-layer stratified ambient: the theory for the steady-state (front condition) and lock-released flows, and experimental confirmations. Phys. Fluids 24, 026601.10.1063/1.3680260
Holyer, J. Y. & Huppert, H. E. 1980 Gravity currents entering a two-layer fluid. J. Fluid Mech. 100, 739767.10.1017/S0022112080001383
Khodkar, M. A., Nasr-Azadani, M. M. & Meiburg, E. 2017 Partial-depth lock-release flows. Phys. Rev. Fluids 2 (6), 064802.10.1103/PhysRevFluids.2.064802
Kilcher, J. D. & Nash, J. D. 2010 Structure and dynamics of the Columbia River tidal plume front. J. Geophys. Res.-Oceans 115, C00B12.10.1029/2009JC006066
Klemp, J. B., Rotunno, R. & Skamarock, W. C. 1997 On the propagation of internal bores. J. Fluid Mech. 331, 81106.10.1017/S0022112096003710
Lawrence, G. 1993 The hydraulics of steady two-layer flow over a fixed obstacle. J. Fluid Mech. 254, 605633.10.1017/S0022112093002277
Maxworthy, T., Leilich, J., Simpson, J. E. & Meiburg, E. H. 2002 The propagation of a gravity current into a linearly stratified fluid. J. Fluid Mech. 453, 371394.10.1017/S0022112001007054
Nash, J. D. & Moum, J. M. 2005 River plumes as a source of large-amplitude internal waves in the coastal ocean. Nature 437, 400403.10.1038/nature03936
Nasr-Azadani, M. M., Hall, B. & Meiburg, E. 2013 Polydisperse turbidity currents propagating over complex topography: comparison of experimental and depth-resolved simulation results. Comput. Geosci. 53, 141153.10.1016/j.cageo.2011.08.030
Nasr-Azadani, M. M. & Meiburg, E. 2011 TURBINS: an immersed boundary, Navier–Stokes code for simulation of gravity and turbidity currents interacting with complex topographies. J. Comput. Fluids 45 (1), 1428.10.1016/j.compfluid.2010.11.023
Rottman, J. W. & Simpson, J. E. 1983 Gravity currents produced by instantaneous releases of a heavy fluid in a rectangular channel. J. Fluid Mech. 135, 95110.10.1017/S0022112083002979
Rottman, J. W. & Simpson, J. E. 1989 The formation of internal bores in the atmosphere: a laboratory model. Q. J. R. Meteorol. Soc. 115, 941963.10.1002/qj.49711548809
Shin, J. O., Dalziel, S. B. & Linden, P. F. 2004 Gravity currents produced by lock exchange. J. Fluid Mech. 521, 134.10.1017/S002211200400165X
Tan, A. W., Nobes, D. S., Fleck, B. A. & Flynn, M. R. 2010 Gravity currents in two-layer stratified media. Environ. Fluid Mech. 11 (2), 203223.10.1007/s10652-010-9174-z
White, B. L. & Helfrich, K. R. 2012 A general description of a gravity current front propagating in a two-layer stratified fluid. J. Fluid Mech. 711, 545575.10.1017/jfm.2012.409
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Gravity currents propagating into two-layer stratified fluids: vorticity-based models

  • M. A. Khodkar (a1), M. M. Nasr-Azadani (a1) and E. Meiburg (a1)


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