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Front dynamics of supercritical non‐Boussinesq gravity currents
Author(s) -
Ancey C.,
Cochard S.,
Wiederseiner S.,
Rentschler M.
Publication year - 2006
Publication title -
water resources research
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.863
H-Index - 217
eISSN - 1944-7973
pISSN - 0043-1397
DOI - 10.1029/2005wr004593
Subject(s) - gravity current , mechanics , geology , wedge (geometry) , current (fluid) , boussinesq approximation (buoyancy) , front (military) , similarity solution , shallow water equations , boundary current , fluid dynamics , geometry , boundary value problem , geophysical fluid dynamics , boundary layer , physics , mathematical analysis , mathematics , meteorology , ocean current , internal wave , oceanography , natural convection , convection , climatology , rayleigh number
In this paper, we seek similarity solutions to the shallow water (Saint‐Venant) equations for describing the motion of a non‐Boussinesq, gravity‐driven current in an inertial regime. The current is supplied in fluid by a source placed at the inlet of a horizontal plane. Gratton and Vigo (1994) found similarity solutions to the Saint‐Venant equations when a Benjamin‐like boundary condition was imposed at the front (i.e., nonzero flow depth); the Benjamin condition represents the resisting effect of the ambient fluid for a Boussinesq current (i.e., a small‐density mismatch between the current and the surrounding fluid). In contrast, for non‐Boussinesq currents the flow depth is expected to be zero at the front in absence of friction. In this paper, we show that the Saint‐Venant equations also admit similarity solutions in the case of non‐Boussinesq regimes provided that there is no shear in the vertical profile of the streamwise velocity field. In that case, the front takes the form of an acute wedge with a straight free boundary and is separated from the body by a bore.