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Models of non-Boussinesq lock-exchange flow

Published online by Cambridge University Press:  08 April 2011

R. ROTUNNO ,
J. B. KLEMP ,
G. H. BRYAN  and
D. J. MURAKI
R. ROTUNNO*
Affiliation:
National Center for Atmospheric Research, Boulder, CO 80307, USA
J. B. KLEMP
Affiliation:
National Center for Atmospheric Research, Boulder, CO 80307, USA
G. H. BRYAN
Affiliation:
National Center for Atmospheric Research, Boulder, CO 80307, USA
D. J. MURAKI
Affiliation:
Department of Mathematics, Simon Fraser University, Burnaby, BC V5A 1S6, Canada
*
†Email address for correspondence: [email protected]
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Abstract

Nearly all analytical models of lock-exchange flow are based on the shallow-water approximation. Since the latter approximation fails at the leading edges of the mutually intruding fluids of lock-exchange flow, solutions to the shallow-water equations can be obtained only through the specification of front conditions. In the present paper, analytic solutions to the shallow-water equations for non-Boussinesq lock-exchange flow are given for front conditions deriving from free-boundary arguments. Analytic solutions are also derived for other proposed front conditions – conditions which appear to the shallow-water system as forced boundary conditions. Both solutions to the shallow-water equations are compared with the numerical solutions of the Navier–Stokes equations and a mixture of successes and failures is recorded. The apparent success of some aspects of the forced solutions of the shallow-water equations, together with the fact that in a real fluid the density interface is a free boundary, shows the need for an improved theory of lock-exchange flow taking into account non-hydrostatic effects for density interfaces intersecting rigid boundaries.

JFM classification

Geophysical and Geological Flows: Gravity currents Geophysical and Geological Flows: Shallow water flows Turbulent Flows: Turbulence simulation
Type
Papers
Information
Journal of Fluid Mechanics , Volume 675 , 25 May 2011 , pp. 1 - 26
Copyright
Copyright © Cambridge University Press 2011

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