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Analytical and numerical results for flow and shock formation in two-layer gravity currents

Published online by Cambridge University Press:  17 February 2009

P. J. Montgomery  and
T. B. Moodie
P. J. Montgomery
Affiliation:
Applied Mathematics Institute, Department of Mathematical Sciences, University of Alberta, Edmonton, Alberta, Canada
T. B. Moodie
Affiliation:
Applied Mathematics Institute, Department of Mathematical Sciences, University of Alberta, Edmonton, Alberta, Canada
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Abstract

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Many gravity driven flows can be modelled as homogeneous layers of inviscid fluid with a hydrostatic pressure distribution. There are examples throughout oceanography, meteorology, and many engineering applications, yet there are areas which require further investigation. Analytical and numerical results for two-layer shallow-water formulations of time dependent gravity currents travelling in one spatial dimension are presented. Model equations for three physical limits are developed from the hydraulic equations, and numerical solutions are produced using a relaxation scheme for conservation laws developed recently by S. Jin and X. Zin [6]. Hyperbolicity of the model equations is examined in conjunction with the stability Froude number, and shock formation at the interface of the two layers is investigated using the theory of weakly nonlinear hyperbolic waves.

Type
Research Article
Information
The ANZIAM Journal , Volume 40 , Issue 1 , July 1998 , pp. 35 - 58
Copyright
Copyright © Australian Mathematical Society 1998

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