Modified shallow water equations which admit the propagation of discontinuous waves over a dry bed |
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Authors: | V V Ostapenko |
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Institution: | (1) Lavrent’ev Institute of Hydrodynamics, Siberian Division, Russian Academy of Sciences, Novosibirsk, 630090 |
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Abstract: | A method for modeling the propagation of discontinuous waves over a dry bed using the first approximation of shallow water
theory is proposed. The method is based on a modified conservation law of total momentum that takes into account the concentrated
momentum losses due to the formation of local turbulent vortex structures in the fluid surface layer at a discontinuous-wave
front. A quantitative estimate of these losses is obtained by deriving the shallow water equations from the Navier-Stokes
equations with allowance for viscosity, which has a rapidly increasing effect in the turbulent flow regions described by discontinuous
waves. The stability of the discontinuous waves admitted by the modified system of conservation laws of shallow water theory
is examined. As an example, a comparative analysis is performed of the solutions of the dam-break problem obtained for the
classical and modified shallow water models.
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Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 48, No. 6, pp. 22–43, November–December, 2007 |
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Keywords: | shallow water equations discontinuous waves modified total-momentum conservation law dam-break problem |
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