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The shallow water equations

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Summary

In this paper a set of exact nonlinear equations is derived for gravity flows. By assuming the flow to be shallow and assuming the vertical acceleration to be small these equations reduce to the classical equations for long waves in shallow water. If only shallowness is assumed a set of equations results, which admits in the steady case periodic solutions for Froude numbers smaller than 1 and laminar jumps for Froude numbers larger than 1. In the last section potential flows are discussed.

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Authors and Affiliations

  1. Mathematics Department, Northwestern University, 60201, Evanston, Illinois, USA

    M. Shinbrot

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  1. M. Shinbrot
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Additional information

Supported, in part, by the National Science Foundation (GP-6632).

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Shinbrot, M. The shallow water equations. J Eng Math 4, 293–304 (1970). https://doi.org/10.1007/BF01534977

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  • DOI: https://doi.org/10.1007/BF01534977

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