Wave Breaking and the Generation of Undular Bores in an Integrable Shallow Water System

El, Gennady, Grimshaw, R. H. J. and Kamchatnov, A. M. (2005) Wave Breaking and the Generation of Undular Bores in an Integrable Shallow Water System. Studies in Applied Mathematics, 114 (4). pp. 395-411. ISSN 0022-2526

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Official URL: https://doi.org/10.1111/j.0022-2526.2005.01560.x

Abstract

The generation of an undular bore in the vicinity of a wave‐breaking point is considered for the integrable Kaup–Boussinesq (KB) shallow water system. In the framework of the Whitham modulation theory, an analytic solution of the Gurevich–Pitaevskii type of problem for a generic “cubic” breaking regime is obtained using a generalized hodograph transform, and a further reduction to a linear Euler–Poisson equation. The motion of the undular bore edges is investigated in detail.

Item Type: Article
Subjects: F300 Physics
Department: Faculties > Engineering and Environment > Mathematics, Physics and Electrical Engineering
Depositing User: John Coen
Date Deposited: 16 Apr 2020 11:30
Last Modified: 16 Apr 2020 11:30
URI: http://nrl.northumbria.ac.uk/id/eprint/42802

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