Wave Breaking and the Generation of Undular Bores in an Integrable Shallow Water System
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.
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Document Type: Research Article
Affiliations: Coventry University Loughborough University Russian Academy of Sciences
Publication date: May 1, 2005