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Generation of solitary waves by transcritical flow over a step

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posted on 2007-01-23, 11:09 authored by Roger Grimshaw, D.H. Zhang, K.W. Chow
It is well-known that transcritical flow over a localised obstacle generates upstream and downstream nonlinear wavetrains. The flow has been successfully modeled in the framework of the forced Korteweg-de Vries equation, where numerical and asymptotic analytical solutions have shown that the upstream and downstream nonlinear wavetrains have the structure of unsteady undular bores, connected by a locally steady solution over the obstacle, which is elevated on the upstream side and depressed on the downstream side. In this paper we consider the analogous transcritical flow over a step, primarily in the context of water waves. We use numerical and asymptotic analytical solutions of the forced Korteweg-de Vries equation, together with numerical solutions of the full Euler equations, to demonstrate that a positive step generates only an upstream-propagating undular bore, and a negative step generates only a downstream-propagating undular bore.

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School

  • Science

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  • Mathematical Sciences

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2632993 bytes

Publication date

2007

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This is a pre-print.

Language

  • en

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