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Title: Generation of solitary waves by transcritical flow over a step
Authors: Grimshaw, Roger H.J.
Zhang, D.H.
Chow, K.W.
Issue Date: 2007
Abstract: 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.
Description: This is a pre-print.
URI: https://dspace.lboro.ac.uk/2134/2612
Appears in Collections:Pre-prints (Maths)

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