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TRANSCRITICAL FLOW PAST AN OBSTACLE

Part of: Waves

Published online by Cambridge University Press:  20 May 2011

R. GRIMSHAW
R. GRIMSHAW*
Affiliation:
Department of Mathematical Sciences, Loughborough University, Loughborough, LE11 3TU, UK (email: [email protected])
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Abstract

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It is well known that transcritical flow past an obstacle may generate undular bores propagating away from the obstacle. This flow has been successfully modelled in the framework of the forced Korteweg–de Vries equation, where numerical simulations and asymptotic analyses have shown that the unsteady undular bores are connected by a locally steady solution over the obstacle. In this paper we present an overview of the underlying theory, together with some recent work on the case where the obstacle has a large width.

Keywords

solitary wavestranscritical flowundular bore

MSC classification

Secondary: 74J30: Nonlinear waves
Type
Research Article
Information
The ANZIAM Journal , Volume 52 , Issue 1 , July 2010 , pp. 2 - 26
Copyright
Copyright © Australian Mathematical Society 2011

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