Transcritical flow past an obstacle

Roger Grimshaw

Abstract


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.

doi:10.1017/S1446181111000599

Keywords


solitary waves; transcritical flow; undular bore



DOI: http://dx.doi.org/10.21914/anziamj.v52i0.4145



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ANZIAM Journal, ISSN 1446-8735, copyright Australian Mathematical Society.