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IDEAL PLANAR FLUID FLOW OVER A SUBMERGED OBSTACLE: REVIEW AND EXTENSION

Published online by Cambridge University Press:  25 October 2021

LAWRENCE K. FORBES*
Affiliation:
School of Natural Sciences, University of Tasmania, HobartTAS 7001, Australia; e-mail: [email protected].
STEPHEN J. WALTERS
Affiliation:
School of Natural Sciences, University of Tasmania, HobartTAS 7001, Australia; e-mail: [email protected].
GRAEME C. HOCKING
Affiliation:
Mathematics & Statistics, Murdoch University, MurdochWA6150, Australia; e-mail: [email protected].

Abstract

A classical problem in free-surface hydrodynamics concerns flow in a channel, when an obstacle is placed on the bottom. Steady-state flows exist and may adopt one of three possible configurations, depending on the fluid speed and the obstacle height; perhaps the best known has an apparently uniform flow upstream of the obstacle, followed by a semiinfinite train of downstream gravity waves. When time-dependent behaviour is taken into account, it is found that conditions upstream of the obstacle are more complicated, however, and can include a train of upstream-advancing solitons. This paper gives a critical overview of these concepts, and also presents a new semianalytical spectral method for the numerical description of unsteady behaviour.

Type
Research Article
Copyright
© The Author(s), 2021. Published by Cambridge University Press on behalf of Australian Mathematical Publishing Association Inc.

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Footnotes

*

This is a contribution to the series of invited papers by past ANZIAM medallists (Editorial, Issue 52(1)). Lawrence K. Forbes was awarded the 2020 ANZIAM medal.

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