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

Part of: Incompressible inviscid fluids Basic methods in fluid mechanics

Published online by Cambridge University Press:  25 October 2021

LAWRENCE K. FORBES Open the ORCID record for LAWRENCE K. FORBES [Opens in a new window] ,
STEPHEN J. WALTERS Open the ORCID record for STEPHEN J. WALTERS [Opens in a new window]  and
GRAEME C. HOCKING Open the ORCID record for GRAEME C. HOCKING [Opens in a new window]
LAWRENCE K. FORBES*
Affiliation:
School of Natural Sciences, University of Tasmania, HobartTAS 7001, Australia; e-mail: stephen.walters@utas.edu.au.
STEPHEN J. WALTERS
Affiliation:
School of Natural Sciences, University of Tasmania, HobartTAS 7001, Australia; e-mail: stephen.walters@utas.edu.au.
GRAEME C. HOCKING
Affiliation:
Mathematics & Statistics, Murdoch University, MurdochWA6150, Australia; e-mail: g.hocking@murdoch.edu.au.
*
e-mail: larry.forbes@utas.edu.au
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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.

Keywords

free-surface flowbottom topographysurface wavesupstream solitonstranscritical flow

MSC classification

Primary: 76B07: Free-surface potential flows
Secondary: 76B15: Water waves, gravity waves; dispersion and scattering, nonlinear interaction 76M22: Spectral methods
Type
Research Article
Information
The ANZIAM Journal , Volume 63 , Issue 4 , October 2021 , pp. 377 - 419
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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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