Ideal planar fluid flow over a submerged obstacle: Review and extension

Authors

DOI:

https://doi.org/10.21914/anziamj.v63.16571

Keywords:

free-surface flow, bottom topography, surface waves, upstream solitons, transcritical flow

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.

doi:10.1017/S1446181121000341

Author Biographies

Larry K. Forbes, University of Tasmania

School of Natural Sciences, University of Tasmania, Hobart TAS 7001, Australia.

Stephen J. Walters, University of Tasmania

School of Natural Sciences, University of Tasmania, Hobart TAS 7001, Australia.

Graeme C. Hocking, Murdoch University

Mathematics & Statistics, Murdoch University, Murdoch WA 6150, Australia.

Published

2021-12-31

Issue

Section

Articles for Printed Issues