ANZIAM J. 47(EMAC2005) pp.C373--C387, 2006.

Moving boundary shallow water flow above parabolic bottom topography

Joe Sampson

Alan Easton

Manmohan Singh
(received 16 October 2005; revised 18 August 2006)

Abstract

Exact solutions of the two dimensional nonlinear shallow water wave equations for flow involving linear bottom friction and with no forcing are found for flow above parabolic bottom topography. These solutions also involve moving shorelines. The motion decays over time. In the solution of the three simultaneous nonlinear partial differential shallow water wave equations it is assumed that the velocity is a function of time only and along one axis. This assumption reduces the three simultaneous nonlinear partial differential equations to two simultaneous linear ordinary differential equations . The solutions found are useful for testing numerical solutions of the nonlinear shallow water wave equations which include bottom friction and whose flow involves moving shorelines.

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Authors

Joe Sampson
Mathematics Discipline, Faculty of Engineering and Industrial Sciences, Swinburne University of Technology, Melbourne, Australia. mailto:jsampson@swin.edu.au
Alan Easton
Mathematics, Statistics and Computer Science Discipline, School of Natural and Physical Sciences,University of Papua New Guinea, Port Moresby, Papua New Guinea. mailto:alan.easton@upng.ac.pg; Mathematics Discipline, Faculty of Engineering and Industrial Sciences, Swinburne University of Technology, Melbourne, Australia.
Manmohan Singh
Mathematics Discipline, Faculty of Engineering and Industrial Sciences, Swinburne University of Technology, Melbourne, Australia. mailto:msingh@swin.edu.au

Published October 16, 2006. ISSN 1446-8735

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Copyright Austral. Mathematical Soc.; prepared October 16, 2006, from Sampson.tex with anziamje.sty (v2.4)