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- Title
- Moving boundary shallow water flow in a region with quadratic bathymetry
- Author(s)
- Sampson, Joe; Easton, Alan; Singh, Manmohan
- Abstract
- Exact solutions of the nonlinear shallow water wave equations for forced flow involving linear bottom friction in a region with quadratic bathymetry have been found. 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 analytical model has been tested against a numerical solution with good agreement between the numerical and analytical solutions. The analytical model is useful for testing the accuracy of a moving boundary shallow water numerical model.
- Publication type
- Journal article
- Research centre
- Swinburne University of Technology. Faculty of Engineering and Industrial Sciences
- Source
- ANZIAM Journal electronic supplement, incorporating the proceedings of the 8th Biennial Engineering Mathematics and Applications Conference (EMAC 2007), Hobart, Tasmania, Australia, 02-04 July 2007, Vol. 49 (2007), pp. C666-C680
- Publication year
- 2007
- FOR Code(s)
- 010299 Applied Mathematics not elsewhere classified
- Keyword(s)
- Model equations; Nonlinear shallow water; Numerical solutions; Quadratic bathymetry; Shallow water; Shorelines
- Publisher
- Australian Mathematical Society
- ISSN
- 1446-1811
- Publisher URL
- http://anziamj.austms.org.au/ojs/index.php/ANZIAMJ/article/view/306
- Copyright
- Copyright © Australian Mathematical Society and Cambridge University Press 2008. Published version of this paper reproduced here with the kind permission of the publisher.
- Full text
- Peer reviewed
