Shallow water dynamics on linear shear flows and plane beaches

Long waves in shallow water propagating over a background shear flow towards a sloping beach are being investigated. The classical shallow-water equations are extended to incorporate both a background shear flow and a linear beach profile, resulting in a non-reducible hyperbolic system. Nevertheless...

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Bibliographic Details
Published in:Physics of fluids (1994) 2017-07, Vol.29 (7)
Main Authors: Bjørnestad, Maria, Kalisch, Henrik
Format: Article
Language:English
Subjects:
Beaches
Fluid dynamics
Hyperbolic systems
Linear equations
Physics
Shallow water equations
Shear flow
Wave propagation
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Summary:Long waves in shallow water propagating over a background shear flow towards a sloping beach are being investigated. The classical shallow-water equations are extended to incorporate both a background shear flow and a linear beach profile, resulting in a non-reducible hyperbolic system. Nevertheless, it is shown how several changes of variables based on the hodograph transform may be used to transform the system into a linear equation which may be solved exactly using the method of separation of variables. This method can be used to investigate the run-up of a long wave on a planar beach including the development of the waterline.
ISSN:1070-6631
1089-7666
DOI:10.1063/1.4994593