| Abstract: |
| 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. |
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