Variational water-wave model with accurate dispersion and vertical vorticity


Cotter, Colin and Bokhove, Onno (2010) Variational water-wave model with accurate dispersion and vertical vorticity. Journal of Engineering Mathematics, 67 (1-2). pp. 33-54. ISSN 0022-0833

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Abstract:A new water-wave model has been derived which is based on variational techniques and combines a depth-averaged vertical (component of) vorticity with depth-dependent potential flow. The model facilitates the further restriction of the vertical profile of the velocity potential to n-th order polynomials or a finite-element profile with a small number of elements (say), leading to a framework for efficient modeling of the interaction of steepening and breaking waves near the shore with a large-scale horizontal flow. The equations are derived from a constrained variational formulation which leads to conservation laws for energy, mass, momentum and vertical vorticity. It is shown that the potential-flow water-wave equations and the shallow-water equations are recovered in the relevant limits. Approximate shock relations are provided, which can be used in numerical schemes to model breaking waves.
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Copyright:© 2010 Springer
Electrical Engineering, Mathematics and Computer Science (EEMCS)
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