Variational water-wave model with accurate dispersion and vertical vorticity

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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.
Item Type:Article
Copyright:© 2010 Springer
Faculty:
Electrical Engineering, Mathematics and Computer Science (EEMCS)
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Link to this item:http://purl.utwente.nl/publications/75745
Official URL:http://dx.doi.org/10.1007/s10665-009-9346-3
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