Variational water-wave model with accurate dispersion and vertical vorticity (2009)

First Author: Cotter C
Attributed to:  Network: Wave-flow interactions funded by EPSRC


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 modelling 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. © 2009 The Author(s).

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Type: Journal Article/Review

Volume: 67

Parent Publication: Journal of Engineering Mathematics

Issue: 1-2