EEMCS

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Official URL: http://www.math.utwente.nl/publications

Abstract

We describe a new water wave model which is variational, 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 (or circulation). We show that the potential flow water wave equations and the shallow-water equations are recovered in the relevant limits, and provide approximate shock relations for the model which can be used in numerical schemes to model breaking waves.

Available Versions of this Item

• A water wave model with horizontal circulation and accurate dispersion (deposited 27 March 2009)
  [Currently Displayed]
  • Variational water-wave model with accurate dispersion and vertical vorticity (deposited 19 January 2011)

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