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Variational water wave model with accurate dispersion and vertical vorticity
 

Summary: Variational water wave model with accurate dispersion and
vertical vorticity
Colin Cotter1
and Onno Bokhove2
1. Department of Aeronautics, Imperial College, London, U.K.
2. Department of Mathematics, University of Twente, Enschede, The Netherlands
August 31, 2009
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 polyno-
mials 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.
1 Introduction
It is always fascinating to watch waves near the shore line. They approach the shore, steepen as the water

  

Source: Al Hanbali, Ahmad - Department of Applied Mathematics, Universiteit Twente

 

Collections: Engineering