Current Depth Refraction using Finite Elements

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Abstract
A computational model is presented for the steady state prediction of currents, waves, and sea surface elevations in a coastal region outside the surf zone. Irrotational flow of surface gravity waves on large-scale steady currents over a gently sloping sea bed is considered. A second order Stokian approach is used, and all dynamic quantities are integrated over depth and averaged over time, in that order. The flow equations and the boundary conditions are presented. A method is developed for the solution of the non-linear steady model by introducing a sequence of two-level calculations, viz. a ‘wave level’ and a ‘current level’. The variables are split on the two levels. The wave field is found, using that the flux of wave action is constant between adjacent wave rays. The current field and the mean sea surface elevation are determined using a Galerkin finite element method. The current field is approximated by triangular elements with linear interpolation functions, and the mean sea surface elevation is approximated by a triangular element with quadratic (parabolic) interpolation functions. A quasi-twodimensional test solution is tabulated.

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