Boussinesq-type equations with second order dispersion are derived for an arbitrary distribution of vorticity. The governing equations have the velocity at an arbitrary depth as a dependent variable and terms involving vorticity are kept as integrals. Linear dispersive properties are shown to be accurate to the order of dispersion when compared to the exact solution. Current input conditions (from a large scale hydrodynamic model) and the scheme for the numerical model are obtained in order to later test model results against measurements from an experiment in a wave flume for the case of waves propagating against a vertically sheared current.
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