In the present work a new post-Boussinesq type dispersive wave propagation model is proposed. The model is based on a system of equations in terms of the free surface elevation and the depth-averaged horizontal velocities. The approach is developed for fully dispersive and weakly nonlinear irregular waves propagating over any constant water depth in two horizontal dimensions, but it can also be applied over a mildly sloping bottom with considerable accuracy. The 1D version of the model involves four terms in the momentum equation, including the classical swallow water equation terms and only one frequency dispersion term. The latter is expressed through convolution integrals, which are estimated using appropriate impulse functions. The formulation is fully explicit in space and thus no equations need to be inverted for the numerical solution. Numerical integration of a convolution integral is also required. The model is applied to simulate the propagation of regular and irregular waves using a simple explicit scheme of Finite Differences. The numerical model was evaluated with respect to waves passing over a bar as well as with linear and nonlinear wave theory.
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