Numerical Modeling of Wave-Current Interactions using Extended Boussinesq Equations

A non-linear model for a wave field coexisting with currents has been developed to investigate the influence of currents on waves propagation. A new form of dispersion relation is derived by extending for the wave-current coexistence field based on special type of depth-integrated Boussinesq equations (Madsen et al. 1991, 1992). The third spatial derivative of surface fluctuation, ∂3S/∂x3 is discretized in terms of surface curvature, ∂2s/∂x2 and subsequently is solved by the cubic spline method. The model is applied to wave propagation in a domain of variable depths with preexisting adverse and following currents of different magnitudes.