Consistent nonlinear mild-slope equation models for wide-angle water waves transformation

Parabolic equation models are constrained by their fixed principal propagation direction, limiting wave fields to small angles. To overcome this limitation, this study proposes two modeling approaches based on a new dispersive nonlinear mild-slope equation model that enable wave propagation across a broad range of directions. The first approach integrates a minimax approximation for linear terms with nonlinear summation under a specialized ordering system, resulting in a higher-order parabolic model. The second approach extends the parabolic equation by incorporating alongshore wavenumber components through Fourier decomposition and modifies the inverse Fourier transform terms with additional forcing to account for interactions between lateral bottom variations and the wave field. We validate the proposed models through comparisons against laboratory experiments involving wave focusing by a topographical lens, an elliptic shoal, and a circular shoal. Overall, the proposed models enhance the prediction of wave propagation under a variety of conditions.