Analytical models of ship hydrodynamic pressure field with dispersive effect in super-supercritical mixed flow

According to potential flow theory and considering the dispersive effect, a shallow-water wave equation that satisfies the Laplace equation and free surface and seabed boundary conditions is established in this study. On the basis of the slender ship assumption and continuous matched conditions on the interface of a dredged channel, the mathematical problems of super-supercritical mixed flow are solved by adopting the Fourier integral transform method and the finite difference method, respectively. Meanwhile, the analytical models of super-supercritical ship hydrodynamic pressure field (SHPF) are derived, and those of the open water or rectangular canal can also be deduced by further simplification. The characteristics of super-supercritical SHPF with the dispersive effect are analyzed, and the influences of transverse distance, inner or outer depth, width, and depth Froude number on SHPF are studied. Comparisons between the calculated and experimental results show that the proposed analytical models of SHPF in this research are reasonable, effective, and accurate.