Analytical models of sub-supercritical ship hydrodynamic pressure field with the dispersive effect

Based on the potential flow theory, taking the dispersive effect into account, a shallow-water wave equation which satisfies Laplace equation, free surface and seabed boundary conditions is established. According to the slender ship assumption and the continuous matched condition on the interface of inner and outer regions, the mathematical problems of sub-supercritical mixed flow are analytically solved by using the Fourier integral transform method, meanwhile, the analytical models of sub-supercritical ship hydrodynamic pressure field (SHPF) in dredged channel are derived, and those of open water, rectangular canal and stepped canal can also be obtained by further simplifying or adopting similar method. The distribution characteristics of sub-supercritical SHPF in dredged channel are acquired, and the effects of transverse distance, inner or outer water depth, width, and depth Froude number on SHPF are analyzed. The SHPF analytical models with the dispersive effect are verified by comparing with the corresponding experimental results.