Numerical calculation and analysis of nonlinear pressure field induced by ship motion at subcritical speed in shallow water

Based on the shallow water wave potential flow theory and the slender ship assumption, a mathematical model for pressure field considering nonlinear effects and the dispersive effects induced by ship motion at subcritical speed in shallow water was established. The pressure field was calculated by using finite difference method. In order to overcome the instability of the nonlinear equation, artificial viscous effects were added in radiation condition and ship boundary conditions. Computation results were compared with experimental results, by which both the mathematical model and calculation method were validated. The nonlinear effects on the ship hydrodynamic pressure field in different width of channel, different depth water and Froude numbers at different depth were analyzed. The results show that the nonlinear effects on the hydrodynamic pressure field became greater, with the width and the depth getting narrow and shallow respectively. If a ship is moving at near-critical speed, then the nonlinear effects must be considered in any channel.