NONLINEAR FREE SURFACE WAVES DUE TO A SHIP MOVING NEAR THE CRITICAL SPEED IN A SHALLOW WATER

Abstract

This paper describes two methods of solution to the nonlinear free-surface waves generated by a ship moving steadily with the trancritical speed in a shallow water. As a mathematical model, a nonlinear initial/boundary-value problem is formulated within the scope of potential theory. One method is based on matched asymptotic expansion techniques and the Kadomtsev - Petviashvili equation is obtained as the leading-order solution for a slender ship. The other one is based on classical Hamilton's principle and the finite element method is implemented for numerical calculations. In order to examine the effect of the tank width on the wave field and resulting hydrodynamic for the Series 60 ship model with Cb = 0.8 by these two different methods. For wider tanks, the pressure distribution on the free surface, equivalent to the ship model, is treated. The results obtained by two different methods are compared each other and with experimental measurements available. Also discussed are the appearance of stem waves at the tank wall and the evolution of the crestline of diverging waves in the wide tank.