On the Nonlinear Calculation of the Steady Bow Wave of a Ship

A nonlinear local analysis of the steady potential flow at a ship bow and stern, and more generally at any point along a ship waterline, is presented. The hull boundary condition and the nonlinear kinematic and dynamic free-surface boundary conditions are satisfied exactly, at the actual position of the free surface, in this analysis. The bow-flow analysis shows that the free surface at a ship bow is tangent to the stem.This theoretical result appears to agree with existing experimental measurements of the steady bow waves of the Wigley hull and the Series 60 CB=0.60 model. Furthermore, simple analytical expressions defining the fluid velocity at the bow and the stern, and at any other point along the ship waterline, in terms of the elevation of the free surface at the corresponding point are also obtained. These analytical expressions and the available experimental measurements of the wave profiles along the Wigley hull show that the velocity of the flow disturbance due to this hull is fairly small compared to the hull speed everywhere along the waterline except in very small regions around the bow and the stern, where the total fluid velocity is nearly equal to the hull speed in magnitude but directed vertically. Nonlinearities therefore appear to be quite important, although only in extremely small regions surrounding a ship bow and stern. A successful nonlinear method of calculation must then be able to represent the very rapid variation in the direction of the fluid velocity occurring within small regions around a ship bow and stern. In particular, a sufficiently fine discretization is required in these regions.