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 steady bow waves of the Wigley hull. Simple analytical expressions defining the fluid velocity at the bow and the stern, and more generally at any point along the wave profile, in terms of the elevation of the free surface at the corresponding point are also given. These analytical expressions and the available experimental measurements of 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 wave profile 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 very small regions surrounding a ship bow and stern. A genuine 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.
Velocity measurements of a free-surface turbulent flow oversmooth and rough beds