Perturbation solution to the nonlinear problem of oblique water exit of an axisymmetric body with a large exit-angle

Abstract

In this paper, a nonlinear, unsteady 3-D free surface problem of the oblique water exit of an axisymmetric body with a large water exit-angle was investigated by means of the perturbation method in which the complementary angle α of the water exit angle was chosen as a small parameter. The original 3-D problem was solved by expanding it into a power series of α and reduced to a number of 2-D problems. The integral expressions for the first three order solutions were given in terms of the complete elliptic functions of the first and second kinds. The zeroth-order solution didn't turn out to be a linear problem as usual but a nonlinear one corresponding to the vertical water exit for the same body. Computational results were presented for the free surface shapes and the forces exerted up to the second order during the oblique water exit of a series of ellipsoids with various ratios of length to diameter at different Froude numbers.