轴对称体大角度斜出水的非线性摄动解

本文处理的是轴对称体大角度斜出水三元非线性问题,以出水角的余角α为小参数进行摄动展开,化为二维非线性问题求解.给出了零阶、一阶和二阶解的积分形式.其中零阶解对应于轴对称体垂直出水的情况,仍是非线性的.数值结果给出了不同Froude数、物体不同长细比情况下各阶自由面形状及各阶力的变化过程.

Perturbation Solution to the Nonlinear Problem of Oblique Water Exit of an Axisymmetric Body with a Large Exit-Angle

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 a 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 a 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.