Nonlinear Ship Waves at Low Froude Number

Abstract

The wave pattern of a thick ship-like object with finite bow and stern angles 0 <β<π/2 is studied. The completely blunt form p = π/2 is excluded. It turns out that the wave pattern is strongly influenced by the nonlinear terms at the free surface. The wave pattern is determined by means of the ray method. The rays are generated mainly at the bow and the stern. A crucial step is the determination of the so-called excitation coefficients. They are constructed by means of an asymptotic evaluation of a distribution of "local"sources at the free surface. It is shown that for small angles β<< 1 the excitation coefficients are the same as the ones obtained by means of an asymptotic expansion for small values of the Froude number of the results of Michell's thin-ship theory. For increasing values of β, the excitation coefficients change asymptotically. The theory herein shows a continuous dependence, nevertheless. Similar changes are observed in the far-field wave pattern.