A comparison of linear and nonlinear computations of waves made by slender submerged bodies

摘要

Potential flow about a slender spheroid beneath a free surface is considered in order to determine the ability of thin-ship theory to reproduce the free-surface elevation accurately. A fully nonlinear code involving interior Rankine sources is used, enabling comparisons between exact('Neumann-Stokes')outputs, outputs with exact body condition but linearised free-surface conditions('Neumann-Kelvin'), and a consistent thin-ship ap- proximation('Michell-Kelvin'). In general, these computations agree to within a few percent, except when the body is so close to the free surface that the nonlinear computation suggests that breaking is imminent at one point above the body, and even then thin-ship theory still compares well except very near to that isolated point.