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

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 approximation (`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. The thin-ship theory has also been implemented in a separate general-purpose code using Havelock sources, and detailed free-surface contours computed by this linear method are shown for spheroids that are too close to the surface for the nonlinear code to converge.