EVALUATION OF THE WAVE-RESISTANCE GREEN FUNCTION: PART 3 - THE SINGLE INTEGRAL NEAR THE SINGULAR AXIS

The single integral part of the wave-resistance Green function is considered near its singular axis. Completing the work of Ursell (1988) an asymptotic expansion is proposed that is valid in the vicinity of the source when this lies on or near the free surface. For the complementary region away from the singular axis an improvement of Bessho's (1964) convergent series is also obtained. Numerically, both expressions along with previous results guarantee fast and accurate evaluations of the single integral within two wavelengths downstream of the source. For larger distances downstream, the result of Ursell (1988) is shown to be still valid within bounded distances of the singular axis. Hence the single integral can be evaluated analytically or numerically in a whole neighbourhood of its singular axis.