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

The single integral part of the wave-resistance Green function is cons idered 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 complement ary region away from the singular axis an improvement of Bessho's (196 4) convergent series is also obtained. Numerically, both expressions a long with previous results guarantee fast and accurate evaluations of the single integral within two wavelengths downstream of the source. F or larger distances downstream, the result of Ursell (1988) is shown t o be still valid within bounded distances of the singular axis. Hence the single integral can be evaluated analytically or numerically in a whole neighborhood of its singular axis.