On the short-wave asymptotic motion due to a cylinder heaving on water of finite depth. II

This paper continues the investigation into the short-wave asymptotic motion due to a cylinder heaving on water of finite constant depth, and we now present a rigorous method for the special case of a half-immersed circular cylinder. The aim is to justify, in one particular case, those assumptions made in a previous paper giving a non-rigorous method for an arbitrary smooth cylinder which intersects the free surface normally, concerning the asymptotic values on the cylinder of the two related auxiliary potentials which were introduced to enable an evaluation of the coefficients describing wave-making and virtual mass. This is done by constructing an integral equation of the second kind whose kernel is small and deducing the leading term in the iteration solution. The method is an extension of the method for infinite depth and it is found that there is a simple relationship between the kernels. In conclusion, computations for these asymptotic results are presented and compared with the trend of known non-asymptotic results.