Exact Solution of the Wave-Resistance Problem for a Submerged Cylinder. II. The Non-linear Problem

Abstract

. We study the problem of wave resistance for a “slender” cylinder submerged in a heavy fluid of finite depth with the cylinder moving at uniform supercritical speed in the direction orthogonal to its generators. We look for a divergence‐free, irrotational flow; the boundary of the region occupied by the fluid (consisting of the free surface, the bottom and the obstacle profile) is assumed to belong to streamlines and the Bernoulli condition is taken on the free surface. The problem is transformed, via the hodograph map, into a problem set in a strip with a cut. By using a “hard” version of the inverse function theorem and by taking account of the results obtained in Part I (which we recall here), we prove the existence of a complex velocity function satisfying all the requirements of the problem. In particular, this function is continuous up to the surface of the obstacle, and the only possible singularities appear at the end‐points where the boundary is not smooth. Moreover, two stagnation points appear near to the extremities of the submerged body.