Generation of Waves of Small Amplitude by an Obstacle Placed Beneath the Free Surface of Running Stream of Infinite Depth

Abstract

The study, under the assumption of linearisation, concerns two-dimensional, irrotational and steady motion. The obstacles are those given by the distribution of singularities such as sources, sinks and doublets. The interesting part of the investigation shows that a source and sink combination moving with velocity U and placed at a distance 2πU²n⁄g apart, n being an integer, would not produce any wave motion. The distance is nothing but the wavelength of the sinusoidal waves travelling with speed U relative to still water. The physical consequence is that obstacles given by such distribution of sources and sinks would not experience any resistance due to the wave formation. Similar results were observed in the author’s earlier paper where studies concerned the motion in the case of a stream of finite depth.