0n Time-Reversed Velocity Potentials in the Theory of Water Waves

Abstract

If we neglect the effect of viscosity as usual in the theory of water waves, the system of water motion would be conservative and the motion would be reversible. However, thus obtained time reversed motion breaks the radiation condition at infinity, so that such motion may not be physically realizable in general but some special cases. In this paper, the author represents the time-reversed velocity potential by the ordinary potentials which suffice with the radiation condition and incident regular wave and deals with its application in the theory of water waves. Also he deals with the relation between the reverse flow velocity potential and the time reversed flow one and gets the formula corresponding to the former case which enables us to estimate the effect of self-diffraction of waves in the wave-making resistance.