The Formulae for a Pulsating Source in a Fluid with a Free Surface and the Methods of Their Numerical Evalutions

Abstract

Expressions of velocity potentials for two dimensional pulsating sources, the so-called Green functions, in a water of finite depth are obtained from a new standpoint, when (1) the water is horizontally unbounded and permits wave radiation, and when (2) the water is bounded by vertical walls and does not permit wave radiation. A general expression of the velocity potential for water motions in a rectangular tank is obtained by using the results of the case (2). Methods of the numerical calculation for the Green function in the case of (1) are discussed.