ON VELOCITY POTENTIALS DUE TO PULSATING PRESSURE DISTRIBUTIONS ON THE FREE SURFACE OF INFINITE-DEPTH WATERS AND THE RADIATION CONDITIONS FOR SECOND-ORDER DIFFRACTION PROBLEMS

In the present paper,two-and three-dimensional velocity potentials generatedby pulsating pressure distributions of infinite extent on the free surface ofinfinite-depth waters are strictly derived based on special cases of concentratedpulsating pressure.The far-field asymptotic behaviour of the potentials and theradiation conditions to be satisfied by them are discussed.It is proved in a general sense that the potentials should be composed of aforced wave component,a free wave component and a local disturbance component.Theradiation condition of the forced wave component should correspond to the far-fieldasymptotic behaviour of the pressure distribution,Hence,the formulation ofradiation conditions for the second-order diffraction potentials has theoreticallybecome clear,The radiation conditions for two-and three-dimensional problems areexplicitly given in the paper.