Unsteady Three-Dimensional Surface Theory with the Free Surface Effect: Supercritical Case

摘要

The unsteady linearized theory in the supercritical case is solved by the integral equation method. The Kernel originating in the potential of the Havelock source is expressed as a Fourier series with respect to the azimuth angle, the coefficients of which are simple integrals. It is shown that convergence disappears on the free-surface downstream, behind the integration point. An asymptotic approximation of the remainder is given. This provides a way of finding the singularity. The integral equation yielding the local lift coefficient is solved by a collocation method similar to that of Multhopp. Numerical results of horizontal and vertical vibrating plates moving horizontally are given.