Radiation and Scattering of Transient Gravity Waves by Vertical Plates

Some initial value problems regarding the radiation and scattering of gravity waves by thin vertical plates in an infinitely deep ocean are studied. The general solution is obtained by transforming the boundary-value problem to one of the Riemann-Hilbert type. Explicit investigations are made for the large time behaviour of the free surface elevation for the case of a rolling plate, and for the Cauchy-Poisson problems in the presence of a stationary plate. By taking the limit as t ↑ ∞, the steady state solution is derived for a harmonic point pressure acting on the free surface near a vertical barrier.