TWO-DIMENSIONAL WAVES GENERATED BY A SURFACE PRESSURE DISTURBANCE OVER A SLOPING BEACH.
NEW YORK UNIV NY COURANT INST OF MATHEMATICAL SCIENCES
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Two-dimensional water waves generated by a prescribed pressure disturbance on the equilibrium surface of a uniformly sloping beach are studied by means of the Laplace transform technique applied to the equations of the linear theory. Both transient and steady problems are considered, and in each case the problem reduces to solving an inhomogeneous equation The arbitrary constants in the solutions of the transient and the steady-state problem are determined by respectively imposing a boundedness condition and a radiation condition at infinity. The example of an oscillatory point pressure acting on the equilibrium surface of a 45 degree beach is worked out in detail. It seems easier to derive the steady-state solution from the transient problem than to find it directly. Author