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On the scattering of short surface waves by a finite dock

1968; Cambridge University Press; Volume: 64; Issue: 4 Linguagem: Inglês

10.1017/s0305004100043875

1469-8064

F. G. Leppington,

Electromagnetic Scattering and Analysis

Abstract A sinusoidal travelling wave-train is at normal incidence upon a two-dimensional finite dock fixed on the surface of a body of water of great depth, and the problem investigated herein is that of finding the limiting form of the induced velocity potential for short waves. Of particular interest are the amplitudes of the wave-trains reflected and transmitted towards infinity by such an obstacle. The potential is expressed as a sum of coupled semi-infinite dock potentials, whence results a pair of weakly coupled integral equations for the solution. This formulation of the problem is shown to be amenable to an approximate solution for large wave-numbers, and the first few terms are derived in formal expansions for the reflection and transmission coefficients.