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Edge waves in the presence of an irregular coastline Fuller, John David

Abstract

Small irregularities in an otherwise straight coast produce certain effects on long waves on a continental shelf. Studied here are the generation of trapped edge waves when a wave from the deep ocean reaches the irregular coast, and alterations in the propagation characteristics of trapped edge waves, due to the irregularities. The continental shelf is modeled by a single, flat-step model, and the irregularities in the coast are represented as a stationary random function of distance along the coast, with zero mean. The wave equations are thus stochastic differential equations, with the randomness introduced through the boundary condition at the coast. Calculations are made for the power flux into trapped edge waves and a continuous spectrum of leaky modes, both generated by the scattering of an incident wave. Numerical results for a section of the northeast Japanese coast show that there is less power transferred to the forward traveling trapped wave than the backward, and less power to the scattered leaky modes than to either the forward or backward trapped modes. Other calculations show that there is attenuation of a trapped edge wave, due to scattering, there is a "tilting" of the wave towards the coast, and in the case of the same Japanese coast, the longshore components of the phase and group velocities are slightly less than in the case of a straight coast. The results are valid for wave periods much shorter than the period associated with the Coriolis parameter of, and for wavelengths much greater than the average size of the coastal irregularities.

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