On the quadratic effect of random gravity waves on a vertical boundary

Abstract

The quadratic effect of random gravity waves in the vicinity of a reflecting boundary is studied. It is shown that in a stochastic wave environment, surface wave effects proportional to the square of the wave amplitude depend upon the third-order free-surface perturbation. Expressions are derived for the quadratic frequency spectrum of the hydrodynamic pressure in the fluid domain in unidirectional and standing waves reflected off a vertical wall. Computations of the spectrum reveal the importance of the effect contributed by the third-order solution, which is found to be at least of comparable magnitude to the corresponding effect obtained from the solution of the second-order problem.