BREAKING WAVE SPECTRUM IN WATER OF FINITE DEPTH IN THE PRESENCE OF CURRENT.

This report presents an approximate method to compute the mean value, the mean-square value, and the spectrum of waves in water of finite depth taking into account the effect of wave breaking in the presence of current. It is assumed that there exists a linear and Gaussian ideal wave train whose spectrum is first obtained using the wave energy flux balance equation without considering wave breaking. The Miche wave breaking criterion for waves in finite water depth is used to limit the wave elevation and establish an expression for the breaking wave elevation in terms of the elevation and its mean-square value and the spectrum are obtained. These results are applied to the case in which a deepwater unidirectional wave train, propagating normally toward a straight shoreline over gently varying sea bottom of parallel and straight contours, encounters an adverse steady current whose velocity is assumed to be uniformly distributed with depth. Numerical results are obtained and presented in graphic form.