The effect of wave breaking on wave spectrum in water of finite depth

An approximate method is devised to compute the energy-containing portion of the spectrum of waves in water of finite depth, taking into account the effect of wave breaking. It is assumed that there exists a linear and Gaussian ideal wave train whose spectrum is first calculated using the wave energy flux balance equation without considering wave breaking. The Miche wave-breaking criterion for waves in water of finite depth is then applied to limit the wave elevation and establish an expression for the breaking wave elevation in terms of the elevation and elevation's second time derivative of the ideal waves. Simple expressions for the mean value, the mean square value, and the spectrum of the breaking waves are then obtained, and numerical results are presented graphically.