A simple model for random wave bottom friction and dissipation

Based on the spectral eddy viscosity model of bottom boundary layers, the spectral representation of bottom friction and dissipation for irregular waves is reduced to an equivalent monochromatic wave representation. The representative wave amplitude and frequency are chosen so that the bottom velocity and bottom shear stress variances of the equivalent wave model are identical to those of the spectral model. Moreover, these variances have to satisfy the same relationship as those of a monochromatic wave with the same frequency. According to the wave bottom boundary layer theory, the ratio between bottom stress spectrum and bottom velocity spectrum has a frequency dependence of ω^q, where the exponent q is a positive constant. The representative wave frequency and direction are obtained based on this power law, whereas in previous studies they were derived using a Taylor expansion of the ratio about a particular frequency or were proposed heuristically. Previous equivalent wave theories are therefore valid only for narrowbanded wave spectra. The present theory, however, is applicable to a wide variety of wave spectra including broadbanded and multimodal spectra.