Similarity relations of wind waves in finite depth

Abstract

Three formulations for the rear face of a growing wind-sea spectrum in finite depth based on Phillips (1958), Toba (1972) and Donelan et al. (1985) are tested using spectral measurements from Lake St. Clair. Assuming spectral similarity in wave number space relations between the energy, equilibrium parameters and peak wave number are derived. Using a regression analysis, relations are obtained from the data and compared to the theoretical relations. Results indicate that the formulation based on a high-frequency /-4 tail (Toba, 1972 andDonelan et al., 1985) is better than the Phillips /-5 high-frequency tail. Based on the effective fetch formulation, wave propagation directions are calculated. Relations between the spectral parameters, growth-stage variables and fetch are also determined from the data. The relations indicate a weak dependence of the spectral parameters on depth. Various source terms in the energy balance equation for wave growth in finite depth water are estimated for two cases of wave evolution. The relative importance of wind input, bottom dissipation, white-capping dissipation and nonlinear transfer in the evolution of the spectra is analyzed.