Spectral Energy Dissipation due to Surface Wave Breaking

Abstract

Abstract A semiempirical determination of the spectral dependence of the energy dissipation due to surface wave breaking is presented and then used to propose a model for the spectral dependence of the breaking strength parameter b, defined in the O. M. Phillips’s statistical formulation of wave breaking dynamics. The determination of the spectral dissipation is based on closing the radiative transport equation for fetch-limited waves, measured in the Gulf of Tehuantepec Experiment, by using the measured evolution of the directional spectra with fetch, computations of the four-wave resonant interactions, and three models of the wind input source function. The spectral dependence of the breaking strength is determined from the Kleiss and Melville measurements of the breaking statistics and the semiempirical spectral energy dissipation, resulting in b = b(k, cp/u*), where k is the wavenumber and the parametric dependence is on the wave age, cp/u*. Guided by these semiempirical results, a model for b(k, cp/u*) is proposed that uses laboratory data from a variety of sources, which can be represented by b = a(S − S0)n, where S is a measure of the wave slope at breaking, a is a constant, S0 is a threshold slope for breaking, and 2.5 < n < 3 is a power law consistent with inertial wave dissipation scaling and laboratory measurements. The relationship between b(S) in the laboratory and b(k) in the field is based on the relationship between the saturation and mean square slope of the wave field. The results are discussed in the context of wind wave modeling and improved measurements of breaking in the field.