Analytical approaches for wave energy dissipation induced by wave-generated turbulence and random wave-breaking

Abstract

This paper is dedicated to investigate the dissipation effects of wave-generated turbulence reacting on ocean waves and to estimate the energy loss due to wave-breaking theoretically. An analytical dissipation source function induced by wave-generated turbulence in the water was proposed through the equilibrium solutions of a second-order turbulence closure model between the wave shear instability generations and the turbulent kinetic energy (TKE) dissipations under the well-founded structural equilibrium closure assumptions. And an improved postbreaking spectrum expression, based on the breaking wave statistical method, was presented to depict more explicitly the intermittent wave-breaking events. Comparisons of the TKE dissipation rates indicate that the model results agree well with the laboratory observations which were directly generated by the waves themselves, but for mechanical and wind waves, dispersions suggest the presence of other dynamic processes. The modeled attenuation coefficients of the breaking spectrum correspond to the decreasing tendency measured from the lake experiment, which yields valuable insights of the physics of dominant breaking, but the statistical approach is less well-suited for simulating the rapid transient regime of wave breaking as well as for the higher frequency in the equilibrium range. Evaluations for more complex situations will be addressed in the future series of papers.