A case study of the energy dissipation of the gravity wave field based on satellite altimeter measurements

Wave breaking is proposed as the primary energy dissipation mechanism for the gravity wave field. The energy dissipation rate is calculated based on the statistical model proposed by Longuet-Higgins (1969) with a modification of the breaking criterion incorporating the surface stress according to Phillips and Banner (1974). From this modified model, an analytic expression is found for the wave attenuation rate and the half-life time of the wave field which depend only on the significant slope of the wave field and the ratio of friction velocity to initial wave phase velocity. These expressions explain why the freshly generated wave field does not last long, but why swells are capable of propagating long distances without substantial change in energy density. It is shown that breaking is many orders of magnitude more effective in dissipating wave energy than the molecular viscosity, if the significant slope is higher than 0.01. Limited observational data from satellite and laboratory are used to compare with the analytic results, and show good agreement.