Estimates of Kinetic Energy Dissipation under Breaking Waves

TLDR

The dissipation of kinetic energy at the surface of natural water bodies critically affects wave dynamics, gas transfer, nutrient mixing, pollutant dispersion, and plankton photosynthesis. The authors propose a scaling for the dissipation rate based on wind and wave parameters, concluding that dissipation under breaking waves varies with depth in three distinct stages. They relate the thickness of the dissipation layer to the normalized energy flux from breaking, which for young waves scales with wave age, thereby linking wind and wave characteristics to the vertical structure of dissipation. Measurements in a large lake under strong wind forcing reveal a surface layer of enhanced dissipation exceeding wall‑layer values by one or two orders of magnitude, a z⁻² decay in an intermediate region, and asymptotic values at depth, with total energy flux up to an order of magnitude greater than conventional estimates and strongly dependent on wave age, indicating a need to revise kinetic‑energy dissipation estimates in wave‑stirred environments.

Abstract

The dissipation of kinetic energy at the surface of natural water bodies has important consequences for many Physical and biochemical processes including wave dynamics, gas transfer, mixing of nutrients and pollutants, and photosynthetic efficiency of plankton. Measurements of dissipation close to the surface obtained in a large lake under conditions of strong wind forcing are presented that show a layer of enhanced dissipation exceeding wall layer values by one or two orders of magnitude. The authors propose a scaling for the rate of dissipation based on wind and wave parameters, and conclude that the dissipation rate under breaking waves depends on depth, to varying degrees, in three stages. Very near the surface, within one significant height, the dissipation rate is high (an order of magnitude greater than that predicted by wall layer theory) and roughly constant. Below this is an intermediate region where the dissipation decays as z−2. The thickness of this layer (relative to the significant wave height) is proportional to the energy flux from breaking normalized by pu3*, which for young waves is proportional to wave age. At sufficient depth the dissipation rate asymptotes to values commensurate with a traditional wall layer. The total energy flux into the water column can be an order of magnitude greater than the conventional estimate of pu3*/2 and depends strongly on wave age. Thew results imply a pronounced shift in our approach to estimating kinetic energy dissipation in wave-stirred regions and in the modeling of various physical, chemical, and biological processes.