Relationship between turbulent energy dissipation and gas transfer through the air–sea interface

Abstract

The nonlinear dependence of gas transfer velocity on wind speed typically results in the best fit of observational data; however, gas transfer velocity is dimensionally inconsistent with the nonlinear wind speeds. The objective of the current study was to show that, in the case of wind waves, gas transfer velocity with a consistent dimension should be determined by turbulent viscosity instead of by the viscosity of water when parameterised using the renewal model. Turbulent kinetic energy (TKE) near the air–sea interface is significantly intensified by breaking wind waves. By analyzing various models, we found that the TKE dissipation rate was explicitly linearly related to wind speed and dependent on wave age, with powers ranging from –2.36 to 4.0. Various models show that wave energy dissipation (WED) due to wind wave breaking explicitly increases with the cube of the wind speed and weakly depends on wave age. Assuming a balance between WED and total TKE dissipation in a constant dissipation layer, the depth of this layer was shown to be comparable to the wave height. Using the traditional renewal model with wind wave turbulent viscosity and TKE dissipation rate at the sea surface, we found that the gas transfer velocity was explicitly linearly related to wind speed in a dimensionally consistent manner, and depended simultaneously on the wave age and drag coefficient. These results are consistent with observational data obtained using the eddy correlation method. We emphasise that the linear dependence on wind speed is only valid when the wave age and drag coefficient are fixed; thus, this finding cannot be directly confirmed by currently available observational data due to a lack of wave state information.