E-epsilon model of sea spray-stratified marine atmospheric layer in high wind conditions

In this work we considered a variable density (non-Bousinessq) E-epsilon turbulence closure to describe spray-stratified marine atmospheric boundary layer dynamics under high-wind conditions of a tropical cyclone. In contrast to the lower-order Turbulent Kinetic Energy (TKE) model considered previously the E-epsilon model accounts for the effects of variation of turbulent energy and turbulent mixing length due to the spray stratification. Asymptotic expressions for the main characteristics of a turbulent flow were obtained for two limiting cases of small and large spray concentrations. The obtained analytical and numerical solutions show significant differences between the current higher-order E-epsilon model and the aforementioned TKE turbulence model. Specifically, it was found that that according to the E-epsilon model and in contrast to the TKE model the turbulent energy, which is suppressed by the spray in a thin layer near the ocean surface, does not necessarily recover to its reference value corresponding to a non-stratified flow far away from the surface. It is shown that the reduction of turbulent energy and mixing length above the wave crest level, where the spray droplets are generated, that is not accounted by the TKE model results in a significant suppression of turbulent mixing in this near-wave layer. In turn, suppression of turbulence causes a flow acceleration and a reduction of the drag coefficient that is qualitatively consistent with field observations if spray is fine (even if its concentration is low) or if droplets are large but their concentration is sufficiently high. In the latter case spray inertia may become important. At these values of concentration the spray inertia effect may become significant and in such situations an intricate interplay between it and the turbulence suppression by the spray determines whether the wind speed increases or decreases. It is shown that spray inertia leads to the reduction of wind velocity in the close proximity of the wave surface relative to the reference logarithmic profile. However at higher altitudes the suppression of flow turbulence by the spray still results in the wind acceleration and the reduction of the local drag coefficient. It was also found that the variable density model predicts a faster decrease of the drag coefficient with the flow speed than the Boussinesq model. In view of these facts the meaningful quantitative comparison of the model predictions with experimental observations would have to account for the vertical distribution of the flow quantities. Limiting such a comparison to a standard but somewhat arbitrary 10 m level may be misleading.