Turbulent kinetic energy balance as a tool for estimating vertical diffusivity in wind‐forced stratified waters

Abstract

Based on microstructure measurements in a simply shaped lake basin, the sources of vertical mixing in the stratified part of the water body were identified and estimates of their relative importance obtained by balancing turbulent kinetic energy introduced by the wind. It was found that (1) ∼1.9% of the vertical wind energy flux P10 (∼39 mW m−2), estimated 10 m above the lake surface, was available for turbulent mixing in the entire lake water body; (2) ∼1.5% of P10 was dissipated by turbulence in the weakly stratified surface layer (epilimnion ;6 m deep), and ∼0.42% of P10 reached the stratified deep water (hypolimnion) as turbulent kinetic energy via internal seiching; (3) ∼90% of the turbulent kinetic energy in the stratified water (i.e., 0.38% of P10 ) was dissipated within the bottom boundary layer of a few meters thickness, whereas only ∼10% was lost in the interior (away from the boundary; 0.04% of P10); and (4) as a consequence mixing within the bottom boundary was found to be the main source of vertical mixing for the deep waters of the whole lake. The ratio of buoyancy flux to dissipation (i.e., the mixing efficiency) was found to be ϒmix ∼ 0.15, leading to agreement between the Osborn‐Cox microstructure diffusivities and basin‐wide tracer diffusivities.Comparison with turbulent kinetic energy balances, performed in five other lakes, demonstrates that this analysis is representative for many enclosed water bodies, as long as wind is the dominant source of turbulent energy (i.e., if other processes, such as convective mixing, double diffusion, or riverine intrusions can be neglected). Although the lakes under consideration were very different in size and shape and although the currents in Lake Baikal were inertial rather than seiching related as in the other lakes, the turbulent kinetic energy balance was very similar and the mixing efficiency was identical. Typically, 0.3 ± 0.1% of P10 is transferred as turbulent kinetic energy into the stratified part of the water body, and 0.04 ± 0.02% of P10 is stored as potential energy in the stratification. This analysis provides a tool for estimating vertical diffusivity for wind‐driven hypolimnetic mixing within a factor of two based on stratification and wind measurements alone.