Recirculation and equilibrium displacement of the thermocline in a wind-driven stratified lake

The equilibrium response of a lake to an applied wind stress has previously been approximated using a two-dimensional, two-density-layer, closed basin with a simple static balance between the barotropic and baroclinic tilts. The next level of sophistication is to allow the wind stress to be distributed over some reduced depth of the upper layer, giving rise to downwind transport near the surface and upwind transport above the thermocline. The existence of the recirculation amplifies or reduces the equilibrium response of the thermocline depending upon the ratio of the wind-mixed layer depth to the epilimnion depth. A deep thermocline (relative to the wind-mixed layer depth) will have a reduced response to wind forcing solely due to the existence of a recirculating flow. These results are of particular interest in the design of numerical models for stratified lakes as they highlight the critical importance of the turbulence model used to capture the wind-mixed layer dynamics: to get the setup of basin-scale internal waves modeled correctly in a stratified lake, it is necessary to have a turbulence model that accurately captures the wind-mixed layer depth.