Three-dimensional modeling of diffusion-gravity flows in ice-covered lakes

Abstract

When a solid inclined surface is submerged in a quiescent stratified fluid, the combined effects of buoyancy forces and diffusion generate an upward gravity flow along the slope. Thermally stratified ice-covered lakes remain in a nearly quiescent state and are potentially prone to this effect. We use three-dimensional hydrodynamic modeling to investigate the diffusion-gravity flow and its impact on lake-wide circulation in idealized ice-covered lakes. The qualitative characteristics of the boundary flow were adequately simulated by the model, supported by a good agreement with theoretical predictions. In enclosed lakes, the modeled diffusion-driven boundary flow generates residual circulation, which overturns the entire lake water column within 1 to 6 months, suggesting a significant contribution of this mechanism to heat and mass transport in lakes with long ice-covered seasons. When the insulation boundary condition is lifted and additional buoyancy is produced by heat flux from lake sediment, a counterflow emerges, resulting in a circulation pattern characterized by the superposition of two opposing boundary flows. At flux magnitudes exceeding one watt per square meter, the counterflow can entirely replace the diffusion-driven circulation. Due to the small magnitudes of these flows, the Coriolis effect substantially influences circulation, partially transforming radial flow into rotational lake-wide "gyres." The number and rotational direction of these gyres depend on the relative contribution of bottom heat flux. The results provide a framework for designing field studies in real lakes and investigating circulation effects on the transport of dissolved matter, such as nutrients, oxygen and greenhouse gases in ice-covered lakes.