A new similarity model for the stratified under-ice boundary layer in lakes and its application to ice-covered Lake Baikal

Seasonal ice cover on lakes and polar seas creates seasonally developing boundary layer at the ice base with specific features: fixed temperature at the solid boundary and stable density stratification beneath. Turbulent transport in the boundary layer determines the ice growth and melting conditions at the ice-water interface, especially in large lakes and marginal seas, where large-scale water circulation can produce highly variable mixing conditions. Since the boundary mixing under ice is difficult to measure, existing models of ice cover dynamics usually neglect or parameterize it in a very simplistic form. We propose a model of the turbulent energy budget in the stably stratified boundary layer under ice, based on the length scale incorporating the dissipation rate and the buoyancy frequency (Dougherty-Ozmidov scaling). The model was verified on fine-scale measurements in Lake Baikal and demonstrated a good agreement with data. The measured ice-water heat fluxes in were among the largest reported in lakes (up to 40 W m⁻²) and scaled well against the proposed relationship. The model yields a scaling relationship for the ice-water heat flux as a function of the shear velocity squared that suggests the traditional bulk parameterizations may significantly underestimate the ice-water heat flux, especially at strong under-ice current velocities. The ultimate result consists in a strong dependence of the water-ice heat flux on the shear velocity under ice.