Thermal convection of air in a two-layers snow cover of immobile sea ice

Sea ice, as a rule, is covered with a heat-insulating snow cover, consisting of an ice skeleton and air-saturated pores. However, the temperature difference between the sea and the atmosphere during the cold season provides favorable conditions for macroscopic air movement, which significantly reduces the thermal resistance of snow and, thereby, affects the thermal and dynamic interaction of the atmosphere with the upper layers of the sea.

Actual snow cover accumulating on the surface of sea ice has significant heterogeneity and anisotropy of geometric and thermophysical characteristics conditioned by snow density stratification. Our work is aimed to studying the occurrence of convective instability in a system of two porous layers with permeable common boundary for boundary conditions taking into account the oceanographic aspect of the problem. The analytical solution of the problem in the Darcy-Boussinesq approximation is obtained by the Galerkin method, by selecting approximations of the vertical amplitudes of dimensionless temperature and velocity perturbations that satisfy the boundary conditions of the problem. A qualitative originality of the problem is revealed in comparison with a similar problem for a homogeneous porous layer. It is shown that the stability criteria (critical filtering Rayleigh numbers) due to the difference in the thermophysical and structural properties (coefficients of thermal conductivity, porosity and air permeability) of the layers can significantly differ from each other. According to detailed measurements of the thermal structure and metric characteristics of the fixed snow-ice cover in Amba Bay (Shokalsky Strait, Severnaya Zemlya Archipelago) during Winter 2015-2016, as well as calculations of its thermodynamic evolution, the values and temporal variability of the Rayleigh numbers are estimated. By comparing the observational and modeling data, the reality of the existence of a convective heat transfer regime in the snow cover is revealed. It is concluded that it is necessary to take into account its contribution to the thermal and mass balance of sea ice during winter period.