Mathematics of Planet Earth

Convection driven by gravitational instability is a widespread phenomenon in the geophysical fluid dynamics, dynamics of stars and planetary interiors. In contrast to the quasi-homogeneous small-scale turbulence, convection is distinguished by the cell-like coherent structure of the flow. Absence of wind shear and non-linear dependene of freshwater density on temperature in vicinity of 4°C are characteristic features of ice-covered lakes. Therefore, a variety of convective flows develop there, driven by solar radiation penetrating the ice, and by salt fluxes at the ice-water and the water-sediment interfaces. In our field studies on ice-covered lakes, we apply modern measurement techniques, like microstructure profiling and acoustic doppler velocimetry, which deliver direct estimations of the mixing characteristics, comparable with the output of the eddy-resolving LES and DNS models. Providing a rare example of ‘pure’ convection in the natural conditions, ice-covered lakes serve as natural laboratories for investigation of convective mixing and for testing of CFD models. Apart from general geophysical studies, a number of ecological applications exist, where field studies on convection can be effectively combined with advanced mathematical modelling of convective mixing.