In deep ice-covered lakes with temperatures below 4 °C the heat flux from the bottom sediment results in a horizontal density gradient and a consequent flow along the bottom slope. Measurements in Lake Pääjärvi, Finland, show a stable temperature field where a heat gain through the bottom and a heat loss through the ice nearly balance each other. The circulation is thermal with low velocities (less than 1.5 cm s–1). We used the 3D hydrodynamic Princeton Ocean Model as a tool to simulate the water circulation and the temperature distribution under the ice. The model forcing was based on field temperature measurements. The model simulations suggest that in midwinter the velocity field of the upper water layers is anticyclonic while that of deep layers is cyclonic. Comparison with current measurements at one site showed good agreement between the modelled and observed results. On the basis of the modelled results it is possible to better understand the distributions of some micro-organisms and the accumulation of oxygen depleted waters in the deepest part of the lake

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We consider two applications of the stochastic discrete particles method. The first one is concerned with the dispersion of a passive pollutant by a turbulent stream with a scale dependent diffusion coefficient. The second application deals with the problem of an oil spill spreading on the water surface described by transport-diffusion equation with a nonlinear diffusion coefficient. For the first problem we develop a discrete particles algorithm provided the diffusion coefficient obeys Richardson's "4/3" law and show good correspondence with the numerical and analytical results. The second problem is more involved and we develop a heuristic procedure based on the standard discrete particles random walk algorithm updating the dependence of each particle step variance on the dependent function. The obtained solution coincides well with analytical and direct one-dimensional finite-difference solutions both for instantaneous and continuous oil release.

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