Compressibility effects in lake hydrodynamics

A non-hydrostatic version of mathematical model of deep temperate lake is formulated. Water is treated as compressible. Nonlinear relation corresponds density with temperature and pressure. Numerical procedure is based on variational principle in the combination with splitting methods. Two-dimensional variant of the model is used in the numerical experiment which presents the influence of differential compressibility of water on the lateral flow through gravitational adjustment. This experiment simulates the possible way of the formation of the winter mid-depth temperature maximum in deep lakes. Such phenomenon is regularly observed in lake Baikal.