The development of the convective instability in a plain layer of water is considered. The density-temperature relation is taken as a quadratic function with a maximum at 4°С. A two-dimensional formulation of the problem is investigated for the case where the point of the density maximum is in the middle plane of the layer in the static state. To study the transition to the stochastic mode, the horizontal scale of the motion was chosen with particular attention. The areas of the hysteresis are explored when motions with different flow structure and different heat fluxes exist, which was illustrated by the dependence of the Nusselt number on super- criticality. The specifics of the formation of steady and periodic regimes are shown. The transition to the stochastic mode is described.
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