ИСТИНА

It is well known that natural water has a density maximum about 4C. There were a number of works with description of peculiarities of steady and some kind of periodic solutions. Here we focus our attention on evolution of two-dimensional convective modes with increase of supercriticality in a plain layer with equal heights of stable and unstable layers, stress-free boundary condition and absence of mean flow. Some known results were revised and detailed analysis is given for periodical motions which are stable on very large horizontal scales. Detailed analysis of Poincare-Andronov-Hopf bifurcation is given and hydrodynamic peculiarities of periodical motion are shown. Branches of hysteresis are found. Loss of stability of periodical motion if associated with loss of symmetry in physical space and occurs through a subcritical Neimark-Sacker bifurcation. After this bifurcation a period-2 motion on torus appears which is quite similar to period-doubling bifurcation but actually is a synchronized motion on a torus. With further increase of supercriticality system passes through saddle-node bifurcation for maps and the motions becomes quasiperiodic. After quasiperiodic solutions there appear intermittency with stochastic bursts on the background of quasiperiodic solution. With increase of superciticallity there is a window of quasiperiodicity and structure (spectral characteristics) of the background quasiperiodical solution alter after passing through this window.