ИСТИНА

We consider a plane layer of water confined between horizontal isothermal stress-free boundaries. It is known that the density of water has a maximum at the temperature 4°С and atmospheric pressure, and the density-temperature dependence an be approximated by the quadratic function for the temperature ranges 0-10°С [1]. The flow is simulated for the Navier-Stokes equations in Boussinesq approximation with the constant viscosity. The two-dimensional problem is studied. The solution is sought in the periodicity cell with stress-free vertical boundaries. The horizontal scale of the periodicity cell was chosen as consistent with the preliminary simulations on the large scales. Here it is equal to the typical horizontal scale Lp of time-periodic regime [2-3]. The evolution of the regimes with the increase of the supercriticality was described and the sequence of bifurcations leading to chaos. The hysteresis domains were found [3]. The transition to chaotic regimes is as follows. First, periodic motion appears after steady regime. Then, there is the secondary subcritical Hopf bifurcation (or Neimark-Sacker bifurcation), but initially it seems as a simple period doubling due to frequency locking [2-3]. After the transition to periodic-2 mode, there is the loss of symmetry with respect to the vertical line in the middle of the computational domain. With further increase of the supercriticality, the second frequency appears. Quasiperiodic and periodic-2 solutions turn out to be unstable on the horizontal scales greater than 2Lp. Then, intermittency arise on the background of the quasiperiodic solution, with strong bursts of the heat flux. At certain value of the supercriticality, the bursts disappear and quasiperiodic motion reappears which differs from initial quasiperiodic regime. After that, intermittency sets in on the background of new quasiperiodic mode. With the increase of supercriticality, intervals between stochastic bursts are shorter and the motion becomes completely chaotic.