Development of attractors for double-diffusive convection in plain layer

Double-diffusive convection between two horizontal planes is investigated. Sequence of bifurcations from stationary motions to stochastic motions is demonstrated. We found that the attractor has the structure of a Mobius band in chaotic regimes. With the help of Poincare sections and Poincare maps we show modifications of the attractor with the increase of supercriticality. First, Poincare map can be represented as a one-valued function. With the growth of supercriticality Poincare map remains one-dimensional but now it has many minima and self-intersections so it can't be approximated by some function. With the help of Lyapunov exponents we show the divergence of trajectories on the attractors. Relative residual of the initial Navier-Stokes equations is calculated for all the numerical solutions, so we can affirm that the numerical solutions almost exactly represent the genuine solution (the third order of accuracy) and properties of the attractor adequately correspond to the initial model. The convergence of Bubnov-Galerkin method is demonstrated with the help norms of kinetic energy and dissipation function.