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Chaotic attractors and bifurcations in double-diffusive convection.

Transition to chaotic regimes and development of stochastic motion
in plain layer of a salt solution are 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 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. Influence of boundary conditions and differences in
two-dimensional and three-dimensional cases are discussed.
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