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Some properties of two-dimensional stochastic regimes of double-diffusive convection in plane layer. (English) Zbl 1080.76564

Summary: The existence of a two-dimensional attracting manifold is established for trajectories emanating from the vicinity of static solution. The structure of this manifold is studied with the help of succession map of points in intersection of trajectories with some coordinate plane. The structure of the attracting manifold varies depending on Rayleigh numbers of heat and salinity. With growth of Rayleigh numbers of heat and salinity the structure of one-dimensional curve becomes more irregular and sophisticated. The convergence of Bubnov-Galerkin approximation with a large number of basic functions was demonstrated in norms of kinetic energy, dissipation function, and directly by norm evaluation of the residual (noncompensated terms in substitution of Bubnov-Galerkin approximation to the initial double-diffusive convection system).

MSC:

76R50 Diffusion
76E06 Convection in hydrodynamic stability
37N10 Dynamical systems in fluid mechanics, oceanography and meteorology
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