Stability and transition of double diffusive convection in a rectangular cavity are investigated analytically and numerically on the assumption of two-dimensional flow fields. We consider the temperature and mass concentration as two physical quantities which diffuse and affect the fluid motion through buoyancy effects. The bottom wall of the cavity is kept at a higher temperature than the top, and the mass concentration at the bottom wall is kept at a constant and higher value than the top. The side boundary walls are assumed to be perfectly insulating and non-permeable of mass. We use two different numerical methods, i.e. numerical simulation and numerical calculation of steady-state solution of the convection. Linear stability of the steady-state solution is also investigated by applying the linear stability theory. The value of the Prandtl number is assumed to be 7 (water), whereas various values of the Schmidt number and thermal and concentration Rayleigh numbers are considered. In all the numerical calculations including numerical simulations, the stream function, temperature and mass concentration are expanded in Chebyshev polynomials for spatial dependences. Steady-state and time-periodic solutions are calculated, and their bifurcation diagrams are obtained. It is our conclusion that any chaotic fluid motion does not appear in the double diffusive convection in a rectangular cavity in the parameter range covered in the present paper.
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