Two-dimensional double diffusive convection of a binary fluid mixture in a square container is investigated by linear and weakly nonlinear stability analyses, numerical simulations and numerical calculations of steady solutions in the present paper. We consider an ethanol-water mixture as the binary fluid, in which the temperature and the ethanol concentration interact through the Soret effect, both affecting the fluid motion via buoyancy force. The bottom of the container is kept at a higher temperature than the top, while the side walls are assumed thermally insulating. The heat conduction state is known to become unstable to an oscillatory mode as well as a stationary mode of disturbance, and the two instability modes exchange at a set of parameter values, called codimension two point. It was reported that the convection often tend to a steady state even if the instability is induced by an oscillatory mode, which is an unusual flow property. We explore its mathematical and physical reason by formally deriving a set of amplitude equations near the codimension two point by applying the center manifold theory. It is shown that the unusual nonlinear behavior of the double diffusive convection is clearly explained from the bifurcation structure of the solutions to the set of amplitude equations.
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