Nonlinear regimes of Soret-driven convection of ternary fluid with fixed vertical heat flux at the boundaries.

Nonlinear regimes of the Soret-induced convection of a ternary mixture in a rectangular cavity with the vertical heat flux at the boundaries are studied numerically. Linear stability analysis performed earlier for a plane horizontal layer has shown that in a wide range of parameters the longwave instability is dominant. Nonlinear calculations performed in the present work for the parameter ranges where the monotonic longwave instability is dominant according to the linear stability analysis, show that at large supercriticalities the multi-vortex stationary flows could be realized. With the decrease of absolute value of the Rayleigh number Ra the series of flow structure transformations takes place. This transformation is accompanied by the decrease of a number of the vortices such that near the threshold the flow becomes two-vortex, i.e. the flow with maximum possible wavelength (minimum possible wave number) is realized. Thus, the nonlinear calculations confirm the conclusions of the linear stability analysis that the longwave instability is dominant. For the parameter ranges where according to the linear stability analysis the oscillatory longwave instability is dominant, the nonlinear calculations show that at small values of the net separation ratio the oscillatory regimes could be observed just in a narrow range of Ra close to the convection threshold and with the growth of net separation ratio the range of Ra where they can be observed is extended.

Onset of Soret-induced convection in a horizontal layer of ternary fluid with fixed vertical heat flux at the boundaries.

The paper deals with the investigation of the onset and weakly nonlinear regimes of the Soret-driven convection of ternary liquid mixture in a horizontal layer with rigid impermeable boundaries subjected to the prescribed constant vertical heat flux. It is found that there are monotonous and oscillatory longwave instability modes. The boundary of the monotonous longwave instability in the parameter plane Rayleigh number Ra - net separation ratio [Formula: see text] at fixed separation ratio of one of solutes consists of two branches of hyperbolic type. One of the branches is located at [Formula: see text], the other one at [Formula: see text]. The oscillatory longwave instability exists at [Formula: see text] only for the heating from below and at [Formula: see text] there exist two oscillatory longwave instability modes: one at [Formula: see text] and the other at [Formula: see text]. Corrections to the Rayleigh number obtained in the higher order of the expansion show that the longwave perturbations can be most dangerous at any values of [Formula: see text]. The numerical solution of the linear stability problem for small perturbations with finite wave numbers confirms this conclusion. The weakly nonlinear analysis shows that all steady solutions are unstable to the modes of larger wavelength and stable to the modes of smaller wavelength, i.e. the solution with maximal possible wavelength is realized.