Bifurcation and Stability of the Traveling-Wave Convection in a Binary Fluid Mixture

Abstract

The Rayleigh–Benard convection of a binary fluid mixture in a horizontal layer is considered for a moderate negative value of the separation ratio S for which the spatio-temporal structure of fully-developed periodic convection rolls is known to take either the stationary overturning convection (SOC) or the traveling-wave (TW) convection state depending on the values of the Rayleigh number. Numerical solutions for the SOC and the TW states are computed using the 2D MAC and the 2D spectral simulations of the governing equations of motion in the finite difference and the Galerkin form respectively. In addition to these, a method for finding their solutions as the steady-state problem of the Galerkin system using the Newton iterative method is presented and the computed results are compared with those obtained previously by others. Linear stability analysis of the linearized dynamical system shows that the transition between the SOC and TW states is involved by the real-mode instability.