Pattern formation in binary mixture convection in cylindrical three-dimensional cells

Abstract

We present numerical results of pattern selection near the onset of convection for a water-ethanol mixture in a cylindrical container heated from below. Parameter values and boundary conditions relevant to experiments are used. The separation ratio of the mixture we consider is S = −0.09 and the radial aspect ratio of the cell is Γ = 11. The onset of convection occurs via a subcritical Hopf bifurcation. Slightly above the onset, in the linear regime, a m = 1 azimuthal mode consisting of radially travelling waves grows in amplitude. As convection evolves, the pattern focuses into one or several diameters of the cell. We do not observe a direct transition to a stable nonlinear state. Instead, collapses in the convection amplitude followed by subsequent growths take place. This behaviour resembles some experimental observations. The numerical results are obtained with an efficient time-evolution spectral code that solves the full convection equations in cylindrical coordinates.