Bifurcation analysis of interacting stationary modes in thermohaline convection

The Boussinesq equations for thermohaline convection in a finite two-dimensional box and with stress-free boundaries are considered. There are critical values of the aspect ratio at which the conduction state becomes unstable to two different roll patterns simultaneously. Near such a critical value a center manifold reduction allows us to reduce the dynamical behavior of the Boussinesq equations to a standard normal form equation that describes the interaction of two stationary modes. We present explicit analytical expressions for the linear and nonlinear coefficients on which the normal form depends. A numerical investigation of these coefficients leads to a division of the space of parameters (Prandtl number, solute Rayleigh number, Lewis number) into various regions that give rise to qualitatively different bifurcation behavior. Besides those encountered in ordinary convection, a variety of further phenomena is found, in particular in a vicinity of double tricritical points