ON THE HOPF-BIFURCATION OCCURRING IN THE 2-LAYER RAYLEIGH-BENARD CONVECTIVE INSTABILITY

The oscillating convective structures appearing at the threshold of th e two-layer Rayleigh-Benard instability are analyzed in the nonlinear regime. By deriving the amplitude equations for left- and right-travel ing waves from the infinite Prandtl number Boussinesq equations, it is shown that one of these waves should generally appear, rather than st anding waves, in sufficiently large cells. Numerical results show that these waves have a limited range of existence, because a hysteretic t ransition to stationary convection occurs when the Rayleigh number is increased (via approach of a heteroclinic orbit for standing waves, an d steady-state bifurcation for traveling waves). From numerical eviden ce and by comparison with similar behaviors encountered in the one-lay er two-component problem, it is inferred that the overall behavior is typical of a codimension-2 Takens-Bogdanov bifurcation.