Chaotic Behaviour in Oscillating Compressible Convection in Extended Boxes for Small Prandtl Numbers

The oscillatory instability occurring in tridimensional Rayleigh-Benard compressible convection gives rise to a Hopf bifurcation with a null critical horizontal wave vector. After eliminating the three parasitic zero eigenvalues resulting from the Galilean invariance, and the mass conservation law, we investigate the large-scale modulations of the time-periodic convective flow, by computing the coefficients of the Ginzburg-Landau equation as a function of the parameters of the problem. We show that the Hopf solution which bifurcates supercritically is unstable for many relevant values of the parameters (due to large-scale perturbations). For these cases, we describe the spatial structure of temperature and vorticity vector fields resulting from this instability.