Phase turbulence in Rayleigh-Bénard convection

We present a three-dimensional simulation of Rayleigh-Bénard convection in a large aspect ratio Γ=60 with stress-free boundaries for a fluid Prandtl number σ=0.5. We find that a spatiotemporal chaotic state (phase turbulence) emerges immediately above onset, which we investigate as a function of the reduced control parameter ε. In particular we find that the correlation length for the vertical velocity field, the time averaged convective current, and the mean square vorticity have power law behaviors near onset, with exponents given by -1/2, 1, and 5/2 respectively. We also find that the time averaged vertical velocity and vertical vorticity fields have the same (disordered) spatial characteristics as the corresponding instantaneous patterns for these fields, and that there is no long-term phase correlation in the system. Finally, we present simple theoretical explanations for the time averaged convective current as a function of the control parameter, and for the fact that the time dependence of three global quantities (characterizing the dissipation of kinetic energy, the release of internal energy by buoyancy, and entropy flow) is essentially the same.