Torsional oscillations of the large-scale circulation in turbulent Rayleigh-Benard convection

Measurements over the Rayleigh-number range 10(8) less than or similar to R less than or similar to 10(11) and Prandtl-number range 4.4 less than or similar to sigma less than or similar to 29 that determine the torsional nature and amplitude of the oscillatory mode of the large-scale circulation (LSC) of turbulent Rayleigh-Benard convection are presented. For cylindrical samples of aspect ratio Gamma = 1 the mode consists of an azimuthal twist of the near-vertical LSC circulation plane, with the top and bottom halves of the plane oscillating out of phase by half a cycle. The data for Gamma = 1 and or sigma = 4.4 showed that the oscillation amplitude varied irregularly in time, yielding a Gaussian probability distribution centred at zero for the displacement angle. This result can be described well by the equation of motion of a stochastically driven damped harmonic oscillator. It suggests that the existence of the oscillations is a consequence of the stochastic driving by the small-scale turbulent background fluctuations of the system, rather than a consequence of a Hopf bifurcation of the deterministic system. The power spectrum of the LSC orientation had a peak at finite frequency with a quality factor Q similar or equal to 5, nearly independent of R. For samples with Gamma >= 2 we did not find this mode, but there remained a characteristic periodic signal that was detectable in the area density rho(p) of the plumes above the bottom-plate centre. Measurements of rho(p) revealed a strong dependence on the Rayleigh number R, and on the aspect ratio Gamma that could be represented by rho(p) similar to Gamma(2.7 +/- 0.3). Movies are available with the online version of the paper.