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

Measurements over the Rayleigh-number range 10 8 ≲ R ≲ 10 11 and Prandtl-number range 4.4≲σ≲29 that determine the torsional nature and amplitude of the oscillatory mode of the large-scale circulation (LSC) of turbulent Rayleigh–Bénard convection are presented. For cylindrical samples of aspect ratio Γ=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 Γ=1 and σ=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 ≃5, nearly independent of R . For samples with Γ≥2 we did not find this mode, but there remained a characteristic periodic signal that was detectable in the area density ρ p of the plumes above the bottom-plate centre. Measurements of ρ p revealed a strong dependence on the Rayleigh number R , and on the aspect ratio Γ that could be represented by ρ p ~ Γ 2.7±0.3 . Movies are available with the online version of the paper.