The cause of oscillations of the large-scale circulation of turbulent Rayleigh-B{\'e}nard convection

摘要

In agreement with a recent experimental discovery by Xia et. al. (2009), wealso find a sloshing mode in experiments on the large-scale circulation (LSC)of turbulent Rayleigh-Benard convection in a cylindrical sample of aspect ratioone. The sloshing mode has the same frequency as the torsional oscillationdiscovered by Funfschilling and Ahlers (2004). We show that both modes can bedescribed by an extension of a model developed previously [Brown and Ahlers(2008)] which consists of permitting a lateral displacement of the LSCcirculation plane away from the vertical center line of the sample as well as avariation in displacements with height (such displacements had been excluded inthe original model). Pressure gradients produced by the side wall of thecontainer on average center the plane of the LSC so that it prefers to reachits longest diameter. If the LSC is displaced away from this diameter, thewalls provide a restoring force. Turbulent fluctuations drive the LSC away fromthe central alignment, and combined with the restoring force they lead tooscillations. These oscillations are advected along with the LSC. This modelpredicts the correct wavenumber and phase of the oscillations, as well asestimates of the frequency, amplitude, and probability distributions of thedisplacements.