Effect of the Earth’s Coriolis force on the large-scale circulation of turbulent Rayleigh-Bénard convection

Abstract

We present measurements of the large-scale circulation (LSC) of turbulent Rayleigh-Bénard convection in water-filled cylindrical samples of heights equal to their diameters. The orientation of the LSC had an irregular time dependence, but revealed a net azimuthal rotation with an average period of about 3 days for Rayleigh numbers R > ∼ 10 10 . On average there was also a tendency for the LSC to be aligned with upflow to the west and downflow to the east, even after physically rotating the apparatus in the laboratory through various angles. Both of these phenomena could be explained as a result of the coupling of the Earth's Coriolis force to the LSC. The rate of azimuthal rotation could be calculated from a model of diffusive LSC orientation meandering with a potential barrier due to the Coriolis force. The model and the data revealed an additional contribution to the potential barrier that could be attributed to the cooling system of the sample top which dominated the preferred orientation of the LSC at high R. The tendency for the LSC to be in a preferred orientation due to the Coriolis force could be cancelled by a slight tilt of the apparatus relative to gravity, although this tilt affected other aspects of the LSC that the Coriolis force did not.

A model of diffusion in a potential well for the dynamics of the large-scale circulation in turbulent Rayleigh–Bénard convection

“…[33] a stochastic model of the LSC that was motivated by the physically relevant terms of the Navier-Stokes (NS) equations for RBC. It is in the same spirit as a model for the effects of Earth's Coriolis force on the flow [24], and we will show in a subsequent paper that the Coriolis-force model is consistent with the strong-damping limit of the current model. The model consists of two coupled stochastic ordinary differential equations (ODEs): one for the strength of the LSC represented by an amplitude δ of the azimuthal temperature variation at the horizontal mid-plane of the sample, and the other for the azimuthal LSC orientation θ 0 .…”

“…The viscous boundarylayer width is assumed to follow the Prandtl-Blasius form λ = LR −1/2 e,i /2 with a fluctuating Reynolds number R e,i ≡ UL/ν. Although this must be regarded as an approximation, the Prandtl-Blasius form for the boundary layer has worked remarkably well in previous models (for example, [24]). It also has been very successful in predicting the dependence of the Reynolds number on the Rayleigh number [37], and in treating non-Boussinesq effects on the Nusselt number and the center temperature [38,39].…”

“…This average can be carried out using the experimental observation [23,24,25,36] that the temperature of the LSC at the side wall at mid-height is given by Eq. 3.…”

“…The LSC also undergoes re-orientations both by azimuthal rotations [14,23], and by cessations in which the LSC slows to a stop and restarts in a random new orientation [23,25]. On longer time scales, Earth's Coriolis force was found to cause a net rotation of the LSC orientation on average once every 3 days, and to align the LSC in a preferred orientation close to West [24]. These LSC dynamics observed in experiments may be related to some natural convection dynamics.…”

“…This orientation has been found to undergo spontaneous diffusive meandering [21,22,23,24]. The LSC also undergoes re-orientations both by azimuthal rotations [14,23], and by cessations in which the LSC slows to a stop and restarts in a random new orientation [23,25].…”