Wind reversals in turbulent Rayleigh-Benard convection

Abstract

The phenomenon of irregular cessation and subsequent reversal of the large-scale circulation in turbulent Rayleigh-Bénard convection is theoretically analysed. The force and thermal balance on a single plume detached from the thermal boundary layer yields a set of coupled nonlinear equations, whose dynamics is related to the Lorenz equations. For Prandtl and Rayleigh numbers in the range $10^{-2}\le \mathrm{Pr}\le 10^3$ and $10^{7} \leq \Ra \leq 10^{12}$, the model has the following features: (i) chaotic reversals may be exhibited at Ra $\ge 10^7$; (ii) the Reynolds number based on the root mean square velocity scales as $\Re_{rms} \sim \Ra^{[0.41 ... 0.47]}$ (depending on Pr), and as ${\Re }_{rms}\sim {\mathrm{Pr}}^{-[\mathrm{0.66...0.76}]}$ (depending on Ra); and (iii) the mean reversal frequency follows an effective scaling law $ω/ (νL^{-2}) \sim \Pr^{-(0.64 \pm 0.01)} \Ra^{0.44 \pm 0.01}$. The phase diagram of the model is sketched, and the observed transitions are discussed.

4 pages, 5 figures