Wind Reversals in Turbulent Rayleigh-Bénard 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 ≤ Pr ≤ 10 3 and 10 7 ≤ Ra ≤ 10 12 , the model has the following features: (i) chaotic reversals may be exhibited at Ra ≥ 10 7 ; (ii) the Reynolds number based on the root mean square velocity scales as Rerms ∼ Ra One important issue in turbulent Rayleigh-Bénard convection is the interplay between the large-scale circulation (the so-called wind) [1] and the dynamics of plumes detached from the thermal boundary layers [2]. In particular, such interplay seems to be relevant in the process of circulation reversals, which occur in an irregular time sequence [3,4,5,6,7,8]. Remarkably, similar reversals are also observed in the wind direction of the atmosphere [9] and in the magnetic polarity of the earth [10].In principle, two reversal scenarios are possible: Reversal through cessation of the convection roll, and reversal through its azimuthal rotation. With two temperature sensors placed close to each other near the sidewall [4,5], one can detect roll reversals, but not distinguish between the two scenarios. With several sensors placed along the azimuth of the cell, Cioni et al.[6] succeeded to detect reversal through azimuthal rotation of the roll. Reversal through rotation was also detected in refs. [7,8]. However, with an ingenious multi-probe setup, Brown, Nikolaenko, and Ahlers [8] were able to distinguish between the rotation and cessation scenarios, and many reversals through cessation were detected. Reversal through cessation was also observed in two-dimensional numerical simulations of the Boussinesq equations (see fig. 8 of ref.[11] and fig. 12 of ref. [12]), where the rotation scenario is of course impossible.Since reversal through cessation is a more surprising scenario, the aim of the present work is to reveal its physical mechanism. Qualitatively, the picture is as follows [13]: If an uprising hot plume gets too fast because of a temperature surplus, it fails to cool down sufficiently when passing the top plate. It then is still warmer than the ambient fluid when advected down along the sidewall. By buoyancy it therefore looses speed and counteracts the large-scale circulation. Indeed, the downward wind may be counteracted so strongly that it stops or even reverses its direction. This mechanism can be effective only for sufficiently strong wind, i.e., for sufficiently large Reynolds number, because for slow motion the thermal diffusivity κ has enough time to reduce the temperature surplus of the originally warmer plume relative to its neighbourhood. Then its power to reverse the circulation by buoyancy is gone.The model : In order to quantify the cessation mechanism discussed above, let us first characterize the s...

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

“…They have their roots in the Navier-Stokes equations and retain terms that are argued to be physically important. One of them [31] again is lacking the azimuthal degree of freedom that is so important to the LSC dynamics found in experiment. The other [32] is based on an exact solution of the Boussinesq equations in the inviscid and unforced limit, but employs physically unrealistic boundary conditions and adds dissipation a posteriori.…”

“…No azimuthal degree of freedom was included, and thus only genuine reversals of the LSC (which are now known to be very rare events) could be produced. Two other models [31,32] describe the LSC with deterministic differential equations that have chaotic solutions. They have their roots in the Navier-Stokes equations and retain terms that are argued to be physically important.…”

Dynamics and symmetries of flow reversals in turbulent convection

“…Broadly, these works involve either stochasticity (e.g., "stochastic resonance" [8,13]), or low-dimensional models with noise [14,15]. Mishra et al [10] studied the large-scale modes of RBC in a cylindrical geometry and showed that the dipolar mode decreases in amplitude and the quadrupolar mode increases during the cessation-led reversals.…”

“…Broadly, these works involve either stochasticity (e.g., "stochastic resonance" [8, 13]), or low-dimensional models with noise [14,15]. Mishra et al…”

Flow Reversals in Turbulent Convection via Vortex Reconnections

“…Benzi and Verzicco [9] and Sreenivasan et al [14] used stochastic resonance, while Arajuo et al [15] employed low-dimensional models with noise to explain reversals. Brown and Ahlers [3] and Mishra et al [11] showed that in a cylindrical geometry, the flow reversals are induced by a rotation or cessation of large-scale flow structures.…”