Rotations and cessations of the large-scale circulation in turbulent Rayleigh–Bénard convection

Abstract

We present a broad range of measurements of the angular orientation θ 0 (t) of the largescale circulation (LSC) of turbulent Rayleigh-Bénard convection as a function of time. We used two cylindrical samples of different overall sizes, but each with its diameter nearly equal to its height. The fluid was water with a Prandtl number of 4.38. The time series θ 0 (t) consisted of meanderings similar to a diffusive process, but in addition contained large and irregular spontaneous reorientation events through angles ∆θ. We found that reorientations can occur by two distinct mechanisms. One consists of a rotation of the circulation plane without any major reduction of the circulation strength. The other involves a cessation of the circulation, followed by a restart in a randomly chosen new direction. Rotations occurred an order of magnitude more frequently than cessations. Rotations occurred with a monotonically decreasing probability distribution p(∆θ), i.e. there was no dominant value of ∆θ and small ∆θ were more common than large ones. For cessations p(∆θ) was uniform, suggesting that information of θ 0 (t) before the cessation is lost. Both rotations and cessations have Poissonian statistics in time, and can occur at any θ 0 . The average azimuthal rotation rate |θ| increased as the circulation strength of the LSC decreased. Tilting the sample relative to gravity significantly reduced the frequency of occurrence of both rotations and cessations.

Low-dimensional dynamics of a turbulent axisymmetric wake

“…In the spectrum of the angular component, a power-law with an exponent close to -2 is obtained at very low frequencies (VLF). This is analogous to the results of Grandemange et al (2013), and consistent with Brownian dynamics (Brown & Ahlers 2006). Hence the VLF oscillation is a random rotation of the CoP in the azimuthal direction around the axis of the body.…”

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

“…We previously reported the frequency of reorientations (spontaneous changes of the LSC orientation) ω r vs. β, and showed that a Gaussian function fit to ω r (β) with a maximum at some β 0 , which has the same physical meaning as before. We found β 0 = 0.0093 ± 0.0010 rad at R = 9.4 × 10 10 in the large sample [16] and β 0 = 0.0022 ± 0.0006 rad at R = 1.1 × 10 10 in the medium sample [12]. The other parameters measured were the coefficient A representing the potential barrier strength; the LSC temperature amplitude δ; the root-mean-square rotation ratė θ rms ; and the Reynolds number R e .…”

“…Examples of such fits have been shown previously [12,13]. The fit parameter δ is a measure of the amplitude of the LSC and θ 0 is the azimuthal orientation of the plane of the LSC circulation in the sample frame.…”

“…We found an effective diffusivity given by [12]. Since re-orientations do not occur very frequently, that analysis had used time series of θ 0 that included all re-orientations even though these events could not be described by simple diffusion.…”

“…Elsewhere we presented measurements of sudden reorientations of the plane of circulation of the LSC through a continuum of possible angles ∆θ [12]. They were relatively rare events in that their collective duration took up only a small fraction of the observation time.…”