Effects of geometric confinement in quasi-2-D turbulent Rayleigh–Bénard convection

Abstract

We report an experimental study of confinement effects in quasi-2-D turbulent Rayleigh-Bénard convection. The experiments were conducted in five rectangular cells with their height H and length L being the same and fixed, while the width W was different for each cell to produce lateral aspect ratios (Γ = W/H) of 0.6, 0.3, 0.2, 0.15 and 0.1. Direct flow field measurements reveal that the large-scale flow slows down as Γ decreases and there are more plumes travelling through the bulk region. Moreover, the reversal frequency of the large-scale flow is found to increase drastically in smaller Γ cells, by more than 1000-fold for the highest value of Rayleigh number reached in the experiment. The reversal frequency can be well described by a stochastic model developed by Ni et al. (J. Fluid Mech., vol. 778, 2015, R5) and the probability density functions (PDF) of the time interval between successive reversals are found to follow Poisson statistics as in the 3-D system. It is further observed that the bulk temperature fluctuation increases significantly and its PDF changes from exponential to Gaussian as Γ decreases. The influences of geometric confinement on the global heat transport are also investigated. The measured Nu-Ra relationship suggests that, as the lateral aspect ratio decreases, the relative weight of the boundary layer contribution in the global heat transport increases compared to that from the bulk. These results demonstrate that in the quasi-2-D geometry, geometric confinement has strong effects on both the global and local properties in turbulent convective flows, which are very different from the previous findings in 3-D and true 2-D systems.

Tristable flow states and reversal of the large-scale circulation in two-dimensional circular convection cells

“…The and scaling exponents in the 2-D circular cell are close to those in a 2-D (or quasi-2-D) square cell, where – (Ciliberto, Cioni & Laroche 1996; van der Poel et al. 2012; Huang & Xia 2016; Zhang, Zhou & Sun 2017) and – (Xia et al. 2003; Sun & Xia 2005; Zhou, Sun & Xia 2007; van der Poel et al.…”

“…This tristable flow state feature is distinguishable from the bistable behaviour in 2-D or quasi-2-D square cells, where the LSC switches only between CLSC and CCLSC, and a double-Gaussian function best fits the PDFs of the flow strength in terms of either global angular momentum or the temperature contrast (Sugiyama et al. 2010; Chandra & Verma 2011; Ni, Huang & Xia 2015; Castillo-Castellanos, Sergent & Rossi 2016; Huang & Xia 2016; Castillo-Castellanos et al. 2019).…”

“…the percentage of time the flow spends in the two circulation states and the chaotic state. The criteria to quantitatively identify these flow state transitions are similar to those used in Huang & Xia (2016). First, the flow should stay at the current state for more than one large-eddy turnover time , where denotes the vorticity at the cell centre.…”

Reversals of coherent structures in turbulent mixed convection

“…At the same time, the heat is not sufficiently removed from the edge vortex, which leads to multiple eruptions of plumes. The latter disturb the main roll and therefore promote its reorientation (see Huang & Xia 2016). Evidence for these plume eruptions is provided by the averaged vertical velocity component in a control plane displayed in figure 10( c ).…”

Reversals in infinite-Prandtl-number Rayleigh-Bénard convection

“…In our numerical simulations for infinite Prandtl number, we also observe that the waiting times between successive reversals exhibit exponential distribution, whereas the crossings (to be defined later for the present case) are distributed as a powerlaw. Moreover, the mean waiting time between two consecutive reversals have also been observed to depend on the Rayleigh number [3,9,23,26], the aspect ratio Γ [7], and the thermal boundary condition at the bottom plate [27].…”