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Register a new userTristable flow states and reversal of the large-scale circulation in two-dimensional circular convection cells
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We present a numerical study of the flow states and reversals of the large-scale circulation (LSC) in a two-dimensional circular Rayleigh-Benard cell. Long-time direct numerical simulations are carried out in the Rayleigh number ($Ra$) range $10^{7} le Ra le 10^{8}$ and Prandtl number ($Pr$) range $2.0 le Pr le 20.0$. We found that a new, long-lived, chaotic flow state exists, in addition to the commonly observed circulation states (the LSC in the clockwise and counterclockwise directions). The circulation states consist of one primary roll in the middle and two secondary rolls near the top and bottom circular walls. The primary roll becomes stronger and larger, while the two secondary rolls diminish, with increasing $Ra$. Our results suggest that the reversal of the LSC is accompanied by the secondary rolls growing, breaking the primary roll and then connecting to form a new primary roll with reversed direction. We mapped out the phase diagram of the existence of the LSC and the reversal in the $Ra$-$Pr$ space, which reveals that the flow is in the circulation states when $Ra$ is large and $Pr$ is small. The reversal of the LSC can only occur in a limited $Pr$ range. The phase diagram can be understood in terms of competition between the thermal and viscous diffusions. We also found that the internal flow states manifested themselves into global properties such as Nusselt and Reynolds numbers.
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In turbulent Rayleigh-Benard convection, a large-scale circulation (LSC) develops in a nearly vertical plane, and is maintained by rising and falling plumes detaching from the unstable thermal boundary layers. Rare but large fluctuations in the LSC amplitude can lead to extinction of the LSC (a cessation event), followed by the re-emergence of another LSC with a different (random) azimuthal orientation. We extend previous models of the LSC dynamics to include momentum and thermal diffusion in the azimuthal plane, and calculate the tails of the probability distributions of both the amplitude and azimuthal angle. Our analytical results are in very good agreement with experimental data.
The two-dimensional regular and chaotic electro-convective flow states of a dielectric liquid between two infinite parallel planar electrodes are investigated using a two-relaxation-time lattice Boltzmann method. Positive charges injected at the metallic planar electrode located at the bottom of the dielectric liquid layer are transported towards the grounded upper electrode by the synergy of the flow and the electric field. The various flow states can be characterized by a non-dimensional parameter, the electric Rayleigh number. Gradually increasing the electric Rayleigh number, the flow system sequentially evolves via quasi-periodic, periodic, and chaotic flow states with five identified bifurcations. The turbulence kinetic energy spectrum is shown to follow the -3 law as the flow approaches turbulence. The spectrum is found to follow a -5 law when the flow is periodic.
We analyse the nonlinear dynamics of the large scale flow in Rayleigh-Benard convection in a two-dimensional, rectangular geometry of aspect ratio $Gamma$. We impose periodic and free-slip boundary conditions in the streamwise and spanwise directions, respectively. As Rayleigh number Ra increases, a large scale zonal flow dominates the dynamics of a moderate Prandtl number fluid. At high Ra, in the turbulent regime, transitions are seen in the probability density function (PDF) of the largest scale mode. For $Gamma = 2$, the PDF first transitions from a Gaussian to a trimodal behaviour, signifying the emergence of reversals of the zonal flow where the flow fluctuates between three distinct turbulent states: two states in which the zonal flow travels in opposite directions and one state with no zonal mean flow. Further increase in Ra leads to a transition from a trimodal to a unimodal PDF which demonstrates the disappearance of the zonal flow reversals. On the other hand, for $Gamma = 1$ the zonal flow reversals are characterised by a bimodal PDF of the largest scale mode, where the flow fluctuates only between two distinct turbulent states with zonal flow travelling in opposite directions.
We studied the properties of the large-scale circulation (LSC) in turbulent Rayleigh-Benard (RB) convection by using results from direct numerical simulations in which we placed a large number of numerical probes close to the sidewall. The LSC orientation is determined by either a cosine or a polynomial fit to the azimuthal temperature or azimuthal vertical velocity profile measured with the probes. We study the LSC in Gamma=D/L=1/2 and Gamma=1 samples, where D is the diameter and L the height. For Pr=6.4 in an aspect ratio Gamma=1 sample at $Ra=1times10^8$ and $5times10^8$ the obtained LSC orientation is the same, irrespective of whether the data of only 8 or all 64 probes per horizontal plane are considered. In a Gamma=1/2 sample with $Pr=0.7$ at $Ra=1times10^8$ the influence of plumes on the azimuthal temperature and azimuthal vertical velocity profiles is stronger. Due to passing plumes and/or the corner flow the apparent LSC orientation obtained using a cosine fit can result in a misinterpretation of the character of the large-scale flow. We introduce the relative LSC strength, which we define as the ratio between the energy in the first Fourier mode and the energy in all modes that can be determined from the azimuthal temperature and azimuthal vertical velocity profiles, to further quantify the large-scale flow. For $Ra=1times10^8$ we find that this relative LSC strength is significantly lower in a Gamma=1/2 sample than in a Gamma=1 sample, reflecting that the LSC is much more pronounced in a Gamma=1 sample than in a Gamma=1/2 sample. The determination of the relative LSC strength can be applied directly to available experimental data to study high Rayleigh number thermal convection and rotating RB convection.
In this numerical study on two-dimensional Rayleigh-Benard convection we consider $10^7 leq Ra leq 10^{12}$ in aspect ratio $0.23 leq Gamma leq 13$ samples. We focus on several cases. First we consider small aspect ratio cells, where at high Ra number we find a sharp transition from a low Ra number branch towards a high Ra number branch, due to changes in the flow structure. Subsequently, we show that the influence of the aspect ratio on the heat transport decreases with increasing aspect ratio, although even at very large aspect ratio of $Gammaapprox10$ variations up to 2.5% in the heat transport as a function of Gamma are observed. Finally, we observe long-lived transients up to at least $Ra=10^9$, as in certain aspect ratio cells we observe different flow states that are stable for thousands of turnover times.
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