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Register a new userEffect of Plumes on Measuring the Large Scale Circulation in Turbulent Rayleigh-Benard Convection
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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.
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The effect of rotation on the boundary layers (BLs) in a Rayleigh-Benard (RB) system at a relatively low Rayleigh number, i.e. $Ra = 4times10^7$, is studied for different Pr by direct numerical simulations and the results are compared with laminar BL theory. In this regime we find a smooth onset of the heat transfer enhancement as function of increasing rotation rate. We study this regime in detail and introduce a model based on the Grossmann-Lohse theory to describe the heat transfer enhancement as function of the rotation rate for this relatively low Ra number regime and weak background rotation $Rogtrsim 1$. The smooth onset of heat transfer enhancement observed here is in contrast to the sharp onset observed at larger $Ra gtrsim 10^8$ by Stevens {it{et al.}} [Phys. Rev. Lett. {bf{103}}, 024503, 2009], although only a small shift in the Ra-Ro-Pr phase space is involved.
For rapidly rotating turbulent Rayleigh--Benard convection in a slender cylindrical cell, experiments and direct numerical simulations reveal a boundary zonal flow (BZF) that replaces the classical large-scale circulation. The BZF is located near the vertical side wall and enables enhanced heat transport there. Although the azimuthal velocity of the BZF is cyclonic (in the rotating frame), the temperature is an anticyclonic traveling wave of mode one whose signature is a bimodal temperature distribution near the radial boundary. The BZF width is found to scale like $Ra^{1/4}Ek^{2/3}$ where the Ekman number $Ek$ decreases with increasing rotation rate.
By utilizing diffusion maps embedding and transition matrix analysis we investigate sparse temperature measurement time-series data from Rayleigh--Benard convection experiments in a cylindrical container of aspect ratio $Gamma=D/L=0.5$ between its diameter ($D$) and height ($L$). We consider the two cases of a cylinder at rest and rotating around its cylinder axis. We find that the relative amplitude of the large-scale circulation (LSC) and its orientation inside the container at different points in time are associated to prominent geometric features in the embedding space spanned by the two dominant diffusion-maps eigenvectors. From this two-dimensional embedding we can measure azimuthal drift and diffusion rates, as well as coherence times of the LSC. In addition, we can distinguish from the data clearly the single roll state (SRS), when a single roll extends through the whole cell, from the double roll state (DRS), when two counter-rotating rolls are on top of each other. Based on this embedding we also build a transition matrix (a discrete transfer operator), whose eigenvectors and eigenvalues reveal typical time scales for the stability of the SRS and DRS as well as for the azimuthal drift velocity of the flow structures inside the cylinder. Thus, the combination of nonlinear dimension reduction and dynamical systems tools enables to gain insight into turbulent flows without relying on model assumptions.
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.
When the classical Rayleigh-Benard (RB) system is rotated about its vertical axis roughly three regimes can be identified. In regime I (weak rotation) the large scale circulation (LSC) is the dominant feature of the flow. In regime II (moderate rotation) the LSC is replaced by vertically aligned vortices. Regime III (strong rotation) is characterized by suppression of the vertical velocity fluctuations. Using results from experiments and direct numerical simulations of RB convection for a cell with a diameter-to-height aspect ratio equal to one at $Ra sim 10^8-10^9$ ($Pr=4-6$) and $0 lesssim 1/Ro lesssim 25$ we identified the characteristics of the azimuthal temperature profiles at the sidewall in the different regimes. In regime I the azimuthal wall temperature profile shows a cosine shape and a vertical temperature gradient due to plumes that travel with the LSC close to the sidewall. In regime II and III this cosine profile disappears, but the vertical wall temperature gradient is still observed. It turns out that the vertical wall temperature gradient in regimes II and III has a different origin than that observed in regime I. It is caused by boundary layer dynamics characteristic for rotating flows, which drives a secondary flow that transports hot fluid up the sidewall in the lower part of the container and cold fluid downwards along the sidewall in the top part.
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