We report an experimental study of the three-dimensional spatial structure of the low-frequency temperature oscillations in a cylindrical Rayleigh-Bénard convection cell. Through simultaneous multipoint temperature measurements it is found that, contrary to the popular scenario, thermal plumes are emitted neither periodically nor alternately, but randomly and continuously, from the top and bottom plates. We further identify a new flow mode-the sloshing mode of the large-scale circulation (LSC). This sloshing mode, together with the torsional mode of the LSC, are found to be the origin of the oscillation of the temperature field.
We present an experimental study of the azimuthal motion of the mean wind in turbulent thermal convection. The experiments were conducted with cylindrical convection cells of unity aspect ratio and over the range of the Rayleigh number from 1 x 10(9) to 1 x 10(10). The azimuthal angle of the circulation plane of the mean wind was measured using both the particle image velocimetry and flow-visualization techniques. It is found that the azimuthal motion consists of erratic fluctuations and a time-periodic oscillation. The orientation of the wind is found to be "locked," i.e., it fluctuates about a preferred direction most of the time with all other orientations appearing as "transient states," and large excursions of the azimuthal angle often result in a net rotation which takes the wind back to the preferred orientation. The rate of erratic rotation of the circulation plane is found to have a strong dependence on Ra. Our result suggests that the oscillatory motion of the wind in its vertically oriented circulation plane and the orientational oscillation of the circulation plane itself have the same dynamic origin.
We investigate the statistical properties of the kinetic $\unicode[STIX]{x1D700}_{u}$ and thermal $\unicode[STIX]{x1D700}_{\unicode[STIX]{x1D703}}$ energy dissipation rates in two-dimensional (2-D) turbulent Rayleigh–Bénard (RB) convection. Direct numerical simulations were carried out in a box with unit aspect ratio in the Rayleigh number range $10^{6}\leqslant Ra\leqslant 10^{10}$ for Prandtl numbers $Pr=0.7$ and 5.3. The probability density functions (PDFs) of both dissipation rates are found to deviate significantly from a log-normal distribution. The PDF tails can be well described by a stretched exponential function, and become broader for higher Rayleigh number and lower Prandtl number, indicating an increasing degree of small-scale intermittency with increasing Reynolds number. Our results show that the ensemble averages $\langle \unicode[STIX]{x1D700}_{u}\rangle _{V,t}$ and $\langle \unicode[STIX]{x1D700}_{\unicode[STIX]{x1D703}}\rangle _{V,t}$ scale as $Ra^{-0.18\sim -0.20}$, which is in excellent agreement with the scaling estimated from the two global exact relations for the dissipation rates. By separating the bulk and boundary-layer contributions to the total dissipations, our results further reveal that $\langle \unicode[STIX]{x1D700}_{u}\rangle _{V,t}$ and $\langle \unicode[STIX]{x1D700}_{\unicode[STIX]{x1D703}}\rangle _{V,t}$ are both dominated by the boundary layers, corresponding to regimes $I_{l}$ and $I_{u}$ in the Grossmann–Lohse (GL) theory (J. Fluid Mech., vol. 407, 2000, pp. 27–56). To include the effects of thermal plumes, the plume–background partition is also considered and $\langle \unicode[STIX]{x1D700}_{\unicode[STIX]{x1D703}}\rangle _{V,t}$ is found to be plume dominated. Moreover, the boundary-layer/plume contributions scale as those predicted by the GL theory, while the deviations from the GL predictions are observed for the bulk/background contributions. The possible reasons for the deviations are discussed.
We report an experimental study of the large-scale circulation (LSC) in a turbulent Rayleigh-Bénard convection cell with aspect ratio unity. The temperature-extremum-extraction (TEE) method for obtaining the dynamic information of the LSC is presented. With this method, the azimuthal angular positions of the hot ascending and cold descending flows along the sidewall are identified from the measured instantaneous azimuthal temperature profile. The motion of the LSC is then decomposed into two different modes based on these two angles: the azimuthal mode and the translational or off-center mode that is perpendicular to the vertical circulation plane of the LSC. Comparing to the previous sinusoidal-fitting (SF) method, it is found that both the TEE and the SF methods give the same information about the azimuthal motion of the LSC, but the TEE method in addition can provide information about the off-center motion of the LSC. The off-center motion is found to oscillate time-periodically around the cell's central vertical axis with an amplitude being nearly independent of the turbulent intensity. It is further found that the azimuthal angular positions of the hot ascending flow near the bottom plate and the cold descending flow near the top plate oscillate periodically out of phase by π, leading to the torsional mode of the LSC. These oscillations are then propagated vertically along the sidewall by the hot ascending and cold descending fluids. When they reach the mid-height plane, the azimuthal positions of the hottest and coldest fluids again oscillate out of phase by π. It is this out-of-phase horizontal positional oscillation of the hottest and coldest fluids at the same horizontal plane that produces the off-center oscillation of the LSC. A direct velocity measurement further confirms the existence of the bulk off-center mode of the flow field near cell center.The paper has been submitted to J. Fluid Mech.
Direct multipoint measurements of the velocity and temperature fields have been made in a turbulent Rayleigh-Bénard convection cell. In the central region of the cell it is found that both velocity and temperature exhibit the same scaling behavior that one would find for the velocity and for a passive scalar in homogeneous and isotropic Navier-Stokes turbulence. This is despite the fact that energy is pumped into the system vertically via buoyancy. Near the cell's sidewall where thermal plumes abound, vertical velocity and temperature exhibit different scalings. A model that takes into account both buoyancy and energy dissipation is proposed and its predictions agree well with the sidewall experimental results.
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