Spatio-temporal regimes in Rayleigh–Bénard convection in a small rectangular cell

1989 ◽  
Vol 209 ◽  
pp. 309-334 ◽  
Author(s):  
M. A. Rubio ◽  
P. Bigazzi ◽  
L. Albavetti ◽  
S. Ciliberto
Keyword(s):  
Travelling Waves ◽  
Rectangular Cell ◽  
Complex Behaviour ◽  
Temporal Behaviour ◽  
Bénard Convection ◽  
Benard Convection ◽  
Spatio Temporal ◽  
Roll Axis ◽  
Rayleigh Benard Convection ◽  
Rayleigh Benard

By means of an original optical technique we have studied the spatio-temporal behaviour in a Rayleigh–Bénard convection experiment of small rectangular geometry. The experimental technique allows complete reconstruction of the temperature field integrated along the roll axis. Two main spatiotemporal regimes have been found, corresponding to localized oscillations and travelling waves respectively. Several parameters are proposed for the quantitative characterization of this complex behaviour.

Turbulent temperature fluctuations in a closed Rayleigh–Bénard convection cell

2019 ◽  
Vol 874 ◽  
pp. 263-284 ◽  
Author(s):  
Yin Wang ◽  
Xiaozhou He ◽  
Penger Tong
Keyword(s):  
Temperature Fluctuations ◽  
Convection Cell ◽  
Thermal Plumes ◽  
Bénard Convection ◽  
Conducting Plate ◽  
Benard Convection ◽  
Analytic Expressions ◽  
Spatio Temporal ◽  
Rayleigh Benard Convection ◽  
Rayleigh Benard

We report a systematic study of spatial variations of the probability density function (PDF) $P(\unicode[STIX]{x1D6FF}T)$ for temperature fluctuations $\unicode[STIX]{x1D6FF}T$ in turbulent Rayleigh–Bénard convection along the central axis of two different convection cells. One of the convection cells is a vertical thin disk and the other is an upright cylinder of aspect ratio unity. By changing the distance $z$ away from the bottom conducting plate, we find the functional form of the measured $P(\unicode[STIX]{x1D6FF}T)$ in both cells evolves continuously with distinct changes in four different flow regions, namely, the thermal boundary layer, mixing zone, turbulent bulk region and cell centre. By assuming temperature fluctuations in different flow regions are all made from two independent sources, namely, a homogeneous (turbulent) background which obeys Gaussian statistics and non-uniform thermal plumes with an exponential distribution, we obtain the analytic expressions of $P(\unicode[STIX]{x1D6FF}T)$ in four different flow regions, which are found to be in good agreement with the experimental results. Our work thus provides a unique theoretical framework with a common set of parameters to quantitatively describe the effect of turbulent background, thermal plumes and their spatio-temporal intermittency on the temperature PDF $P(\unicode[STIX]{x1D6FF}T)$.

Heat transport and the large-scale circulation in rotating turbulent Rayleigh–Bénard convection

2010 ◽  
Vol 665 ◽  
pp. 300-333 ◽  
Author(s):  
JIN-QIANG ZHONG ◽  
GUENTER AHLERS
Keyword(s):  
Large Scale ◽  
Maximum Enhancement ◽  
Large Scale Circulation ◽  
Complex Behaviour ◽  
Number Range ◽  
Rotation Rates ◽  
Bénard Convection ◽  
Benard Convection ◽  
Rayleigh Benard Convection ◽  
Rayleigh Benard

Measurements of the Nusselt number Nu and of properties of the large-scale circulation (LSC) for turbulent Rayleigh–Bénard convection are presented in the presence of rotation about a vertical axis at angular speeds 0 ≤ Ω ≲ 2 rad s−1. The sample chamber was cylindrical with a height equal to the diameter, and the fluid contained in it was water. The LSC was studied by measuring sidewall temperatures as a function of azimuthal position. The measurements covered the Rayleigh-number range 3 × 108 ≲ Ra ≲ 2 × 1010, the Prandtl-number range 3.0 ≲ Pr ≲ 6.4 and the Rossby-number range 0 ≤ (1/Ro ∝ Ω) ≲ 20. At modest 1/Ro, we found an enhancement of Nu due to Ekman-vortex pumping by as much as 20%. As 1/Ro increased from zero, this enhancement set in discontinuously at and grew above 1/Roc. The value of 1/Roc varied from about 0.48 at Pr = 3 to about 0.35 at Pr = 6.2. At sufficiently large 1/Ro (large rotation rates), Nu decreased again, due to the Taylor–Proudman (TP) effect, and reached values well below its value without rotation. The maximum enhancement increased with increasing Pr and decreasing Ra and, we believe, was determined by a competition between the Ekman enhancement and the TP depression. The temperature signature along the sidewall of the LSC was detectable by our method up to 1/Ro ≃ 1. The frequency of cessations α of the LSC grew dramatically with increasing 1/Ro, from about 10−5 s−1 at 1/Ro = 0 to about 2 × 10−4 s−1 at 1/Ro = 0.25. A discontinuous further increase of α, by about a factor of 2.5, occurred at 1/Roc. With increasing 1/Ro, the time-averaged and azimuthally averaged vertical thermal gradient along the sidewall first decreased and then increased again, with a minimum somewhat below 1/Roc. The Reynolds number of the LSC, determined from oscillations of the time correlation functions of the sidewall temperatures, was constant within our resolution for 1/Ro ≲ 0.3 and then decreased with increasing 1/Ro. The retrograde rotation rate of the LSC circulation plane exhibited complex behaviour as a function of 1/Ro even at small rotation rates corresponding to 1/Ro < 1/Roc.

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