Temperature and velocity profiles of turbulent convection in water

Tilgner, A.; Belmonte, Andrew; Libchaber, Albert

doi:10.1103/physreve.47.r2253

Cited by 148 publications

(120 citation statements)

References 14 publications

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“…Because container shape can be important in understanding fluctuations for non-rotating convection [18,19], we note below where geometry may play a role in the interpretation of the results. There have been a number of reports of temperature field measurements in convection without rotation (see, for example, [20][21][22][23][24]), but only a few such experiments [13,14,25,26] and numerical simulations [4,7,27,28] for rotating convection. Without rotation, thermal plumes are generated in thin thermal boundary layers near the top and bottom boundaries where heat enters and exits the convection cell [29,30].…”

Section: Introductionmentioning

confidence: 99%

Local temperature measurements in turbulent rotating Rayleigh-Bénard convection

Liu

Ecke

2011

Phys. Rev. E

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We present local temperature measurements of turbulent Rayleigh-Bénard convection with rotation about a vertical axis. The fluid, water with Prandtl number about 6, was confined in a cell with a square cross section of 7.3 × 7.3 cm 2 and a height of 9.4 cm. Temperature fluctuations and boundary-layer profiles were measured for Rayleigh numbers 1 × 10 7 < Ra < 5 × 10 8 and Taylor numbers 0 < Ta < 5 × 10 9 . We present statistics of the temperature field measured by a single thermistor located along the vertical centerline of the cell or by an array of thermistors distributed laterally from that centerline. The statistics include the mean temperature, standard deviation, skewness, and the probability distribution functions at various locations in the cell, especially near and inside the thermal boundary layer. The effects of rotation on these quantities are discussed including the presence of a rotation-dependent mean vertical temperature gradient, the negative skewness of temperature fluctuations in the boundary layer, and the horizontal homogenization of temperature.

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Section: Introductionmentioning

confidence: 99%

Local temperature measurements in turbulent rotating Rayleigh-Bénard convection

Liu

Ecke

2011

Phys. Rev. E

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“…The remainder of the fluid, known as the 'bulk', has long been considered isothermal in the time average (Malkus 1954;Priestley 1954Priestley , 1959Spiegel 1971), albeit with a vigorously fluctuating temperature. More recent investigations (see, for instance, Tilgner, Belmonte & Libchaber 1993;Brown & Ahlers 2007b) revealed that the bulk does contain some temperature variations, but these were thought to consist mostly of constant gradients caused by plumes emanating from the thermal BLs and propagating through the bulk. For a cylindrical sample, these gradients were found to depend on the radial position (Brown & Ahlers 2007b) as well as on the ratio of the kinematic viscosity to the thermal diffusivity, known as the Prandtl number Pr; see (2.2) below.…”

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confidence: 98%

Logarithmic temperature profiles in the bulk of turbulent Rayleigh–Bénard convection for a Prandtl number of 12.3

Wei

Ahlers

2014

J. Fluid Mech.

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We report measurements of logarithmic temperature profiles Θ(z, r) = A(r) × ln(z/L) + B(r) in the bulk of turbulent Rayleigh-Bénard convection (here Θ is a scaled and timeaveraged local temperature in the fluid, z is the vertical and r the radial position, and L is the sample height). Two samples had aspect ratios Γ ≡ D/L = 1.00 and 0.50 (where D = 190 mm is the diameter). The fluid was a fluorocarbon with a Prandtl number of Pr = 12.3. The measurements covered the Rayleigh-number range 2 × 10 10 Ra 2 × 10 11 for Γ = 1.00 and 3 × 10 11 Ra 2 × 10 12 for Γ = 0.50. In contradistinction to what had been found for Γ = 0.50 and Pr = 0.78 by Ahlers et al. (Phys. measurements revealed no Ra dependence of the amplitude A(r) of the logarithmic term. Within the experimental resolution, the amplitude was also found to be independent of Γ . It varied with r in a manner consistent with the function A(ξ ) = A 1 / 2ξ − ξ 2 , where ξ ≡ (R − r)/R with R = D/2 and A 1 0.0016. The results for A(r) are smaller than those obtained from experiments and direct numerical simulations (Ahlers et al., Phys. Rev. Lett., vol. 109, 2012, art. 114501) at similar values of Ra for Pr = 0.7 and Γ = 1 2 by a factor that depended slightly upon Ra but was close to 2.

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“…For the viscous boundary layer, the large temperature fluctuations make conventional laser Doppler velocimetry ineffective because the temperature fluctuations cause fluctuations in the refractive index of the fluid that in turn make it difficult to steadily focus two laser beams to cross each other in the fluid (Xia, Xin & Tong 1995). Tilgner et al (1993) introduced an electrochemical labeling method and measured the velocity profile and boundary layer thickness near the top plate of a cubic cell filled with water, but only at a single value of Ra. In a later study, , 1994 developed an indirect method -the correspondence between the peak position of the cutoff frequency profile of the temperature power spectrum and the peak position of the velocity -to infer the viscous boundary boundary layer thickness in gaseous convection.…”

Section: Boundary Layer Measurements In Turbulent Thermal Convectionmentioning

confidence: 99%

Viscous boundary layer properties in turbulent thermal convection in a cylindrical cell: the effect of cell tilting

Wei

Xia

2013

J. Fluid Mech.

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We report an experimental study of the properties of the velocity boundary layer in turbulent Rayleigh-Bénard convection in a cylindrical cell. The measurements were made at Rayleigh numbers Ra in the range 2.8 × 10 8 < Ra < 5.6 × 10 9 and were conducted with the convection cell tilted with an angle θ relative to gravity, at θ = 0. and 3.4 o , respectively. The fluid was water with Prandtl number P r = 5.3. It is found that at small tilt angles (θ 1 o ), the measured viscous boundary layer thickness δ v scales with the Reynolds number Re with an exponent close to that for a Prandtl-Blasius laminar boundary layer, i.e. δ v ∼ Re −0.46±0.03 . For larger tilt angles, the scaling exponent of δ v with Re decreases with θ. The normalized mean horizontal velocity profiles measured at the same tilt angle but with different Ra are found to have an invariant shape. But for different tilt angles, the shape of the normalized profiles is different.It is also found that the Reynolds number Re based on the maximum mean horizontal velocity scales with Ra as Re ∼ Ra 0.43 and the Reynolds number Re σ based on the maximum rms velocity scales with Ra as Re σ ∼ Ra 0.55 , with both exponents do not seem to depend on the tilt angle θ.Several wall quantities are also measured directly and their dependency on Re are found to agree well with those predicted for a classical laminar boundary layer. These are the wall shear stress τ (∼ Re 1.46 ), the viscous sublayer δ w (∼ Re 0.75 ), the friction velocity u τ (∼ Re −0.86 ) and the skin friction coefficient c f (∼ Re −0.46 ). Again, all these near-wall quantities do not seem to depend on the tilt angle.We also examined the dynamical scaling method proposed bys Zhou and Xia [Phys. Rev. Lett. 104, 104301 (2010)] and found that in both the laboratory and the dynamical frames the mean velocity profiles show deviations from the theoretical Prandtl-Blasius profile, with the deviations increase with Ra. But profiles obtained from dynamical scaling in general have better agreement with the theoretical profile. It is also found that the effectiveness of this method appears to be independent of Ra.1. Introduction Rayleigh-Bénard convectionRayleigh-Bénard (RB) convection, which is a fluid layer heated from below and cooled from the top, is an idealized model to study turbulent flows involving heat transport and has attracted much attention during the past few decades (Siggia 1994;Kadanoff 2001;Ahlers, Grossmann & Lohse 2009;. The system is characterized by two control parameters: the Rayleigh number Ra, Prandtl number P r, which are defined arXiv:1209.6415v1 [physics.flu-dyn]

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Temperature and velocity profiles of turbulent convection in water

Cited by 148 publications

References 14 publications

Local temperature measurements in turbulent rotating Rayleigh-Bénard convection

Local temperature measurements in turbulent rotating Rayleigh-Bénard convection

Logarithmic temperature profiles in the bulk of turbulent Rayleigh–Bénard convection for a Prandtl number of 12.3

Viscous boundary layer properties in turbulent thermal convection in a cylindrical cell: the effect of cell tilting

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