Fine-scale statistics of temperature and its derivatives in convective turbulence

Emran, Mohammad S.; Schumacher, Jörg

doi:10.1017/s0022112008002954

Cited by 87 publications

(112 citation statements)

References 55 publications

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“…We define the planar average of temperature, T m (z) = T xy . Experiments and numerical simulations reveal that T m (z) ≈ 1/2 in the bulk, and it drops abruptly in the boundary layers near the top and bottom plates 39,52 , as shown in Fig. 1.…”

Section: Temperature Profile and Boundary Layermentioning

confidence: 85%

Scaling of large-scale quantities in Rayleigh-Bénard convection

Pandey

Verma

2016

Physics of Fluids

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We derive a formula for the Péclet number (Pe) by estimating the relative strengths of various terms of the momentum equation. Using direct numerical simulations in three dimensions we show that in the turbulent regime, the fluid acceleration is dominated by the pressure gradient, with relatively small contributions arising from the buoyancy and the viscous term; in the viscous regime, acceleration is very small due to a balance between the buoyancy and the viscous term. Our formula for Pe describes the past experiments and numerical data quite well. We also show that the ratio of the nonlinear term and the viscous term is ReRa −0.14 , where Re and Ra are Reynolds and Rayleigh numbers respectively; and that the viscous dissipation, where U is the root mean square velocity and d is the distance between the two horizontal plates. The aforementioned decrease in nonlinearity compared to free turbulence arises due to the wall effects.

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Section: Temperature Profile and Boundary Layermentioning

confidence: 85%

Scaling of large-scale quantities in Rayleigh-Bénard convection

Pandey

Verma

2016

Physics of Fluids

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“…(34) from (17) and (26). The coefficients c 1 to c 4 and the cut-off Reynolds number Re c follow when experimental data are matched by a nonlinear fit.…”

Section: Scaling Theory By Grossmann and Lohsementioning

confidence: 99%

“…In case of the Earth mantle and solar convection the circumferences at mid height have been taken for L. Vapor, water and ice; Anelastic limit Solar convection zone [12,13] hot at the bottom for T /ΔT = 0.7 in red, cold at the top for T /ΔT = 0.3 in blue. Parameters are here: Ra = 10 9 , P r = 0.7 and Γ = 3 (see [26,27] for the corresponding simulations).…”

Section: Introductionmentioning

confidence: 99%

New perspectives in turbulent Rayleigh-Bénard convection

2012

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Abstract. Recent experimental, numerical and theoretical advances in turbulent Rayleigh-Bénard convection are presented. Particular emphasis is given to the physics and structure of the thermal and velocity boundary layers which play a key role for the better understanding of the turbulent transport of heat and momentum in convection at high and very high Rayleigh numbers. We also discuss important extensions of Rayleigh-Bénard convection such as non-Oberbeck-Boussinesq effects and convection with phase changes.

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“…Usually at P r ∼ O(1) the number of grid points within the thermal boundary layer to be used for accurate results vary from 6 to 14 ([78], [28]) and this condition is more restrictive than that imposed by Batchelor scale. Therefore a non-uniform distribution of grid points is generally used, with more points clustered close to the boundaries [78].…”

Section: Grid Resolution Criteriamentioning

confidence: 99%

“…3 Usually in numerical works the N u error bar is considered equal to the standard deviation of the N u number profile in the vertical direction (average over time and horizontal planes) [28] or to the root-meansquare of the N u number signal in time (average over the whole volume) [78]. In the first case the error is basically due to the primitive fields of temperature and vertical velocity and to the derivative of the temperature close to the horizontal walls, since the conductive term is negligible in the bulk.…”

Section: Error Checks and Error Barsmentioning

confidence: 99%

Numerical Simulations of Thermal Convection at High Prandtl Numbers

Silano

Sreenivasan

Verzicco

2010

Direct and Large-Eddy Simulation VII

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In this thesis we present the results of an extensive campaign of direct numerical simulations of Rayleigh-Bénard convection at high Prandtl numbers (10 −1 ≤ P r ≤ 10 4 ) and moderate Rayleigh numbers (10 5 ≤ P r ≤ 10 9 ). The computational domain is a cylindrical cell of aspect-ratio (diameter over cell height) Γ = 1/2, with the no-slip condition imposed to the boundaries.By scaling the results, we find a 1/ √ P r correction to apply to the free-fall velocity, obtaining a more appropriate representation of the large scale velocity at high P r. We investigate the Nusselt and the Reynolds number dependence on Ra and P r, comparing the results to previous numerical and experimental work. At high P r the scaling behavior of the Nusselt number with respect to Ra is generally consistent with the power-law exponent 0.309.The Nusselt number is independent of P r, even at the highest Ra simulated. The Reynolds number scales as Re ∼ √ Ra/P r, neglecting logarithmic corrections. We analyze the global and local features of viscous and thermal boundary layers and their scaling behavior with respect to Rayleigh and Prandtl numbers, and with respect to Reynolds and Peclet numbers.We find that the flow approaches a saturation regime when Reynolds number decreases below the critical value Re s ≃ 40. The thermal boundary layer thickness turns out to increase slightly even when the Peclet number increases. We explain this behavior as a combined effect of the Peclet number and the viscous boundary layer influences.The range of Ra and P r simulated contains steady, periodic and turbulent solutions.A rough estimate of the transition from steady to unsteady flow is obtained by monitoring the time-evolution of the system until it reaches stationary solutions (Ra U ≃ 7.5 × 10 6 at P r = 10 3 ). We find multiple solutions as long-term phenomena at Ra = 10 8 and P r = 10 3 which, however, do not result in significantly different Nusselt number. One of these multiple solutions, even if stable for a long time interval, shows a break in the mid-plane symmetry of the temperature profile. The result is similar to that of some non-Boussinesq effects. We analyze the flow structures through the transitional phases by direct visualizations of the temperature and velocity fields. We also describe how the behavior of the flow structures changes for increasing P r. A wide variety of large-scale circulations and plumes structures are found. The single-roll circulation is characteristic only of the steady and periodic solutions. For other solutions, at lower P r, the mean flow generally consists of two opposite toroidal structures; at higher P r, the flow is organized in multi-cell structures extending mostly in the vertical direction. At high P r, plumes detach from sheet-like structures. The different large-scale-structure signatures are generally reflected in the data trends with rei spect to Ra, but not in those with respect to P r. In particular, the Nusselt number is independent of P r, even when the flow structures appear strongly diffe...

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Fine-scale statistics of temperature and its derivatives in convective turbulence

Cited by 87 publications

References 55 publications

Scaling of large-scale quantities in Rayleigh-Bénard convection

Scaling of large-scale quantities in Rayleigh-Bénard convection

New perspectives in turbulent Rayleigh-Bénard convection

Numerical Simulations of Thermal Convection at High Prandtl Numbers

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