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Castaño D, Navarro MC, Herrero H. Cyclonic and anticyclonic rotation in a cylinder cooled inhomogeneously on the top. CHAOS (WOODBURY, N.Y.) 2021; 31:093108. [PMID: 34598456 DOI: 10.1063/5.0061312] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/25/2021] [Accepted: 08/19/2021] [Indexed: 06/13/2023]
Abstract
In this work, we study the development of vortical structures generated in a rotating cylinder non-homogeneously cooled on the top. In the axisymmetric regime, for moderate vertical temperature differences and any rotation rate, cyclonic and anticyclonic rotations coexist in the flow: a counterclockwise motion at upper levels, giving place to a vertical top-down vortex, and a clockwise rotation at lower levels that generates a spin up motion. For lower rotation rates and high enough vertical temperature differences, only cyclonic top-down vortices survive and get stronger. We perform a force balance analysis to explain the phenomena. In the non-axisymmetric regime, no anticyclonic rotation at the bottom is reported and the cyclonic top-down vortex either disappears or splits up in two top-down vortices, depending on the ambient rotation rate. The intensity of the cooling on the top and how localized this cool region is affect the flow developed. When the horizontal temperature difference on the top is larger than the vertical temperature difference between top and bottom, stable axisymmetric top-down vortices with an inner updraft of warmer air are reported. The more localized the cooling above, the more difficult the development of the inner updraft becomes. Results may contribute to the understanding of the relevance of thermal processes in tornadogenesis.
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Affiliation(s)
- D Castaño
- Departamento de Matemáticas, Escuela de Ingeniería Industrial y Aeroespacial-IMACI, Universidad de Castilla-La Mancha, 45071 Toledo, Spain
| | - M C Navarro
- Departamento de Matemáticas, Facultad de Ciencias y Tecnologías Químicas-IMACI, Universidad de Castilla-La Mancha, 13071 Ciudad Real, Spain
| | - H Herrero
- Departamento de Matemáticas, Facultad de Ciencias y Tecnologías Químicas-IMACI, Universidad de Castilla-La Mancha, 13071 Ciudad Real, Spain
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2
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Fujita K, Tasaka Y, Yanagisawa T, Noto D, Murai Y. Three-dimensional visualization of columnar vortices in rotating Rayleigh–Bénard convection. J Vis (Tokyo) 2020. [DOI: 10.1007/s12650-020-00651-0] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/24/2022]
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3
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Zhang X, van Gils DPM, Horn S, Wedi M, Zwirner L, Ahlers G, Ecke RE, Weiss S, Bodenschatz E, Shishkina O. Boundary Zonal Flow in Rotating Turbulent Rayleigh-Bénard Convection. PHYSICAL REVIEW LETTERS 2020; 124:084505. [PMID: 32167333 DOI: 10.1103/physrevlett.124.084505] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/15/2019] [Revised: 11/21/2019] [Accepted: 01/07/2020] [Indexed: 06/10/2023]
Abstract
For rapidly rotating turbulent Rayleigh-Bénard 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.
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Affiliation(s)
- Xuan Zhang
- Max Planck Institute for Dynamics and Self-Organization, 37077 Göttingen, Germany
| | - Dennis P M van Gils
- Max Planck Institute for Dynamics and Self-Organization, 37077 Göttingen, Germany
- Physics of Fluids Group, J.M. Burgers Center for Fluid Dynamics, University of Twente, P.O. Box 217, 7500 AE Enschede, Netherlands
| | - Susanne Horn
- Max Planck Institute for Dynamics and Self-Organization, 37077 Göttingen, Germany
- Department of Earth, Planetary, and Space Sciences, University of California, Los Angeles, California 90095, USA
- Centre for Fluid and Complex Systems, Coventry University, Coventry CV1 5FB, United Kingdom
| | - Marcel Wedi
- Max Planck Institute for Dynamics and Self-Organization, 37077 Göttingen, Germany
| | - Lukas Zwirner
- Max Planck Institute for Dynamics and Self-Organization, 37077 Göttingen, Germany
| | - Guenter Ahlers
- Max Planck Institute for Dynamics and Self-Organization, 37077 Göttingen, Germany
- Department of Physics, University of California, Santa Barbara, California 93106, USA
| | - Robert E Ecke
- Max Planck Institute for Dynamics and Self-Organization, 37077 Göttingen, Germany
- Center for Nonlinear Studies, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
| | - Stephan Weiss
- Max Planck Institute for Dynamics and Self-Organization, 37077 Göttingen, Germany
- Max Planck-University of Twente Center for Complex Fluid Dynamics
| | - Eberhard Bodenschatz
- Max Planck Institute for Dynamics and Self-Organization, 37077 Göttingen, Germany
- Institute for the Dynamics of Complex Systems, Georg-August-University Göttingen, 37073 Göttingen, Germany
- Laboratory of Atomic and Solid-State Physics and Sibley School of Mechanical and Aerospace Engineering, Cornell University, Ithaca, New York 14853, USA
| | - Olga Shishkina
- Max Planck Institute for Dynamics and Self-Organization, 37077 Göttingen, Germany
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Chong KL, Yang Y, Huang SD, Zhong JQ, Stevens RJAM, Verzicco R, Lohse D, Xia KQ. Confined Rayleigh-Bénard, Rotating Rayleigh-Bénard, and Double Diffusive Convection: A Unifying View on Turbulent Transport Enhancement through Coherent Structure Manipulation. PHYSICAL REVIEW LETTERS 2017; 119:064501. [PMID: 28949632 DOI: 10.1103/physrevlett.119.064501] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/14/2017] [Indexed: 06/07/2023]
Abstract
Many natural and engineering systems are simultaneously subjected to a driving force and a stabilizing force. The interplay between the two forces, especially for highly nonlinear systems such as fluid flow, often results in surprising features. Here we reveal such features in three different types of Rayleigh-Bénard (RB) convection, i.e., buoyancy-driven flow with the fluid density being affected by a scalar field. In the three cases different stabilizing forces are considered, namely (i) horizontal confinement, (ii) rotation around a vertical axis, and (iii) a second stabilizing scalar field. Despite the very different nature of the stabilizing forces and the corresponding equations of motion, at moderate strength we counterintuitively but consistently observe an enhancement in the flux, even though the flow motion is weaker than the original RB flow. The flux enhancement occurs in an intermediate regime in which the stabilizing force is strong enough to alter the flow structures in the bulk to a more organized morphology, yet not too strong to severely suppress the flow motions. Near the optimal transport enhancements all three systems exhibit a transition from a state in which the thermal boundary layer (BL) is nested inside the momentum BL to the one with the thermal BL being thicker than the momentum BL. The observed optimal transport enhancement is explained through an optimal coupling between the suction of hot or fresh fluid and the corresponding scalar fluctuations.
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Affiliation(s)
- Kai Leong Chong
- Department of Physics, The Chinese University of Hong Kong, Shatin, Hong Kong, China
| | - Yantao Yang
- Physics of Fluids Group and Max Planck Center Twente, MESA+Institute, J. M. Burgers Centre for Fluid Dynamics, University of Twente, 7500 AE Enschede, Netherlands
- SKLTCS and Department of Mechanics and Engineering Science, College of Engineering, Peking University, Beijing 100871, China
| | - Shi-Di Huang
- Department of Physics, The Chinese University of Hong Kong, Shatin, Hong Kong, China
| | - Jin-Qiang Zhong
- Shanghai Key Laboratory of Special Artificial Microstructure Materials and Technology and School of Physics Science and Engineering, Tongji University, Shanghai 200092, China
| | - Richard J A M Stevens
- Physics of Fluids Group and Max Planck Center Twente, MESA+Institute, J. M. Burgers Centre for Fluid Dynamics, University of Twente, 7500 AE Enschede, Netherlands
| | - Roberto Verzicco
- Physics of Fluids Group and Max Planck Center Twente, MESA+Institute, J. M. Burgers Centre for Fluid Dynamics, University of Twente, 7500 AE Enschede, Netherlands
- Dipartimento di Ingegneria Industriale, University of Rome Tor Vergata, Rome 00133, Italy
| | - Detlef Lohse
- Physics of Fluids Group and Max Planck Center Twente, MESA+Institute, J. M. Burgers Centre for Fluid Dynamics, University of Twente, 7500 AE Enschede, Netherlands
- Max-Planck Institute for Dynamics and Self-Organization, Am Fassberg 17, 37077 Göttingen, Germany
| | - Ke-Qing Xia
- Department of Physics, The Chinese University of Hong Kong, Shatin, Hong Kong, China
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Weiss S, Wei P, Ahlers G. Heat-transport enhancement in rotating turbulent Rayleigh-Bénard convection. Phys Rev E 2016; 93:043102. [PMID: 27176385 DOI: 10.1103/physreve.93.043102] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/22/2015] [Indexed: 06/05/2023]
Abstract
We present new Nusselt-number (Nu) measurements for slowly rotating turbulent thermal convection in cylindrical samples with aspect ratio Γ=1.00 and provide a comprehensive correlation of all available data for that Γ. In the experiment compressed gasses (nitrogen and sulfur hexafluride) as well as the fluorocarbon C_{6}F_{14} (3M Fluorinert FC72) and isopropanol were used as the convecting fluids. The data span the Prandtl-number (Pr) range 0.74<Pr<35.5 and are for Rayleigh numbers (Ra) from 3×10^{8} to 4×10^{11}. The relative heat transport Nu_{r}(1/Ro)≡Nu(1/Ro)/Nu(0) as a function of the dimensionless inverse Rossby number 1/Ro at constant Ra is reported. For Pr≈0.74 and the smallest Ra=3.6×10^{8} the maximum enhancement Nu_{r,max}-1 due to rotation is about 0.02. With increasing Ra, Nu_{r,max}-1 decreased further, and for Ra≳2×10^{9} heat-transport enhancement was no longer observed. For larger Pr the dependence of Nu_{r} on 1/Ro is qualitatively similar for all Pr. As noted before, there is a very small increase of Nu_{r} for small 1/Ro, followed by a decrease by a percent or so, before, at a critical value 1/Ro_{c}, a sharp transition to enhancement by Ekman pumping takes place. While the data revealed no dependence of 1/Ro_{c} on Ra, 1/Ro_{c} decreased with increasing Pr. This dependence could be described by a power law with an exponent α≃-0.41. Power-law dependencies on Pr and Ra could be used to describe the slope S_{Ro}^{+}=∂Nu_{r}/∂(1/Ro) just above 1/Ro_{c}. The Pr and Ra exponents were β_{1}=-0.16±0.08 and β_{2}=-0.04±0.06, respectively. Further increase of 1/Ro led to further increase of Nu_{r} until it reached a maximum value Nu_{r,max}. Beyond the maximum, the Taylor-Proudman (TP) effect, which is expected to lead to reduced vertical fluid transport in the bulk region, lowered Nu_{r}. Nu_{r,max} was largest for the largest Pr. For Pr=28.9, for example, we measured an increase of the heat transport by up to 40% (Nu_{r}-1=0.40) for the smallest Ra=2.2×10^{9}, even though we were unable to reach Nu_{r,max} over the accessible 1/Ro range. Both Nu_{r,max}(Pr,Ra) and its location 1/Ro_{max}(Pr,Ra) along the 1/Ro axis increased with Pr and decreased with Ra. Although both could be given by power-law representations, the uncertainties of the exponents are relatively large.
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Affiliation(s)
- Stephan Weiss
- Department of Physics, University of California, Santa Barbara, California 93106, USA
- Max Planck Institute for Dynamics and Self-Organization (MPIDS), D-37077 Göttingen, Germany
| | - Ping Wei
- Department of Physics, University of California, Santa Barbara, California 93106, USA
| | - Guenter Ahlers
- Department of Physics, University of California, Santa Barbara, California 93106, USA
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6
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Bai K, Ji D, Brown E. Ability of a low-dimensional model to predict geometry-dependent dynamics of large-scale coherent structures in turbulence. Phys Rev E 2016; 93:023117. [PMID: 26986423 DOI: 10.1103/physreve.93.023117] [Citation(s) in RCA: 24] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/19/2015] [Indexed: 11/07/2022]
Abstract
We test the ability of a general low-dimensional model for turbulence to predict geometry-dependent dynamics of large-scale coherent structures, such as convection rolls. The model consists of stochastic ordinary differential equations, which are derived as a function of boundary geometry from the Navier-Stokes equations [Brown and Ahlers, Phys. Fluids 20, 075101 (2008); Phys. Fluids 20, 105105 (2008)]. We test the model using Rayleigh-Bénard convection experiments in a cubic container. The model predicts a mode in which the alignment of a convection roll stochastically crosses a potential barrier to switch between diagonals. We observe this mode with a measured switching rate within 30% of the prediction.
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Affiliation(s)
- Kunlun Bai
- Department of Mechanical Engineering and Materials Science, Yale University, New Haven, Connecticut 06511, USA
| | - Dandan Ji
- Department of Mechanical Engineering and Materials Science, Yale University, New Haven, Connecticut 06511, USA
| | - Eric Brown
- Department of Mechanical Engineering and Materials Science, Yale University, New Haven, Connecticut 06511, USA
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7
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Canonical Models of Geophysical and Astrophysical Flows: Turbulent Convection Experiments in Liquid Metals. METALS 2015. [DOI: 10.3390/met5010289] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/16/2022]
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8
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Ecke RE, Niemela JJ. Heat transport in the geostrophic regime of rotating Rayleigh-Bénard convection. PHYSICAL REVIEW LETTERS 2014; 113:114301. [PMID: 25259983 DOI: 10.1103/physrevlett.113.114301] [Citation(s) in RCA: 18] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/19/2013] [Indexed: 06/03/2023]
Abstract
We report experimental measurements of heat transport in rotating Rayleigh-Bénard convection in a cylindrical convection cell with an aspect ratio of Γ=1/2. The fluid is helium gas with a Prandtl number Pr=0.7. The range of control parameters for Rayleigh numbers 4×10^{9}<Ra<4×10^{11} and for Ekman numbers 2×10^{-7}<Ek<3×10^{-5} (corresponding to Taylor numbers 4×10^{9}<Ta<1×10^{14} and convective Rossby numbers 0.07<Ro<5). We determine the transition from weakly rotating turbulent convection to rotation dominated geostrophic convection through experimental measurements of the heat transport Nu. The heat transport, best collapsed using a parameter RaEk^{β} with 1.65<β<1.8, defines two boundaries in the phase diagram of Ra/Ra_{c} versus Ek and elucidates properties of the geostrophic turbulence regime of rotating thermal convection. We find Nu∼(Ra/Ra_{c})^{γ} with γ≈1 from direct measurement and 1.2<γ<1.6 inferred from scaling arguments.
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Affiliation(s)
- Robert E Ecke
- Center for Nonlinear Studies, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
| | - Joseph J Niemela
- International Centre for Theoretical Physics, Strada Costiera 11, 34014 Trieste, Italy
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Abstract
The magnetic fields of Earth and other planets are generated by turbulent, rotating convection in liquid metal. Liquid metals are peculiar in that they diffuse heat more readily than momentum, quantified by their small Prandtl numbers, Pr << 1. Most analog models of planetary dynamos, however, use moderate Pr fluids, and the systematic influence of reducing Pr is not well understood. We perform rotating Rayleigh-Bénard convection experiments in the liquid metal gallium (Pr = 0.025) over a range of nondimensional buoyancy forcing (Ra) and rotation periods (E). Our primary diagnostic is the efficiency of convective heat transfer (Nu). In general, we find that the convective behavior of liquid metal differs substantially from that of moderate Pr fluids, such as water. In particular, a transition between rotationally constrained and weakly rotating turbulent states is identified, and this transition differs substantially from that observed in moderate Pr fluids. This difference, we hypothesize, may explain the different classes of magnetic fields observed on the Gas and Ice Giant planets, whose dynamo regions consist of Pr < 1 and Pr > 1 fluids, respectively.
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10
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Julien K, Knobloch E, Rubio AM, Vasil GM. Heat transport in low-Rossby-number Rayleigh-Bénard convection. PHYSICAL REVIEW LETTERS 2012; 109:254503. [PMID: 23368470 DOI: 10.1103/physrevlett.109.254503] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/16/2012] [Revised: 10/17/2012] [Indexed: 06/01/2023]
Abstract
We demonstrate, via simulations of asymptotically reduced equations describing rotationally constrained Rayleigh-Bénard convection, that the efficiency of turbulent motion in the fluid bulk limits overall heat transport and determines the scaling of the nondimensional Nusselt number Nu with the Rayleigh number Ra, the Ekman number E, and the Prandtl number σ. For E << 1 inviscid scaling theory predicts and simulations confirm the large Ra scaling law Nu-1 ≈ C(1)σ(-1/2)Ra(3/2)E(2), where C(1) is a constant, estimated as C(1) ≈ 0.04 ± 0.0025. In contrast, the corresponding result for nonrotating convection, Nu-1 ≈ C(2)Ra(α), is determined by the efficiency of the thermal boundary layers (laminar: 0.28 ≤ α ≤ 0.31, turbulent: α ~ 0.38). The 3/2 scaling law breaks down at Rayleigh numbers at which the thermal boundary layer loses rotational constraint, i.e., when the local Rossby number ≈ 1. The breakdown takes place while the bulk Rossby number is still small and results in a gradual transition to the nonrotating scaling law. For low Ekman numbers the location of this transition is independent of the mechanical boundary conditions.
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Affiliation(s)
- Keith Julien
- Department of Applied Mathematics, University of Colorado, Boulder, Colorado 80309, USA
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Stevens RJAM, Clercx HJH, Lohse D. Breakdown of the large-scale circulation in Γ=1/2 rotating Rayleigh-Bénard flow. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2012; 86:056311. [PMID: 23214880 DOI: 10.1103/physreve.86.056311] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/25/2012] [Revised: 09/09/2012] [Indexed: 06/01/2023]
Abstract
Experiments and simulations of rotating Rayleigh-Bénard convection in cylindrical samples have revealed an increase in heat transport with increasing rotation rate. This heat transport enhancement is intimately related to a transition in the turbulent flow structure from a regime dominated by a large-scale circulation (LSC), consisting of a single convection roll, at no or weak rotation to a regime dominated by vertically aligned vortices at strong rotation. For a sample with an aspect ratio Γ=D/L=1 (D is the sample diameter and L is its height) the transition between the two regimes is indicated by a strong decrease in the LSC strength. In contrast, for Γ=1/2, Weiss and Ahlers [J. Fluid Mech. 688, 461 (2011)] revealed the presence of a LSC-like sidewall temperature signature beyond the critical rotation rate. They suggested that this might be due to the formation of a two-vortex state, in which one vortex extends vertically from the bottom into the sample interior and brings up warm fluid while another vortex brings down cold fluid from the top; this flow field would yield a sidewall temperature signature similar to that of the LSC. Here we show by direct numerical simulations for Γ=1/2 and parameters that allow direct comparison with experiment that the spatial organization of the vertically aligned vortical structures in the convection cell do indeed yield (for the time average) a sinusoidal variation of the temperature near the sidewall, as found in the experiment. This is also the essential and nontrivial difference with the Γ=1 sample, where the vertically aligned vortices are distributed randomly.
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Affiliation(s)
- Richard J A M Stevens
- Department of Science and Technology and J.M. Burgers Center for Fluid Dynamics, University of Twente, Post Office Box 217, 7500 AE Enschede, The Netherlands
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Pharasi HK, Kannan R, Kumar K, Bhattacharjee JK. Turbulence in rotating Rayleigh-Bénard convection in low-Prandtl-number fluids. Phys Rev E 2011; 84:047301. [PMID: 22181319 DOI: 10.1103/physreve.84.047301] [Citation(s) in RCA: 11] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/28/2011] [Indexed: 11/07/2022]
Abstract
The heat flux in rotating Rayleigh-Bénard convection in a fluid of Prandtl number Pr=0.1 enclosed between free-slip top and bottom boundaries is investigated using direct numerical simulation in a wide range of Rayleigh numbers (10(4)≤Ra≤10(8)) and Taylor numbers (0≤Ta≤10(8)). The Nusselt number Nu scales with the Rayleigh number Ra as Ra(β) with β=2/7 for values of Nu greater than a critical value Nu(c), which occurs for Ta/Ra∼1. The exponent β is not universal for Nu<Nu(c) (for Ta/Ra>1) but a function of Ta showing a minimum for some intermediate value of Ta. The critical Nusselt number Nu(c) and the corresponding critical Rossby number Ro(c) scale with Ta as Ta(0.277±0.001) and Ta(-0.015±0.003), respectively.
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Affiliation(s)
- Hirdesh K Pharasi
- Department of Physics and Meteorology, Indian Institute of Technology, Kharagpur-721 302, India
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Stevens RJAM, Overkamp J, Lohse D, Clercx HJH. Effect of aspect ratio on vortex distribution and heat transfer in rotating Rayleigh-Bénard convection. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2011; 84:056313. [PMID: 22181504 DOI: 10.1103/physreve.84.056313] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/23/2011] [Indexed: 05/31/2023]
Abstract
Numerical and experimental data for the heat transfer as a function of the Rossby number Ro in turbulent rotating Rayleigh-Bénard convection are presented for the Prandtl number Pr=4.38 and the Rayleigh number Ra=2.91×10(8) up to Ra=4.52×10(9). The aspect ratio Γ≡D/L, where L is the height and D the diameter of the cylindrical sample, is varied between Γ=0.5 and 2.0. Without rotation, where the aspect ratio influences the global large-scale circulation, we see a small-aspect-ratio dependence in the Nusselt number for Ra=2.91×10(8). However, for stronger rotation, i.e., 1/Ro>>1/Ro(c), the heat transport becomes independent of the aspect ratio. We interpret this finding as follows: In the rotating regime the heat is mainly transported by vertically aligned vortices. Since the vertically aligned vortices are local, the aspect ratio has a negligible effect on the heat transport in the rotating regime. Indeed, a detailed analysis of vortex statistics shows that the fraction of the horizontal area that is covered by vortices is independent of the aspect ratio when 1/Ro>>1/Ro(c). In agreement with the results of Weiss et al. [Phys. Rev. Lett. 105, 224501 (2010)], we find a vortex-depleted area close to the sidewall. Here we show that there is also an area with enhanced vortex concentration next to the vortex-depleted edge region and that the absolute widths of both regions are independent of the aspect ratio.
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Affiliation(s)
- Richard J A M Stevens
- Department of Science and Technology, University of Twente, Enschede, The Netherlands
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Liu Y, Ecke RE. Local temperature measurements in turbulent rotating Rayleigh-Bénard convection. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2011; 84:016311. [PMID: 21867308 DOI: 10.1103/physreve.84.016311] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/09/2011] [Indexed: 05/31/2023]
Abstract
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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Affiliation(s)
- Yuanming Liu
- Center for Nonlinear Studies, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
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