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Rayleigh and Prandtl number scaling in the bulk of Rayleigh-Bénard turbulence (Articolo in rivista)
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- Rayleigh and Prandtl number scaling in the bulk of Rayleigh-Bénard turbulence (Articolo in rivista) (literal)
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- 2005-01-01T00:00:00+01:00 (literal)
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Calzavarini E., Lohse D., Toschi F., Tripiccione R. (2005)
Rayleigh and Prandtl number scaling in the bulk of Rayleigh-Bénard turbulence
in Physics of fluids (1994)
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- Calzavarini E., Lohse D., Toschi F., Tripiccione R. (literal)
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- Dipartimento di Fisica, Università di Ferrara, Via Paradiso 12, I-43100 Ferrara, Italy and INFN, Via Paradiso 12, I-43100 Ferrara, Italy
Department of Applied Physics and J. M. Burgers Centre for Fluid Dynamics, University of Twente, 7500 AE Enschede, The Netherlands
IAC-CNR, Istituto per le Applicazioni del Calcolo and INFN, Via Paradiso 12, I-43100 Ferrara, Italy Viale del Policlinico 137, I-00161 Roma, Italy
Dipartimento di Fisica, Università di Ferrara, Via Paradiso 12, I-43100 Ferrara, Italy and INFN, Via Paradiso 12, I-43100 Ferrara, Italy (literal)
- Titolo
- Rayleigh and Prandtl number scaling in the bulk of Rayleigh-Bénard turbulence (literal)
- Abstract
- The Ra and Pr number scaling of the Nusselt number Nu, the Reynolds number Re, the temperature fluctuations, and the kinetic and thermal dissipation rates is studied for (numerical) homogeneous RayleighBénard turbulence, i.e., RayleighBénard turbulence with periodic boundary conditions in all directions and a volume forcing of the temperature field by a mean gradient. This system serves as model system for the bulk of RayleighBénard flow and therefore as model for the so-called \"ultimate regime of thermal convection.\" With respect to the Ra dependence of Nu and Re we confirm our earlier results [D. Lohse and F. Toschi, \"The ultimate state of thermal convection,\" Phys. Rev. Lett. 90, 034502 (2003)] which are consistent with the Kraichnan theory [R. H. Kraichnan, \"Turbulent thermal convection at arbitrary Prandtl number,\" Phys. Fluids 5, 1374 (1962)] and the GrossmannLohse (GL) theory [S. Grossmann and D. Lohse, \"Scaling in thermal convection: A unifying view,\" J. Fluid Mech. 407, 27 (2000); \"Thermal convection for large Prandtl number,\" Phys. Rev. Lett. 86, 3316 (2001); \"Prandtl and Rayleigh number dependence of the Reynolds number in turbulent thermal convection,\" Phys. Rev. E 66, 016305 (2002); \"Fluctuations in turbulent RayleighBénard convection: The role of plumes,\" Phys. Fluids 16, 4462 (2004)], which both predict Nu~Ra1/2 and Re~Ra1/2. However the Pr dependence within these two theories is different. Here we show that the numerical data are consistent with the GL theory Nu~Pr1/2, Re~Pr1/2. For the thermal and kinetic dissipation rates we find epsilontheta/(kappaDelta2L2)~(Re Pr)0.87 and epsilonu/(nu3L4)~Re2.77, both near (but not fully consistent) the bulk dominated behavior, whereas the temperature fluctuations do not depend on Ra and Pr. Finally, the dynamics of the heat transport is studied and put into the context of a recent theoretical finding by Doering et al. [\"Comment on ultimate state of thermal convection\" (private communication)]. (literal)
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