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  Scaling relations in large-Prandtl-number natural thermal convection

Shishkina, O., Emran, M. S., Grossmann, S., & Lohse, D. (2017). Scaling relations in large-Prandtl-number natural thermal convection. Physical Review Fluids, 2(10): 103502. doi:10.1103/PhysRevFluids.2.103502.

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Item Permalink: http://hdl.handle.net/11858/00-001M-0000-002E-24C6-9 Version Permalink: http://hdl.handle.net/21.11116/0000-0003-D980-7
Genre: Journal Article

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Shishkina, Olga1, Author              
Emran, Mohammad Shah1, Author              
Grossmann, S., Author
Lohse, Detlef2, Author              
Affiliations:
1Laboratory for Fluid Dynamics, Pattern Formation and Biocomplexity, Max Planck Institute for Dynamics and Self-Organization, Max Planck Society, ou_2063287              
2Max Planck Institute for Dynamics and Self-Organization, Max Planck Society, ou_2063285              

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Free keywords: Boundary layers; Convection & buoyancy-driven flows; Free convection; Geophysical fluid dynamics; Rayleigh-Bénard convection; Turbulent convection
 Abstract: In this study, we follow Grossmann and Lohse [Phys. Rev. Lett. 86, 3316 (2001)], who derived various scalings regimes for the dependence of the Nusselt number Nu and the Reynolds number Re on the Rayleigh number Ra and the Prandtl number Pr. We focus on theoretical arguments as well as on numerical simulations for the case of large-Pr natural thermal convection. Based on an analysis of self-similarity of the boundary layer equations, we derive that in this case the limiting large-Pr boundary-layer dominated regime is I-infinity(<), introduced and defined by Grossmann and Lohse [Phys. Rev. Lett. 86, 3316 (2001)], with the scaling relations Nu similar to Pr-0 Ra-1/3 and Re similar to Pr-1 Ra-2/3. Our direct numerical simulations for Ra from 10(4) to 10(9) and Pr from 0.1 to 200 showthat the regime I-infinity(<) is almost indistinguishable from the regime III infinity, where the kinetic dissipation is bulk-dominated. With increasing Ra, the scaling relations undergo a transition to those in IVu of Grossmann and Lohse [Phys. Rev. Lett. 86, 3316 (2001)], where the thermal dissipation is determined by its bulk contribution.

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Language(s): eng - English
 Dates: 2017-10-25
 Publication Status: Published online
 Pages: -
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 Table of Contents: -
 Rev. Method: Peer
 Identifiers: DOI: 10.1103/PhysRevFluids.2.103502
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Title: Physical Review Fluids
Source Genre: Journal
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Pages: 9 Volume / Issue: 2 (10) Sequence Number: 103502 Start / End Page: - Identifier: -