Dynamics of large-scale quantities in Rayleigh-Bénard convection

Ambrish Pandey; Abhishek Kumar; Anando G. Chatterjee; Mahendra K. Verma

doi:10.1103/PhysRevE.94.053106

Dynamics of large-scale quantities in Rayleigh-Bénard convection

Ambrish Pandey, Abhishek Kumar, Anando G. Chatterjee, Mahendra K. Verma

Indian Institute of Technology Kanpur

Research output: Contribution to journal › Article › peer-review

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Abstract

In this paper we estimate the relative strengths of various terms of the Rayleigh-Bénard equations. Based on these estimates and scaling analysis, we derive a general formula for the large-scale velocity U or the Péclet number that is applicable for arbitrary Rayleigh number Ra and Prandtl number Pr. Our formula fits reasonably well with the earlier simulation and experimental results. Our analysis also shows that the wall-bounded convection has enhanced viscous force compared to free turbulence. We also demonstrate how correlations deviate the Nusselt number scaling from the theoretical prediction of Ra1/2 to the experimentally observed scaling of nearly Ra0.3.

Original language	English
Article number	053106
Number of pages	7
Journal	Physical Review E
Volume	94
DOIs	https://doi.org/10.1103/PhysRevE.94.053106
Publication status	Published - 7 Nov 2016
Externally published	Yes

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title = "Dynamics of large-scale quantities in Rayleigh-B{\'e}nard convection",

abstract = "In this paper we estimate the relative strengths of various terms of the Rayleigh-B{\'e}nard equations. Based on these estimates and scaling analysis, we derive a general formula for the large-scale velocity U or the P{\'e}clet number that is applicable for arbitrary Rayleigh number Ra and Prandtl number Pr. Our formula fits reasonably well with the earlier simulation and experimental results. Our analysis also shows that the wall-bounded convection has enhanced viscous force compared to free turbulence. We also demonstrate how correlations deviate the Nusselt number scaling from the theoretical prediction of Ra1/2 to the experimentally observed scaling of nearly Ra0.3.",

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AU - Pandey, Ambrish

AU - Kumar, Abhishek

AU - Chatterjee, Anando G.

AU - Verma, Mahendra K.

N1 - Copyright © and Moral Rights are retained by the author(s) and/ or other copyright owners. A copy can be downloaded for personal non-commercial research or study, without prior permission or charge. This item cannot be reproduced or quoted extensively from without first obtaining permission in writing from the copyright holder(s). The content must not be changed in any way or sold commercially in any format or medium without the formal permission of the copyright holders.

PY - 2016/11/7

Y1 - 2016/11/7

N2 - In this paper we estimate the relative strengths of various terms of the Rayleigh-Bénard equations. Based on these estimates and scaling analysis, we derive a general formula for the large-scale velocity U or the Péclet number that is applicable for arbitrary Rayleigh number Ra and Prandtl number Pr. Our formula fits reasonably well with the earlier simulation and experimental results. Our analysis also shows that the wall-bounded convection has enhanced viscous force compared to free turbulence. We also demonstrate how correlations deviate the Nusselt number scaling from the theoretical prediction of Ra1/2 to the experimentally observed scaling of nearly Ra0.3.

AB - In this paper we estimate the relative strengths of various terms of the Rayleigh-Bénard equations. Based on these estimates and scaling analysis, we derive a general formula for the large-scale velocity U or the Péclet number that is applicable for arbitrary Rayleigh number Ra and Prandtl number Pr. Our formula fits reasonably well with the earlier simulation and experimental results. Our analysis also shows that the wall-bounded convection has enhanced viscous force compared to free turbulence. We also demonstrate how correlations deviate the Nusselt number scaling from the theoretical prediction of Ra1/2 to the experimentally observed scaling of nearly Ra0.3.

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DO - 10.1103/PhysRevE.94.053106

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VL - 94

JO - Physical Review E

JF - Physical Review E

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ER -

Dynamics of large-scale quantities in Rayleigh-Bénard convection

Abstract

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