Most theoretical studies of Rayleigh–Bénard Convection assume that the velocity boundary layer develops on the whole width or height $H$ of the convection cell, or that the development length $h$ scales with $H$. We argue that it is probably not the case, and examine the consequences of an intermediate asymptotics hypothesis in the sense of Barenblatt [1], the development length $h$ scaling with the Nusselt number: $h\propto H\mathrm{Nu}^{-\alpha }$. This hypothesis is checked through existing experimental data, which show that $\alpha $ can take several different values. The analysis of Grossmann and Lohse [2] is reexamined with this new point of view, stressing on pure scaling regimes.
La plupart des études théoriques sur la convection de Rayleigh–Bénard supposent que la couche limite de vitesse se développe sur toute la largeur ou la hauteur $H$ de la cellule de convection, ou que la longueur de développement $h$ est proportionnelle à $H$. Nous soutenons qu’il est probablement incorrect de faire cette supposition, et nous examinons les conséquences d’une hypothèse d’asymptotique intermédiaire au sens de Barenblatt [1], où la longueur de développement $h$ dépend du nombre de Nusselt : $h \propto H\mathrm{Nu}^{-\alpha }$. Cette hypothèse est vérifiée à partir de données expérimentales existantes, qui montrent que $\alpha $ peut prendre plusieurs valeurs différentes. L’analyse de Grossmann et Lohse [2] est réexaminée sous cette nouvelle perspective, en mettant l’accent sur les régimes d’échelle pure.
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Mots-clés : Hydrodynamique, Convection thermique, Turbulence, Couches limites, Lois d’échelle
Bernard Castaing 1; Francesca Chillà 2; Julien Salort 2; Yann Fraigneau 3; Anne Sergent 3
CC-BY 4.0
@article{CRPHYS_2025__26_G1_587_0,
author = {Bernard Castaing and Francesca Chill\`a and Julien Salort and Yann Fraigneau and Anne Sergent},
title = {The inertial regimes in {Rayleigh{\textendash}B\'enard} convection},
journal = {Comptes Rendus. Physique},
pages = {587--617},
year = {2025},
publisher = {Acad\'emie des sciences, Paris},
volume = {26},
doi = {10.5802/crphys.257},
language = {en},
}
TY - JOUR AU - Bernard Castaing AU - Francesca Chillà AU - Julien Salort AU - Yann Fraigneau AU - Anne Sergent TI - The inertial regimes in Rayleigh–Bénard convection JO - Comptes Rendus. Physique PY - 2025 SP - 587 EP - 617 VL - 26 PB - Académie des sciences, Paris DO - 10.5802/crphys.257 LA - en ID - CRPHYS_2025__26_G1_587_0 ER -
%0 Journal Article %A Bernard Castaing %A Francesca Chillà %A Julien Salort %A Yann Fraigneau %A Anne Sergent %T The inertial regimes in Rayleigh–Bénard convection %J Comptes Rendus. Physique %D 2025 %P 587-617 %V 26 %I Académie des sciences, Paris %R 10.5802/crphys.257 %G en %F CRPHYS_2025__26_G1_587_0
Bernard Castaing; Francesca Chillà; Julien Salort; Yann Fraigneau; Anne Sergent. The inertial regimes in Rayleigh–Bénard convection. Comptes Rendus. Physique, Volume 26 (2025), pp. 587-617. doi: 10.5802/crphys.257
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