Revisiting Reynolds and Nusselt numbers in turbulent thermal convection

Abstract

In this paper, we extend Grossmann and Lohse's (GL) model [Phys. Rev. Lett. {\bf 86}, 3316 (2001)] for the predictions of Reynolds number (Re) and Nusselt number (Nu) in turbulent Rayleigh-Bénard convection (RBC). Towards this objective, we use functional forms for the prefactors of the dissipation rates in the bulk and the boundary layers. The functional forms arise due to inhibition of nonlinear interactions in the presence of walls and buoyancy compared to free turbulence, along with a deviation of viscous boundary layer profile from Prandtl-Blasius theory. We perform 60 numerical runs on a three-dimensional unit box for a range of Rayleigh numbers (Ra) and Prandtl numbers (Pr) and determine the aforementioned functional forms using machine learning. The revised predictions are in better agreement with the past numerical and experimental results than those of the GL model, especially for extreme Prandtl numbers.

arXiv comment16 pages, 9 figures

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Cited by in corpus (7)

• Predictions of Reynolds and Nusselt numbers in turbulent convection using machine-learning models
• Large-eddy simulation of Rayleigh-Bénard convection at extreme Rayleigh numbers
• Prandtl number dependence of the small-scale properties in turbulent Rayleigh-Bénard convection
• Convective heat transport in slender cells is close to that in wider cells at high Rayleigh and Prandtl numbers
• Refined mean field model of heat and momentum transfer in magnetoconvection
• Effects of strong fringing magnetic fields on turbulent thermal convection
• The effect of tilt on turbulent thermal convection for a heated soap bubble