Revisiting Reynolds and Nusselt numbers in turbulent thermal convection

TL;DR

This paper refines the Grossmann-Lohse model for turbulent Rayleigh-Bénard convection by incorporating wall effects and buoyancy influences, leading to more accurate predictions of flow parameters across a range of conditions.

Contribution

It introduces functional forms for dissipation rate prefactors based on wall and buoyancy effects, improving the model's accuracy with machine learning calibration.

Findings

Enhanced model predictions align better with numerical and experimental data.

Improved accuracy at extreme Prandtl numbers.

Validated functional forms through extensive numerical simulations.

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-B\'{e}nard 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.