Abstract
In this paper, we extend Grossmann and Lohse’s (GL) model [S. Grossmann and D. Lohse, “Thermal convection for large Prandtl numbers,”
Phys. Rev. Lett. 86, 3316 (2001)] for the predictions of Reynolds number (Re) and Nusselt number (Nu) in turbulent Rayleigh–Bénard
convection. Toward this objective, we use functional forms for the prefactors of the dissipation rates in the bulk and 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 the 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
| Original language | English (US) |
|---|---|
| Pages (from-to) | 015113 |
| Journal | Physics of Fluids |
| Volume | 33 |
| Issue number | 1 |
| DOIs | |
| State | Published - Jan 1 2021 |
Bibliographical note
KAUST Repository Item: Exported on 2021-01-13Acknowledgements: The authors thank Arnab Bhattacharya, K. R. Sreenivasan, Jörg Schumacher, and Ambrish Pandey for useful discussions. The authors thank Roshan Samuel, Ali Asad, Soumyadeep Chatterjee, and Syed Fahad Anwer for their contributions to the development of the finite-difference solver SARAS. Our numerical simulations were performed on Shaheen II of KAUST supercomputing laboratory, Saudi Arabia (Project No. k1416) and on HPC2013 of IIT Kanpur, India.