Revisiting Reynolds and Nusselt numbers in turbulent thermal convection
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AbstractIn 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
CitationBhattacharya, S., Verma, M. K., & Samtaney, R. (2021). Revisiting Reynolds and Nusselt numbers in turbulent thermal convection. Physics of Fluids, 33(1), 015113. doi:10.1063/5.0032498
SponsorsThe 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.
JournalPhysics of Fluids