Forecasting Reynolds and Nusselt numbers in turbulent thermal convection using modified Grossmann-Lohse model

Abstract

In this paper, we revise Grossmann and Lohse's model [Phys. Rev. Lett. 86, 3316 (2001)] for the predictions of Reynolds number (Re) and Nusselt number (Nu) in turbulent Rayleigh-B\'{e}nard convection (RBC). The revision incorporates two anomalies observed in thermal convection: the viscous and thermal dissipation rates in the bulk are suppressed compared to free turbulence, and the viscous boundary layer profile deviates from Prandtl-Blasius theory. We perform 60 numerical runs on a three-dimensional unit box for range of Rayleigh numbers (Ra) and Prandtl numbers (Pr) and construct the revised model using four free constants (more appropriately, functions) that are determined using machine learning. The predictions of the revised model are in good agreement with the past numerical and experimental results, and they are sometimes better than those of Grossmann and Lohse's model.