Reynolds numbers of the large-scale flow in turbulent Rayleigh-Benard Convection

TL;DR

This study measures Reynolds numbers in turbulent Rayleigh-Benard convection across a wide range of parameters, confirming some theoretical predictions while revealing a sharp transition that challenges existing models.

Contribution

It provides extensive experimental data on Reynolds numbers over a broad parameter space and identifies a transition point where the Grossmann-Lohse theory no longer applies.

Findings

Reynolds number scales as R^0.46 below R_c

Reynolds number scales as sigma^-3/4 R^1/2 above R_c

Sharp transition at R_c indicates a change in flow regime

Abstract

We measured Reynolds numbers R_e of turbulent Rayleigh-Benard convection over the Rayleigh-number range 2 times 10^8 < R < 10^11 and Prandtl-number range 3.3 < sigma < 29 for cylindrical samples of aspect ratio Gamma = 1. For R < R_c = 3 times 10^9 we found R_e ~ R^beta_eff with beta_eff = 0.46 < 1/2. Here both the sigma- and R-dependences are quantitatively consistent with the Grossmann-Lohse (GL) prediction. For R > R_c we found R_e = 0.106 sigma^-3/4 R^1/2, which differs from the GL prediction. The relatively sharp transition at R_c to the large-R regime suggests a qualitative and sudden change that renders the GL prediction inapplicable.