Scaling of hard thermal turbulence in Rayleigh-Bénard convection

TLDR

The study assumes the boundary layer persists and diverges even when its Rayleigh number greatly exceeds unity. The authors propose a new scaling theory for hard thermal turbulence. Experiments were conducted in a helium cell at ~5 K with aspect ratio 1, analyzing hard‑turbulence data (Ra 4×10⁷–6×10¹², Pr 0.65–1.5) and performing a stability analysis showing buoyancy–wind interactions can stabilize the boundary layer. They observed a simple scaling of the Nusselt number over the entire Ra range, with an exponent near 2/7 rather than the classical 1/3, and the new theory predicts indices close to this value.

Abstract

An experimental study of Rayleigh-Bénard convection in helium gas at roughly 5 K is performed in a cell with aspect ratio 1. Data are analysed in a ‘hard turbulence’ region (4 × 10 7 < Ra < 6 × 10 12 ) in which the Prandtl number remains between 0.65 and 1.5. The main observation is a simple scaling behaviour over this entire range of Ra . However the results are not the same as in previous theories. For example, a classical result gives the dimensionless heat flux, Nu , proportional to $Ra^{\frac{1}{3}}$ while experiment gives an index much closer to $\frac{2}{7}$ . A new scaling theory is described. This new approach suggests scaling indices very close to the observed ones. The new approach is based upon the assumption that the boundary layer remains in existence even though its Rayleigh number is considerably greater than unity and is, in fact, diverging. A stability analysis of the boundary layer is performed which indicates that the boundary layer may be stabilized by the interaction of buoyancy driven effects and a fluctuating wind.