Breakdown of wind in turbulent thermal convection

Abstract

We report experiments on turbulent Rayleigh-B\'enard convection of air in a cylindrical large-scale facility with a diameter of $7\phantom{\rule{0.3em}{0ex}}\text{meters}$ and Rayleigh numbers up to $\mathrm{Ra}\ensuremath{\approx}{10}^{12}$. The facility is used to explore the structure of the large-scale circulation for continuously varying aspect ratios between $\ensuremath{\Gamma}\ensuremath{\approx}1$ and $\ensuremath{\Gamma}\ensuremath{\approx}10$. Using autocorrelation functions derived from high-resolution time series of temperature and velocity near the cooling plate we demonstrate that the well-known single-roll structure (often called ``wind'') breaks down when the aspect ratio increases beyond the critical value ${\ensuremath{\Gamma}}_{1}=1.68\ifmmode\pm\else\textpm\fi{}0.22$. We further show that at ${\ensuremath{\Gamma}}_{2}=3.66\ifmmode\pm\else\textpm\fi{}0.46$ a second transition from an oscillatory two-roll structure to an unstable multi-roll structure takes place. The value of ${\ensuremath{\Gamma}}_{2}$ represents a lower bound for the aspect ratio that is necessary to reach homogeneous convection---a turbulent state that is free from the influence of lateral walls.