The spatial structure of turbulent Rayleigh-Benard convection

The main objective of this study was to examine the spatial structure of turbulent Rayleigh-Benard convection in a high aspect-ratio experimental cell. Particle-image velocimetry was used to obtain an ensemble of velocity fields that was used to calculate the two-point velocity correlation tensor R_ij(x,x′ ). Proper orthogonal decomposition and linear stochastic estimation were used to interpret the information contained in the velocity correlation tensor.; Turbulent Rayleigh-Benard convection in high aspect-ratio cells was found to be horizontally homogeneous, statistically axisymmetric about the vertical axis, and reflectionally symmetric about vertical planes. The visualization of the large-scale motions by linear stochastic estimation was consistent with vertical sections through circulation cells encompassing the layer depth.; The two-dimensional proper orthogonal decomposition (POD) of the velocity correlation tensor was used to examine the distribution of turbulent kinetic energy among the scales. The large scales, represented by the low-order POD modes, were found to contain most of the kinetic energy. In particular, the nine lowest-order modes, which represent less than 0.1% of the total number of modes in the decomposition, carry approximately 60% of the energy. The large-scale structures, which were visualized by projecting individual PIV realizations onto a small set of the low-order modes, were consistent with vertical sections through circulation cells that encompass the layer depth.; The circulation cells visualized in the present study are a manifestation, in the fully turbulent regime, of the cellular structures commonly observed at low Rayleigh numbers. The circulation cells are proposed as a physical description (not an explanation) of the phenomenon referred to in the literature as the wind of turbulence. They were found to contain approximately 40% of the total kinetic energy, and this fraction was found to be approximately independent of the Rayleigh number. This leads to the conclusion that the wind of turbulence (U) scales with the velocity fluctuations (u_fluct), U ∼ u _fluct. The visualizations indicate that the large-scale circulation engulfs the small-scale structures and advect them across the layer. The engulfment of small-scale buoyant elements may be the mechanism by which the large-scale circulation obtains the buoyancy required to maintain its kinetic energy.