How is the large-scale flow influenced by the aspect-ratio in turbulent cylindrical Rayleigh-B\'enard samples?*

In turbulent Rayleigh-B\'enard convection the fluid develops a large-scale flow (LSF). The shadowgraph method is used to visualize plumes in cylindrical samples that are emitted from a top and bottom boundary layer. These plumes serve as tracers of the LSF. In aspect-ratio $\Gamma \equiv D/L$ = 1 ($D$ and $L$ are the diameter and height of the cell respectively), the LSF consists of a single roll circulating in a near-vertical plane and oscillating azimuthally with a well defined frequency\footnote{D. Funfschilling and G. Ahlers, Phys. Rev. Lett. {\bf 92}, 194502 (2004).}. For $\Gamma$ = 2 and 3, the LSF still consists of a single roll but has no detectable oscillations. For $\Gamma$ = 2 and 3 the ``density" of plumes above the bottom plate (the ratio of the area occupied by the plumes to the total area) does show clear oscillations at a well defined frequency. This later observation adds new interest to a model of plume emission by Villermaux\footnote{E. Villermaux, Phys. Rev. Lett. {\bf 75}, 4618 (1995)}. Our results provide evidence for a transition in the LSF dynamics between $\Gamma$ = 1 and $\Gamma$ = 2.