Breakdown of the large-scale wind in \Gamma=1/2 rotating Rayleigh-B\'enard flow

Experiments and simulations of rotating Rayleigh-B\'enard convection in cylindrical samples have revealed an increase in heat transport with increasing rotation rate. This heat transport enhancement is intimately related to a transition in the turbulent flow structure from a regime dominated by a large-scale circulation (LSC), consisting of a single convection roll, at no or weak rotation to a regime dominated by vertically-aligned vortices at strong rotation. For a sample with an aspect ratio \Gamma = D/L = 1 (D is the sample diameter and L its height) the transition between the two regimes is indicated by a strong decrease in the LSC strength. In contrast, for \Gamma = 1/2 Weiss and Ahlers [J. Fluid Mech. {\bf{688}}, 461 (2011)] revealed the presence of a LSC-like sidewall temperature signature beyond the critical rotation rate. They suggested that this might be due to the formation of a two-vortex state, in which one vortex extends vertically from the bottom into the sample interior and brings up warm fluid, while another vortex brings down cold fluid from the top; this flow field would yield a sidewall temperature signature similar to that of the LSC. Here we show by direct numerical simulations for \Gamma= 1/2 and parameters that allow direct comparison with experiment that the spatial organization of the vertically-aligned vortical structures in the convection cell do indeed yield (for the time average) a sinusoidal variation of the temperature near the sidewall, as found in the experiment. This is also the essential and non-trivial difference with the \Gamma=1 sample, where the vertically-aligned vortices are distributed randomly.