Turbulent thermal superstructures in Rayleigh-Benard convection

We report the observation of superstructures, i.e., very large-scale and long living coherent structures in highly turbulent Rayleigh-Benard convection up to Rayleigh Ra = 10(9). We perform direct numerical simulations in horizontally periodic domains with aspect ratios up to Gamma = 128. In the considered Ra number regime the thermal superstructures have a horizontal extend of six to seven times the height of the domain and their size is independent of Ra. Many laboratory experiments and numerical simulations have focused on small aspect ratio cells in order to achieve the highest possible Ra. However, here we show that for very high Ra integral quantities such as the Nusselt number and volume averaged Reynolds number only converge to the large aspect ratio limit around Gamma approximate to 4, while horizontally averaged statistics such as standard deviation and kurtosis converge around Gamma approximate to 8, the integral scale converges around Gamma approximate to 32, and the peak position of the temperature variance and turbulent kinetic energy spectra only converge around Gamma approximate to 64.