Large-scale mean patterns in turbulent convection

Large-scale patterns, which are well-known from the spiral defect chaos (SDC) regime of thermal convection at Rayleigh numbers Ra < 10(4), continue to exist in three-dimensional numerical simulations of turbulent Rayleigh-Benard convection in extended cylindrical cells with an aspect ratio Gamma = 50 and Ra > 10(5). They are revealed when the turbulent fields are averaged in time and turbulent fluctuations are thus removed. We apply the Boussinesq closure to estimate turbulent viscosities and diffusivities, respectively. The resulting turbulent Rayleigh number Ra-*, that describes the convection of the mean patterns, is indeed in the SDC range. The turbulent Prandtl numbers are smaller than one, with 0.2 <= Pr-* <= 0.4 for Prandtl numbers 0.7 <= Pr <= 10. Finally, we demonstrate that these mean flow patterns are robust to an additional finite-amplitude sidewall forcing when the level of turbulent fluctuations in the flow is sufficiently high.