Wavelength selection mechanism for turbulent superstructures in turbulent Rayleigh Bénard convection

Large-scale flow patterns are observed in Rayleigh-Bénard cells both close and far from the onset of convection. Experiments and direct numerical simulations reveal that the characteristic spatial scale of these structures significantly increases in the turbulent regime compared to the one at the onset of convection and grows with the Rayleigh number. Here, we propose a mechanism that can account for this departure. We model the effect of turbulent fluctuations on the heat transport of the large scales by introducing a height-dependent turbulent thermal diffusivity. Such a model is motivated by how the height dependence of the background temperature profile varies between the boundary layers and the bulk. We conduct a linear stability analysis and show that a gradient in the effective thermal diffusivity between the boundary layers and the bulk leads to an instability where the wavelength of the critical mode is higher than in a cell with homogeneous diffusivity. By linking the magnitude of this gradient with the Rayleigh number, we illustrate how an increase in the intensity of turbulent velocity fluctuations modifies the spatial scale of the turbulent superstructures.