Shell models for confined Rayleigh-Taylor turbulent convection

Abstract For the confined Rayleigh-Taylor turbulent convection with large aspect ratio, different scaling behaviors such as Bolgiano-Obukhov (BO) scaling and Kolmogorov-Obukhov (KO) scaling are coexistent in the system. Traditional shell models cannot reproduce dual scaling properties with scale independent parameters. Boffetta et al. [Phys Rev E 2011; 83, 066302] firstly introduced geometrical constraints and two sets of model parameters into the original SabraT model to investigate the dual scaling properties of such complex convective turbulence. However, the present numerical results reveal that the enstrophy cascade scaling instead of BO scaling is setup at scales larger than the confinement scale for the modified 2D-3D SabraT model in the studied range of model parameter. Moreover, a 2D-3D Brandenburg model is constructed with the same idea and numerically investigated. Results show that two coexistence subranges of BO and KO scalings are respectively setup above and below the Bolgiano scale, which exactly relates to the confinement scale.