3D Transient Superstructures in Mantle Convection using Lattice Boltzmann Method

Recent advances in modeling Rayleigh-Benard convection have demonstrated the existence of turbulent superstructures, whose life and morphology largely varies with Rayleigh (Ra) and Prandtl (Pr) numbers. These structures appear as a two scale phenomena, where small scale rolls organize in larger convection cells, and can be modelled only in 3D on a simulation box characterized by a very large (>10) width/height (W/L) ratio, and sufficiently refined to resolve the boundary layer up to Ra = 10⁸ (>100 divisions in height) and to Ra = 10¹⁰ (>200 divisions). To achieve this goal, we use our own 3D Parallel Python implementation of the Lattice Boltzmann Method, tested to run with linear efficiency on thousands of cores. We show the dependency of horizontal fluctuations of RMS of temperature and vertical velocity in the middle of the box and illustrate how the superstructures emerge for W/L ratios of Terrestrial Planets and Super Earths, and quantify the duration of these superstructures and the likely implications for the evolution of their surface features. The effect of the P/T dependent viscosity and thermal conductivity is finally discussed.