Simulation of 3D transient superstructures in mantle convection and variable viscosity via the Lattice Boltzmann Method

Transient superstructures in mantle convection whose life and morphology vary with Rayleigh and Prandtl number have recently been demonstrated. These superstructures appear to be a two-scale phenomenon where smaller scale rolls organize into larger scale convection cells. Simulation of such superstructures requires the ability to model 3D convection in box with very large width/height ratio of order greater than 10, and with resolution to resolve the thermal boundary layer at Rayleigh numbers of 10⁸ to 10¹⁰, respectively at least 100 height levels and 200 height levels. We achieve this with an efficient parallel implementation of the Lattice Boltzmann Method using Python which operates with high efficiency and linear speedup on thousands of cores. We present simulations with Rayleigh numbers of up to 10¹⁰ and Prandtl numbers from 1 to 100 to illustrate covering regimes from a magma ocean to solid mantle convection. We further present simulations using the LBM to model variable viscosity – specifically, temperature dependent– and illustrate the existence of pulsating plumes. We further demonstrate power law scaling between Nusselt number and Rayleigh number Nu  ~ Ra^g, which to first order is consistent with the Grossmann and Lohse theory.