Rotating convection-driven flows are common throughout the universe but are often inaccessible to observation due to their remoteness. Typically, numerical techniques are used to explore these flows, but simulating them is challenging at realistic extreme parameter values due to the broad range of spatial and temporal scales involved. This thesis evaluates two methods of studying geophysical and astrophysical flows: parametric studies and hyperdiffusion.
Parametric studies utilise dynamically self-similar simulations to construct scaling laws that relate input parameters to output parameters. I compare three methods used to determine the dynamics of simulations and show where they agree and disagree. I do this with both the momentum equation and the vorticity equation. When evaluated at the mid-plane, I find that the ordering of terms disagrees with the ordering of terms when integrating each term over the domain. When integrating each term over the domain, I find that the effect of the boundary layer persists if only one viscous boundary layer thickness is removed.
Hyperdiffusion (HD) is a numerical technique for artificially diffusing energy at small scales, which in turn stabilises numerical simulations. Although it is used in geophysical and astrophysical simulations, the scheme's effects are unclear. To determine the impact of hyperdiffusion, I conduct 107 plane layer Rotating Rayleigh Benard simulations, in which HD is applied to the viscous operator. I find two different primary effects of HD: at low supercriticality, flow speeds and heat transfer are increased compared to direct numerical simulations due to a weakening of the rotational constraint; at high supercriticality, heat transfer and flow speeds are decreased compared to direct numerical simulations owing to suppression of energy. I conduct 75 simulations in a spherical shell geometry. I find similar effects in this geometry to those in the plane layer. However, I also see a bottleneck effect form for simulations conducted at higher supercriticality due to the disruption of the cascade of kinetic energy caused by hyperdiffusion. At low supercriticality, I find that hyperdiffusion destabilises modes that are not destabilised in direct numerical simulations, creating time-dependent heat transfer and flow speeds.
