Simulations of Rotating Anelastic Convection: Entropy Boundary Conditions

Abstract

In this dissertation we focus on numerical models of rotating anelastic convection, in particular the entropy boundary condition, with application to the giant planets. The first chapter details atmospheric features of giant planets and the numerical formulation of anelastic convection. The second chapter details entropy gradient boundary conditions compared to constant entropy boundary conditions used in previous studies. The third chapter considers a Gaussian perturbation on the lower boundary condition to examine surface effects of a plume from the deep interior. The fourth chapter considers high resolution simulations that are closer to a planetary parameter space. Most previous works on models of anelastic convection use a constant entropy difference boundary condition. For a strongly stratified system this requires a large entropy gradient near the surface to maintain the difference. This makes for strong convection at the outer boundary that disrupts coherent vortices. We use constant entropy gradient boundary conditions with entropy sinks so that the convection is strongest at the inner boundary and grades into neutral buoyancy at the outer boundary. A thermal plume from the deep interior is modelled using a Gaussian perturbation on the lower boundary. The parametrization of the plume is examined considering its amplitude, width, the latitudinal offset, and the background convective state. The flow produced at the surface typically includes a constant cyclonic vortex at the pole and short lived anticyclones at a lower latitude. Lowering the Ekman number allows for models that are less viscous and more representative of planets. These models have relaxation oscilations that are relatively quiet at the minimum and produce strong storms at the peak. We use these models to study the quasiperiodic Great White Spot storms that are observed on Saturn with a periodicity of about 1 Saturnian year.