Flexible spectral algorithms for simulating astrophysical and geophysical flows

Abstract

Large-scale numerical simulations are key to studying the complex physical systems that surround us. Simulations provide the ability to perform simplified numerical experiments to build our understanding of large-scale processes which cannot be controlled and examined in the laboratory. This dissertation develops a new open-source computational framework, Dedalus, for solving a diverse range of equations used to model such systems and applies the code to the study of stellar and oceanic fluid flows. In the first part, the spectral algorithms used in Dedalus are introduced and the design and development of the code are described. In particular, the code's symbolic equation specification, arbitrary-dimensional parallelization, and sparse spectral discretization systems are detailed. This project provides the scientific community with an easy-to-use tool that can efficiently and accurately simulate many processes arising in geophysical and astrophysical fluid dynamics.

In the second part, Dedalus is used to study the turbulent boundary layers that form at the interface between marine-terminating glaciers and the ocean. A simplified model considering the heat transfer from a heated or cooled wall in a stratified fluid is investigated. We find new scaling laws for the turbulent heat transfer from the wall as a function of the imposed thermal forcing, with potential implications for the sensitivity of glacier melting to warming ocean temperatures. In the third part, Dedalus is used to study the stability of the tidal deformations experienced by binary neutron stars as they inspiral. We develop a numerical workflow for determining the weakly nonlinear stability of a tidally forced plane-parallel atmosphere and verify the results using fully nonlinear simulations.

This framework may help determine whether tidal instabilities can be observed in gravitational wave signatures of binary neutron stars, which could provide observational constraints on the equation of state of matter above nuclear densities.