%0 PhD Thesis
%D 2021
%T Numerical Simulations of Convection and Convection-Driven Dynamos in Spherical Shells
%A Orvedahl, R. J.
%I ProQuest Dissertations and Theses
%U https://www.proquest.com/dissertations-theses/numerical-simulations-convection-driven-dynamos/docview/2533381505/se-2?accountid=14505
%K Rayleigh, Convection, Dynamos, Force balances, Magnetic field, Rotating convection, Stars, Astrophysics, Fluid mechanics, Plasma physics
%X he majority of Solar System planets, in addition to the Sun and other stars, possess global, or large-scale, magnetic fields. These magnetic fields are all thought to be generated by the dynamo mechanism, whereby the kinetic energy associated with convectively stirred motions of an electrically conducting fluid is converted into electromagnetic energy. The large-scale magnetic fields of most of these bodies are aligned with their respective rotation axis, and often are characterized by a relatively strong dipolar component. In this work, large-scale magnetic field properties are investigated using two separate cases: a simplified model similar to the Sun, and a more comprehensive model that shares similarities with the Earth. For the Sun-similar cases, the beginning of the dynamo process is studied more closely to see how the kinetic energy of the system behaves as the fluid properties are varied. The simplified model has no magnetic fields and no rotation. Scaling relations for the kinetic energy are established enabling description of how the boundary layer influences the dynamics. The Earth-like cases include rotation and magnetic fields in an effort to study the saturation of the large-scale magnetic field as the thermal forcing is increased. This saturation is explored over a wide range of system parameters and is found to be a robust feature of rapidly rotating dynamo simulations. These results are described using a semi-magnetostrophic force balance, where the Lorentz force enters the leading-order mean force balance in only a single component direction. Techniques from asymptotic theory are applied in order to determine the scaling behavior of the fields as well as the scaling behavior of the individual forces present in the mean momentum equation.