title: Exploring the dynamics of convection-driven dynamos in rotating spherical shells
Creators: name: Gupta, Parag
Publisher: name: University of Glasgow
Year: 2024

description: This thesis explores the dynamics of convection-driven dynamos in rotating spherical shells through three detailed studies. The first study investigates the relative importance of helicity and cross-helicity electromotive dynamo effects for the self-sustained generation of magnetic fields by chaotic thermal convection in rotating spherical shells as a function of shell thickness. Direct numerical simulations reveal two distinct branches of dynamo solutions coexisting for shell aspect ratios between 0.25 and 0.6: a mean-field dipolar regime and a fluctuating dipolar regime. The study compares and contrasts the properties of these coexisting dynamo attractors, including differences in temporal behavior and the spatial structures of both magnetic fields and rotating thermal convection. In the fluctuating dipolar regime, the helicity a-effect and the cross-helicity g-effect are found to be of comparable intensity, with their ratio remaining relatively constant across different shell thicknesses. Conversely, in the mean-field dipolar regime, the helicity a-effect is dominant, exceeding the cross-helicity g-effect by approximately two orders of magnitude, and its strength increases as the shell thickness decreases. The second study focuses on the importance of global magnetic helicity in self-consistent spherical dynamos. Magnetic helicity serves as a fundamental constraint in both ideal and resistive magnetohydrodynamics, offering crucial insights into the internal dynamics of dynamo processes that generate global magnetic fields on celestial bodies like the Sun and stars. This study investigates the behavior of global relative magnetic helicity through three self-consistent spherical dynamo solutions of increasing complexity. Magnetic helicity describes the global linkage between poloidal and toroidal magnetic fields weighted by magnetic flux. Our findings reveal distinct preferred states of this linkage, suggesting that global magnetic field reversals may act to preserve this preferred state. Specifically, when either the poloidal or toroidal field alone undergoes reversal, the preferred linkage state is disrupted. We demonstrate that magnetic helicity serves as a predictive indicator for the onset of these reversals, potentially observable at the outer surface of celestial bodies. The third study investigates differential rotation in convecting spherical shells with nonuniform viscosity and entropy diffusivity. Current three-dimensional, physics-based simulations of the solar convection zone show significant discrepancies when compared to observations. These simulations present differential rotation patterns that are notably different from those inferred by solar helioseismology and display convective "Busse" columns that are absent in actual observations. To address this "convection conundrum," we employ a three-dimensional pseudospectral simulation code to explore the impact of radially non-uniform viscosity and entropy diffusivity on differential rotation and convective flow patterns in density-stratified, rotating spherical fluid shells. Our findings indicate that radial non-uniformity in fluid properties enhances polar convection, which creates significant lateral entropy gradients, leading to substantial deviations from differential rotation geostrophy due to thermal wind balance. We demonstrate simulations where this mechanism sustains differential rotation patterns closely resembling the true solar profile outside the tangent cylinder, although some discrepancies persist at high latitudes. This is particularly important as differential rotation is crucial for sustaining solar-like cyclic dipolar dynamos. This thesis uncovers new insights into how magnetic fields are created and sustained in rotating spherical fluid shells, revealing the intricate relationships between fluid dynamics, magnetic fields, and convective motions. These findings contribute to a deeper understanding of solar, stellar, and geomagnetic dynamo mechanisms, with implications for advancing research in both astrophysics and geophysics.