Document Type

Dissertation

Date of Award

5-31-2021

Degree Name

Doctor of Philosophy in Applied Physics - (Ph.D.)

Department

Physics

First Advisor

Alexander G. Kosovichev

Second Advisor

Gelu M. Nita

Third Advisor

Gregory D. Fleishman

Fourth Advisor

Haimin Wang

Fifth Advisor

Yuan N. Young

Sixth Advisor

Daniel Ely Murnick

Abstract

Computational fluid dynamic simulations have become one of the most prolific avenues of study in the fields of solar and stellar physics within the last several decades. With the advent of ever increasing computing power, high-definition global models of the Sun have become indispensable in understanding the complex and chaotic nature of flows in the solar interior, as well as their impact on the evolution of the global solar dynamo. The mechanisms that connect the generation of the toroidal magnetic field at the base of the convection zone to the emergence of a poloidal field onto the solar surface can be explored with the non-linear global model: EULAG-MHD (EULerian/semi-LAGrangian fluid solver—MagnetoHydroDynamic extension). This model is used to investigate the role that subsurface shear plays in shaping the extended solar magnetic cycle. The simulation of a wide range of convective near-surface transport regimes demonstrates that increased subsurface convection appears to have a significant impact on the distribution of angular momentum and the development of the a-effect—responsible for transforming the toroidal magnetic field into a poloidal one. These changes result in a global shift of the surface expression of the solar dynamo, from a North-South symmetric pattern to a staggered anti-symmetric emergence, more in line with solar observations.

The results of these global MHD models illustrate the significance of the near-surface shear layer (NSSL) and the radiative-convective interface (the tachocline) in shaping the evolution of the global magnetic field. The crucial key connecting the magnetic activity in these two layers is the action of the meridional circulation in the convection zone. The exact nature of meridional structure, however, is uncertain, with techniques in helioseismology showing inferences for both single-cell and double-cell meridional profiles—results that carry large implications for the transport of magnetic flux near the tachocline. In order to address this controversy from a modeling perspective, this dissertation presents the formulation of a 3-dimensional (3D) numerical solver of the linearized compressible Euler equations (GALE—Global Acoustic Linearized Euler), on a full spherical mesh. The application of an efficient pseudo-spectral computational method is used to calculate the contribution of the material derivative dyad in its conservative form, simulating the impact internal solar mass flows on helioseismic signatures. This algorithm is employed in a forward-modeling capacity, investigating profiles of single-cell meridional circulation with deep and shallow return flows, as well as double-cell meridional circulation with strong and weak reversals. The travel-time signatures for the four profiles are measured in an attempt to explore whether deviations in these regimes can be distinguished from realization noise—simulated by the stochastic excitation of resonant modes in the convective interior. This analysis shows that even though the low-end of differences between profiles of single- and double-cell meridional circulation may be indistinguishable, the analysis of meridional circulation generated by mean-field models may offer the opportunity to better understand and constrain inferences of helioseismology in the context of their impact on global dynamics.

The pseudo-spectral method used in the formulation of the GALE code presents the possibility of extending its numerical techniques to the contributions of all external forces in their conservative form. This allows for the development of a new efficient non-linear compressible global MHD algorithm, computed entirely in frequency-space. Such a global solar model can be used to explore the connection between the action of the dynamo on the solar surface and at the tachocline as a single interconnected evolving system, something that cannot be adequately achieved in the anelastic approximation employed in many global solar MHD models.

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