The formation and evolution of magnetic structures in the solar interior

This thesis presents a series of three-dimensional fully-nonlinear numerical studies of certain magnetohydrodynamic processes that are believed to be crucial to the operation of the solar global dynamo. First, we examine the creation and evolution of strong toroidal magnetic structures by the action of localized velocity shear on a seed poloidal magnetic field. We find that a steadily forced shear flow can produce a sequence of buoyantly-rising magnetic tube-like structures via an instability of a non-static MHD equilibrium. Secondary instabilities can also be triggered, including a three-dimensional Kelvin-Helmholtz instability, that is magnetically induced in the originally stable flow, which destroys the axial symmetry of the magnetic structures by twisting them into helical geometries. Examining the topology of the magnetic field within these simulations, we find that, as the symmetries of the initial conditions are broken, one fieldline can explore two-dimensional surfaces, or even three-dimensional volumes of the domain, tending towards ergodicity. Often, the fieldlines are not confined to any organized flux surfaces and therefore these structures are distinctly different from the idealized flux tubes of earlier MHD theory.; The three-dimensional magnetically-induced Kelvin-Helmholtz instability can lead to a nonlinear form of “α-effect”, reproducing poloidal field from toroidal field. The mechanism relies on the kinking of the magnetic structures and remarkably does not require any rotational dynamics. This system can act as an α–ω dynamo, maintaining very strong magnetic fields against the effects of resistive diffusion indefinitely. Interestingly, in certain parameter regimes, the dynamo can reverse polarity repeatedly.; We finally consider the long term evolution of such magnetic structures. We present simulations of the transit of a buoyant twisted flux tube from a convectively-stable region through a turbulent penetrative convection zone. Although other parameters, such as the twist and size of the magnetic structure, affect the rise somewhat, we find mainly the surprising result that the magnetic energy density of the structure must be significantly greater than the maximum kinetic energy density of the convection or else the structure is shredded and pumped back down to the stable region. Structures in equipartition with the rms convective energy are quickly destroyed.