Study of Oscillations and Flows in Solar Magnetic Active Regions

The use of waves as a diagnostic tool for determining unknown parameters has been indispensable in the research of the Sun. Since the discovery of the mystery of solar coronal heating in the 1940s, solar structures have been studied using seismology, particularly in the corona, in hope of finding the root cause of magnetic energy release. In this thesis, waves, flows, and oscillations associated with solar coronal loop structures and their origins beneath the surface are examined, since the dissipation of waves is believed to contribute to the bulk heating of the corona. First, a waveguide in Cartesian coordinates is studied, modelling a coronal loop arcade with curved magnetic field lines embedded in plasma with density decreasing exponentially in height. Investigating a small perturbation around the equilibrium, the fast and Alfv\'{e}n modes are decoupled. Depending on the ratio between the gas and magnetic pressure scale heights, the fast modes were shown to either be decaying or growing in height. In the presence of a Gaussian perturbation at the loop apex, the power in the Alfv\'{e}n mode, and for a special case of the fast mode, could be calculated for each eigenfrequency. It was shown that the power was highest for small eigenfrequencies in both cases, with the largest frequencies contributing the least. Since we see coronal loops as brighter than their surroundings, a ``two-shell'' (and later ``three-shell'') density profile of a magnetic field lines in a model in cylindrical coordinates is introduced. The coronal loops are considered to sit at the interface, and for the line-tying condition resultant eigenfrequencies are investigated. We investigate the resulting eigenfunctions for a “two-shell” (and later “three-shell”) density profile model that introduces sharp density contrast. we find that waves are elliptically polarised, but the eigenmodes can differ significantly when considering small changes to density profile. Hence, we conclude that the choice of density structure for use with observational data must be made with caution so that mode identification can be made more accurately. Finally, by using the local helioseismological technique known as ``Ring Diagram Analysis" with Doppler velocity shift data of the solar surface, the subsurface flows of flaring active regions from the rising phase of Solar Cycle 24 are examined. Consideration of morphological features, including $X$-class flare size, magnetic activity index, coronal mass ejection production and sunspot area, indicate that subsurface flow information should be used in tandem with the active regions morphology to ascertain the capability of large-scale flare production.