Chairperson, Graduate Committee: David E. McKenzieScott, Roger BenezetDana W. Longcope and David E. McKenzie were co-authors of the article, 'Peristaltic pumping near post-CME supra-arcade current sheets' in the journal 'The astrophysical journal' which is contained within this thesis.Dana W. Longcope and David E. McKenzie were co-authors of the article, 'Numerical simulations of plasma dynamics in the vicinity of a retracting flux tube' submitted to the journal 'The astrophysical journal' which is contained within this thesis.David E. McKenzie and Dana W. Longcope were co-authors of the article, 'Inferring the magnetohydrodynamic structure of solar flare supra-arcade plasmas from a data assimilated field transport model' submitted to the journal 'The astrophysical journal' which is contained within this thesis.2016-10-172016-10-172016https://scholarworks.montana.edu/handle/1/9585Among the myriad of interesting phenomenon in the solar corona is the highly dynamic region above active region arcades, commonly referred to as the "supra-arcade" region. In the minutes and hours following the formation of an arcade of post-flare loops, we commonly observe the development of a curtain like structure, with spiny rays of enhanced emission in X-Ray and extreme ultra-violet. Additionally, these structures often exhibit dynamics over a variety of length scales, from large-amplitude coherent transverse oscillations, to the appearance of low-emission columns that seem to descend toward the solar limb. The wealth of dynamical aspects that are present in the supra-arcade seems to indicate that the plasma there is subject to a complex balance of influencing factors, which makes it difficult to develop a self-consistent hypothesis for describing all of the various features simultaneously. In this work we undertake to explain one such behavior as an isolated phenomenon. We argue that the descending low-emission voids, sometimes called Supra-Arcade Downflows (SADs) are consistent with the formation of a particular kind of shock in the vicinity of a retracting element of reconnected magnetic flux. We then use numerical simulations to expand this result to a broader parameter space, as well as investigating the details of a variety of other behavioral regimes. Finally, in an effort to understand the broader dynamics of the supra-arcade region, we undertake a study that incorporates imaging data into a numerical simulation, which can then be used to estimate the ambient plasma parameters in the supra-arcade region. In this way we show that the balance of influencing factors in the supra-arcade is indeed highly dynamic and that the simplifications offered in certain extremes of magnetohydrodynamics are ill-applied in this case.enSolar flaresMathematical modelsDissertationCopyright 2016 by Roger Benezet Scott