Nolting, Chris2020-11-172020-11-172020-07https://hdl.handle.net/11299/217144University of Minnesota Ph.D. dissertation.July 2020. Major: Astrophysics. Advisors: Thomas Jones, Lawrence Rudnick. 1 computer file (PDF); xii, 122 pages.We report the results of multiple three-dimensional magnetohydrodynamic (MHD) simulation studies focusing on the dynamics of Active Galactic Nuclei (AGN) jets. The goal of these studies is to understand the interactions of such jets with dynamical features of galaxy cluster media such as winds and shock waves, and to use the recognizable observed features as diagnostic tools when examining real radio sources in clusters to better understand the state of the environment surrounding radio galaxies (RG). We describe in detail the physics of jet propagation in a wind, including the rate of advancement of the jet head in the presence of a head or tail wind, the bending of a jet by ram pressure due to a cross wind, and the combination of the two effects when there is some intermediate alignment. We show simulation results that confirm analytic predictions for the jet head advancement and bending, as well as the effects on a RG jet due to an encounter with a shock wave at various angles and shock strengths. In a perfectly aligned case, a sufficiently strong shock can cause a jet to be stripped of its cocoon material, its forward progression slowed, and in some cases the jet can be reversed entirely. Shocks propagating through low density cocoons produce vorticity which can result in a vortex ring, possibly disrupting the jet and creating a distinct ring structure. These rings can remain visible for significant time due to magnetic field amplification, but if they are overlapping active jets in projection, the emission from the fresh cosmic ray electrons (CRe) in the jets may overwhelm the aged electrons in the ring. The dynamics of vortex rings is discussed, and theoretical predictions are confirmed in simulation. Re-energization of aged CRe by shocks is examined, and adiabatic compression is sufficient to explain the brightened and spectrally flattened sources, while Diffusive Shock Acceleration is not required. Lastly, looking to future simulations, we outline an ongoing comparison study of two methods for solving the MHD equations, a 2nd order Total Variation Diminishing (TVD) method and a 5th order Weighted Essentially Non-Oscillating (WENO) method. Appendices include other work on numerical methods used in the completion of this dissertation. We find that RG jets make excellent "weather-vanes" for understanding the dynamics of their surrounding media, and useful tools for understanding the motions in galaxy clusters.enGalaxy ClusterJetsMHDRadio GalaxySimulationThesis or Dissertation