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Hydromagnetic Oscillations and Instabilities in Astrophysical Discs 10.17863/CAM.40691 Dewberry, Janosz Walker Latter, Henrik Nils Highly supersonic, magnetized and differentially rotating, accretion flows provide an environment for the propagation of waves and the growth of instabilities unlike those normally encountered on Earth. In this dissertation, I investigate the properties of oscillations and instabilities in accretion discs, developing theoretical and numerical models to explore the physical nature of variability encountered in a variety of astrophysical contexts. Through linear theory and semi-analytical calculations, I first consider the physical properties of magnetically altered inertial waves. ‘Trapped inertial waves’ provide an attractive explanation of the fast variability observed in the emission from low-mass black hole binary systems, but such oscillations can be affected by magnetic tension provided by large-scale poloidal magnetic fields threading the accretion disc. Through local and global analyses, I constrain the modification of trapped inertial waves by poloidal, toroidal and helical magnetic fields. I then investigate the excitation of oscillations in deformed discs with eccentric, non-circular streamlines. Many processes can lead to the growth of eccentricity in accretion discs, and turbulence deriving from the excitation of inertial waves by a local parametric instability provides one mechanism for curbing this growth. However, eccentric discs also provide an environment for the excitation of additional, inherently global oscillations, and I present a framework facilitating a semi-analytical investigation of these modes. I finally employ numerical simulations to explore the dynamics of accretion disc oscillations in the non-linear regime. I first follow the non-linear saturation of inertial waves driven by parametric resonance in non-relativistic discs, and confirm the growth of a second family of large-scale, low-frequency oscillations. Using a pseudo-Newtonian framework to approximate relativistic effects, I then demonstrate the excitation of trapped inertial waves through non-linear coupling with accretion disc deformations in a black hole accretion disc, providing preliminary evidence that trapped inertial waves can be excited even in the presence of MHD turbulence University of Cambridge 2019-07-20 Thesis Doctoral Doctor of Philosophy (PhD) en PhD primarily funded by a Cambridge International Scholarship provided by the Cambridge Commonwealth European and International Trust. Additional funding provided by the Vassar College De Golier Trust, the Cambridge Philosophical Society, and Churchill College. https://www.repository.cam.ac.uk/handle/1810/293553 controlled.access https://apollo8-f-pro.lib.cam.ac.uk/bitstreams/93088a9d-166a-44da-8bb6-00db133f2336/download 8c3196125ce62b6289bf81db34c7cc1b https://apollo8-f-pro.lib.cam.ac.uk/bitstreams/e789c90a-29db-4048-bcf1-cd2361ed12f6/download 87eda9de84448d1f82354d60eee3eb5f https://www.rioxx.net/licenses/all-rights-reserved/ Astrophysics Magnetohydrodynamics Accretion discs Waves Magnetic fields Fluid dynamics Black holes Cataclysmic variables Protoplanetary discs AGN Numerical analysis Numerical astrophysics Instabilities X-ray astronomy Hydrodynamics Eccentric discs