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In this dissertation, I describe theoretical and numerical studies that address the three-dimensional behavior of spiral shocks in protoplanetary disks and the controversial topic of gas giant formation by disk instability. For this work, I discuss characteristics of gravitational instabilities (GIs) in bursting and asymptotic phase disks; outline a theory for the three-dimensional structure of spiral shocks, called shock bores, for isothermal and adiabatic gases; consider convection as a source of cooling for protoplanetary disks; investigate the effects of opacity on disk cooling; use multiple analyses to test for disk stability against fragmentation; test the sensitivity of GI behavior to radiation boundary conditions; measure shock strengths and frequencies in GI-bursting disks; evaluate temperature fluctuations in unstable disks; and investigate whether spiral shocks can form chondrules when GIs activate. The numerical methods developed for these studies are discussed, including a radiation transport routine that explicitly couples the low and high optical depth regimes and a routine that models ortho and parahydrogen. Finally, I explore the hypothesis that chondrule formation and the FU Ori phenomenon are driven by GI activation in dead zones.
We investigate the evolution of grains composed of an ice shell surrounding an olivine core as they pass through a spiral shock in a protoplanetary disk. We use published three-dimensional radiation-hydrodynamics simulations of massive self-gravitati
Recent observations of protoplanetary disks, as well as simulations of planet-disk interaction, have suggested that a single planet may excite multiple spiral arms in the disk, in contrast to the previous expectations based on linear theory (predicti
The structure and evolution of protoplanetary disks (PPDs) are largely governed by disk angular momentum transport, mediated by magnetic fields. In the most observable outer disk, PPD gas dynamics is primarily controlled by ambipolar diffusion as the
High-resolution imaging of protoplanetary disks has unveiled a rich diversity of spiral structure, some of which may arise from disk-planet interaction. Using 3D hydrodynamics with $beta$-cooling to a vertically-stratified background, as well as radi
Understanding how accretion proceeds in proto-planetary discs and more generally their dynamics is a crucial issue for explaining the conditions in which planets form. The role that accretion of gas from the surrounding molecular cloud onto the disc