  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.
