<p> Through HI observations, galactic gas discs can be observed to extend past the edge of the star forming disk. Observations of HI in these extended galactic disks consistently show significant velocity dispersion, which suggests a non-thermal origin. This suggests that turbulence in the gas is contributing significantly to the observed velocity dispersion. To address this, a new parallel adaptive mesh three dimensional shearing-box implementation with adaptions for evening numerical diffusion effects, self-gravity in the shearing boundary conditions and appropriate vertical boundary conditions has been built, based on the FLASH code. This code is used to perform local simulations, incorporating differential rotation, self-gravity, stratification, hydrodynamics and cooling. These simulations explore possible mechanisms for driving turbulent motions through thermal and self-gravitational instabilities coupling to differential rotation. In isothermal simulations a marginally stable disk is found to be stable against forming a gravitoturbulent quasi-steady state. In simulations including cooling, where the disk conditions do not trigger the formation of a two-phase medium, it is found that perturbations to the flow damp without leading to a sustained mechanism for driving turbulence. In cases where a two-phase medium develops, gravitational angular momentum transporting stresses are much greater, creating a possible mechanism for transferring energy from galactic rotation to turbulence, though a gravitoturbulent quasi-steady state is not found. The differing angular momentum transport properties of the single phase and two phase regimes of the disk suggests a significant dynamical division can be drawn between the two, which may occur far outside the star formation cutoff in a galactic disk. </p> / Thesis / Master of Science (MSc)