  Although quasi-periodic oscillations (QPOs) have been discovered in different
X-ray sources, their origin is still a matter of debate. Analytical studies of
hydrodynamic accretion disks have shown three types of trapped global modes
with properties that appear to agree with the observations. However, these
studies take only linear effects into account and do not address the issues of
mode excitation and decay. Moreover, observations suggest that resonances
between modes play a crucial role. A systematic, numerical study of this
problem is therefore needed. In this paper, we use a pseudo-spectral algorithm
to perform a parameter study of the inner regions of hydrodynamic disks. By
assuming alpha-viscosity, we show that steady state solutions rarely exist. The
inner edges of the disks oscillate and excite axisymmetric waves. In addition,
the flows inside the inner edges are sometimes unstable to non-axisymmetric
perturbations. One-armed, or even two-armed, spirals are developed, which
provides a plausible explanation for the high-frequency QPOs observed from
accreting black holes. When the Reynolds numbers are above certain critical
values, the inner disks go through some transient turbulent states
characterized by strong trailing spirals; while large-scale leading spirals
developed in the outer disks. We compared our numerical results with standard
thin disk oscillation models. Although the non-axisymmetric features have their
analytical counterparts, more careful study is needed to explain the
axisymmetric oscillations.
