  We perform detailed variability analysis of two-dimensional viscous,
radiation hydrodynamic numerical simulations of Shakura-Sunyaev thin disks
around a stellar mass black hole. Disk models are initialized on both the gas-,
as well as radiation-, pressure-dominated branches of the thermal equilibrium
curve, with mass accretion rates spanning the range from $\dot{M} = 0.01
L_\mathrm{Edd}/c^2$ to $10 L_\mathrm{Edd}/c^2$. An analysis of temporal
variations of the numerically simulated disk reveals multiple robust, coherent
oscillations. Considering the local mass flux variability, we find an
oscillation occurring at the maximum radial epicyclic frequency, $3.5\times
10^{-3}\,t_\mathrm{g}^{-1}$, a possible signature of a trapped fundamental
${\it g}$-mode. Although present in each of our simulated models, the trapped
${\it g}$-mode feature is most prominent in the gas-pressure-dominated case.
The total pressure fluctuations in the disk suggest strong evidence for
standing-wave ${\it p}$-modes, some trapped in the inner disk close to the
ISCO, others present in the middle/outer parts of the disk. Knowing that the
trapped ${\it g}$-mode frequency and maximum radial epicyclic frequency differ
by only $0.01\%$ in the case of a non-rotating black hole, we simulated an
additional initially gas-pressure-dominated disk with a dimensionless black
hole spin parameter $a_* = 0.5$. The oscillation frequency in the spinning
black hole case confirms that this oscillation is indeed a trapped ${\it
g}$-mode. All the numerical models we report here also show a set of high
frequency oscillations at the vertical epicyclic and breathing mode
frequencies. The vertical oscillations show a 3:2 frequency ratio with
oscillations occurring approximately at the radial epicyclic frequency, which
could be of astrophysical importance in observed twin peak, high-frequency
quasi-periodic oscillations.
