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, $3.5times 10^{-3},t_mathrm{g}^{-1}$, 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.
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