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We perform detailed variability analysis of two-dimensional viscous,radiation hydrodynamic numerical simulations of Shakura-Sunyaev thin disksaround a stellar mass black hole. Disk models are initialized on both the gas-,as well as radiation-, pressure-dominated branches of the thermal equilibriumcurve, with mass accretion rates spanning the range from $\dot{M} = 0.01L_\mathrm{Edd}/c^2$ to $10 L_\mathrm{Edd}/c^2$. An analysis of temporalvariations of the numerically simulated disk reveals multiple robust, coherentoscillations. Considering the local mass flux variability, we find anoscillation occurring at the maximum radial epicyclic frequency, $3.5\times10^{-3}\,t_\mathrm{g}^{-1}$, 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 forstanding-wave ${\it p}$-modes, some trapped in the inner disk close to theISCO, others present in the middle/outer parts of the disk. Knowing that thetrapped ${\it g}$-mode frequency and maximum radial epicyclic frequency differby only $0.01\%$ in the case of a non-rotating black hole, we simulated anadditional initially gas-pressure-dominated disk with a dimensionless blackhole spin parameter $a_* = 0.5$. The oscillation frequency in the spinningblack hole case confirms that this oscillation is indeed a trapped ${\itg}$-mode. All the numerical models we report here also show a set of highfrequency oscillations at the vertical epicyclic and breathing modefrequencies. The vertical oscillations show a 3:2 frequency ratio withoscillations occurring approximately at the radial epicyclic frequency, whichcould be of astrophysical importance in observed twin peak, high-frequencyquasi-periodic oscillations.

Relativistic, Viscous, Radiation Hydrodynamic Simulations of Geometrically Thin Disks. II. Disk Variability