Evolution of a Mode of Oscillation Within Turbulent Accretion Disks

We investigate the effects of turbulence on a normal mode of oscillation (a possible origin of high-frequency QPOs), in particular within a black hole accretion disk. We consider perturbations of a time-dependent background (steady state disk plus turbulence), obtaining an oscillator equation with stochastic damping, (mildly nonlinear) restoring, and driving forces. Assuming no spatial correlations between the turbulence and the mode, the (long-term) mean values of our four turbulent functions vanish. In particular, turbulence does not damp the oscillation modes, so ‘turbulent viscosity’ is not operative. However, the frequency components of the driving force near that of the mode can produce significant changes in the amplitude of the mode, and there is a long-term increase of the mode’s energy. In the absence of another source of damping, this leads to an eventual runaway.