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Stochastic Dynamics of Keplerian Accretion Disks

In this work we study the growth of perturbations in Keplerian disks. Despite the asymptotic stability of the disk, a subset of optimal perturbations are found to exhibit large transient growth. The transient growth is due to the nonnormality of the underlying operator which governs the perturbation dynamics. It is shown that the amplifying perturbations produce positive momentum fluxes and a tendency of outward angular momentum expulsion during amplification. We calculate the statistical steady state that emerges under white forcing in space and time. The perturbation structure is found to be organized in coherent structures that invariably export angular momentum outward. The radial structure of the resulting angular momentum flux is in agreement with the predictions of the equilibrium theory of accretion disks. The effect of spatial localization and temporal band limiting of the forcing on the maintained momentum fluxes is investigated. We find that if the forcing is broadband and adequately distributed, accretion to the main body can be maintained by stochastic forcing.