Accretion disk instability revisited - Transient dynamics of rotating shear flow

Accretion disk flow in a local Cartesian (or shearing box) approximation is examined for viscous three-dimensional linear disturbances. Eigenvalue computations predict that the flow is asymptotically stable unless the rotation number falls in the range 0 < Ro < 1/2, in agreement with predictions of inviscid theory; Keplerian flow (Ro = 1/q = 2/3) is accordingly stable. Analysis of non-modal disturbances predicts large transient amplification factors, implying that the flow, although asymptotically stable, may be transiently unstable. Strong rotation, including Keplerian, two-dimensionalizes the system: the largest growth factors are found for disturbances which are uniform along the direction of the rotation axis and amplification occurs via the Orr mechanism, as in 2D shear flow. Amplification factors scale as Re 2/3, implying very strong growth in actual disks. The implications of transient instability of rotating shear on disk turbulence are discussed.