VERTICAL SHEAR INSTABILITY IN ACCRETION DISKS

Two-dimensional shear flows in the (R-z) and (phi-z) planes in thin accretion discs are studied. The vertical shear is set up by the resonant response of a disc with small tilt. It is shown that the flow is dynamically unstable, with growth rates in excess of approximately 0.1OMEGA-1, corresponding to a growth time-scale of one orbital period at a given radius. Standard analytical results for the two-dimensional flow instability are extended to take the effect of finite-density free boundaries into account. Ray theory is used to trace the path of energy transport. A small-wavelength approximation (WKBJ) is used to study the energy transport and leakage which lead to instability. The behaviour of longer wavelength modes is studied numerically, and interpreted in terms of mode coupling and wave action.