We study the 2-D, time-dependent hydrodynamics of radiation-driven winds from accretion disks in which the radiation force is mediated by spectral lines. If the dominant contribution to the total radiation field comes from the disk, then we find the outflow is intrinsically unsteady and characterised by large amplitude velocity and density changes. Both infall and outflow can occur in different regions of the wind at the same time. On the other hand, if the total luminosity of the system is dominated by the central star, then the outflow is steady. In either case, we find the 2-D structure of the wind consists of a dense, slow outflow, typically confined to angles within about 45$^o$ of the equatorial plane, that is bounded on the polar side by a high -velocity, lower density stream. The flow geometry is controlled largely by the geometry of the radiation field. Global properties e.g., the total mass loss rate and terminal velocity depend more on the system luminosity and are insensitive to geometry. Matter is fed into the fast wind from within a few stellar radii of the central star. Our solutions agree qualitatively with the kinematics of outflows in CV systems inferred from spectroscopic observations. We predict that low luminosity systems may display unsteady behavior in wind-formed spectral lines. Our study also has application to winds from active galactic nuclei and from high mass YSOs.
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