  We consider accretion disks consisting of counter-rotating gaseous components
with an intervening shear layer. Configurations of this type may arise from the
accretion of newly supplied counter-rotating gas onto an existing co-rotating
gas disk. For simplicity we consider the case where the gas well above the disk
midplane is rotating with angular rate $+\Omega$ and that well below has the
same properties but is rotating with rate $-\Omega$. Using the Shakura-Sunyaev
alpha turbulence model, we find self-similar solutions where a thin (relative
to the full disk thickness) equatorial layer accretes very rapidly, essentially
at free-fall speed. As a result the accretion speed is much larger than it
would be for an alpha disk rotating in one direction. Counter-rotating
accretion disks may be a transient stage in the formation of counter-rotating
galaxies and in the accretion of matter onto compact objects.

Astrophysics;Condensed Matter