  Hydrodynamic simulations have been used to study accretion disks consisting
of counterrotating components with an intervening shear layer(s).
Configurations of this type can arise from the accretion of newly supplied
counterrotating matter onto an existing corotating disk. The grid-dependent
numerical viscosity of our hydro code is used to simulate the influence of a
turbulent viscosity of the disk. Firstly, we consider the case where the gas
well above the disk midplane rotates with angular rate +\Omega(r) and that well
below has the same properties but rotates with rate -\Omega(r). We find that
there is angular momentum annihilation in a narrow equatorial boundary layer in
which matter accretes supersonically with a velocity which approaches the
free-fall velocity and the average accretion speed of the disk can be
enormously larger than that for a conventional \alpha-disk rotating in one
direction. Secondly, we consider the case of a corotating accretion disk for
r<r_t and a counterrotating disk for r>r_t. In this case we observed, that
matter from the annihilation layer lost its stability and propagated inward
pushing matter of inner regions of the disk to accrete. Thirdly, we
investigated the case where counterrotating matter inflowing from large radial
distances encounters an existing corotating disk. Friction between the
inflowing matter and the existing disk is found to lead to fast boundary layer
accretion along the disk surfaces and to enhanced accretion in the main disk.
These models are pertinent to the formation of counterrotating disks in
galaxies and possibly in Active Galactic Nuclei and in X-ray pulsars in binary
systems.
