||In astrophysical disks, e.g. protoplanetary disks and disks around black holes, excessive angular momentum refrains matter from accreting. Megnetohyrodynamical stress can be effective for transporting angular momentum outward, but magnetic field does not necessary exist in all such systems. We study, by two dimensional hydrodynamical simulations, the role that stratified flow can create enough viscosity to drive the accretion in astrophysical disks, without any magnetic field. Urpin & Brandenburg (1998) suggested that rotating disks have angular velocity Ω = Ω(r, z) dependent on both radial and vertical coordinates r and z. Such a rotation law produces vertical shear and the disk can be fragile to short wavelength hydrodynamical perturbations. Turbulence can be induced to transport angular momentum outward and mass inward. We have established separately this stratified Ω for thick disks and non-stratifield Ω for thin disks. However, no obvious dynamical difference is observed between the two distinguishable cases. The stratified Ω distributions do not provide a workable mechanism to cause instability. We find an upper limit α ~ 10-5 which is too small to be effective. This upper limit of alpha is close to that obtained by Stones & Balbus (1996) previously with more restrictive assumptions. We conclude that a purely hydrodynamical process alone is not adequate to drive the accretion flow.