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We explore the effect of forcing on the linear shear flow or plane Couetteflow, which is also the background flow in the very small region of theKeplerian accretion disk. We show that depending on the strength of forcing andboundary conditions suitable for the systems under consideration, thebackground plane shear flow and, hence, accretion disk velocity profilemodifies to parabolic flow, which is plane Poiseuille flow orCouette-Poiseuille flow, depending on the frame of reference. In the presenceof rotation, plane Poiseuille flow becomes unstable at a smaller Reynoldsnumber under pure vertical as well as threedimensional perturbations. Hence,while rotation stabilizes plane Couette flow, the same destabilizes planePoiseuille flow faster and forced local accretion disk. Depending on thevarious factors, when local linear shear flow becomes Poiseuille flow in theshearing box due to the presence of extra force, the flow becomes unstable evenfor the Keplerian rotation and hence turbulence will pop in there. This helpsin resolving a long standing problem of sub-critical transition to turbulencein hydrodynamic accretion disks and laboratory plane Couette flow.

Forced linear shear flows with rotation: rotating Couette-Poiseuille flow, its stability and astrophysical implications