  Origin of hydrodynamical instability and turbulence in the Keplerian
accretion disc as well as similar laboratory shear flows, e.g. plane Couette
flow, is a long standing puzzle. These flows are linearly stable. Here we
explore the evolution of perturbation in such flows in the presence of an
additional force. Such a force, which is expected to be stochastic in nature
hence behaving as noise, could be result of thermal fluctuations (however small
be), Brownian ratchet, grain-fluid interactions and feedback from outflows in
astrophysical discs etc. We essentially establish the evolution of nonlinear
perturbation in the presence of Coriolis and external forces, which is modified
Landau equation. We show that even in the linear regime, under suitable forcing
and Reynolds number, the otherwise least stable perturbation evolves to a very
large saturated amplitude, leading to nonlinearity and plausible turbulence.
Hence, forcing essentially leads a linear stable mode to unstable. We further
show that nonlinear perturbation diverges at a shorter timescale in the
presence of force, leading to a fast transition to turbulence. Interestingly,
emergence of nonlinearity depends only on the force but not on the initial
amplitude of perturbation, unlike original Landau equation based solution.
