  Rotating shear flows, when angular momentum increases and angular velocity
decreases as functions of radiation coordinate, are hydrodynamically stable
under linear perturbation. The Keplerian flow is an example of such systems
which appears in astrophysical context. Although decaying eigenmodes exhibit
large transient energy growth of perturbation which could govern nonlinearity
into the system, the feedback of inherent instability to generate turbulence
seems questionable. We show that such systems exhibiting growing
pseudo-eigenmodes easily reach an upper bound of growth rate in terms of the
logarithmic norm of the involved nonnormal operators, thus exhibiting feedback
of inherent instability. This supports the existence of turbulence of
hydrodynamic origin in the Keplerian accretion disc in astrophysics. Hence,
this enlightens the mismatch between the linear theory and
experimental/observed data and helps in resolving the outstanding question of
origin of turbulence therein.
