  We investigate the evolution of magnetohydrodynamic/hydromagnetic
perturbations in the presence of stochastic noise in rotating shear flows. The
particular emphasis is the flows whose angular velocity decreases but specific
angular momentum increases with increasing radial coordinate. Such flows,
however, are Rayleigh stable, but must be turbulent in order to explain
astrophysical observed data and, hence, reveal a mismatch between the linear
theory and observations/experiments. The mismatch seems to have been resolved,
atleast in certain regimes, in the presence of weak magnetic field revealing
magnetorotational instability. The present work explores the effects of
stochastic noise on such magnetohydrodynamic flows, in order to resolve the
above mismatch generically for the hot flows. We essentially concentrate on a
small section of such a flow which is nothing but a plane shear flow
supplemented by the Coriolis effect, mimicking a small section of an
astrophysical accretion disk around a compact object. It is found that such
stochastically driven flows exhibit large temporal and spatial
auto-correlations and cross-correlations of perturbation and hence large energy
dissipations of perturbation, which generate instability. Interestingly,
auto-correlations and cross-correlations appear independent of background
angular velocity profiles, which are Rayleigh stable, indicating their
universality. This work, to the best of our knowledge, is the first attempt to
understand the evolution of three-dimensional hydromagnetic perturbations in
rotating shear flows in the presence of stochastic noise.
