  Origin of linear instability resulting in rotating sheared accretion flows
has remained a controversial subject for long. While some explanations of such
non-normal transient growth of disturbances in the Rayleigh stable limit were
available for magnetized accretion flows, similar instabilities in absence of
magnetic perturbations remained unexplained. This dichotomy was resolved in two
recent publications by Chattopadhyay, {\it et al} where it was shown that such
instabilities, especially for non-magnetized accretion flows, were introduced
through interaction of the inherent stochastic noise in the system (even a
\enquote{cold} accretion flow at 3000K is too \enquote{hot} in the statistical
parlance and is capable of inducing strong thermal modes) with the underlying
Taylor-Couette flow profiles. Both studies, however, excluded the additional
energy influx (or efflux) that could result from nonzero cross-correlation of a
noise perturbing the velocity flow, say, with the noise that is driving the
vorticity flow (or equivalently the magnetic field and magnetic vorticity flow
dynamics). In this article we show that nonzero noise cross-correlations
essentially renormalize the strength of temporal correlations. Apart from an
overall boost in the energy rate (both for spatial and temporal correlations,
and hence in the ensemble averaged energy spectra), this results in mutual
competition in growth rates of affected variables often resulting in
suppression of oscillating Alfven waves at small times while leading to faster
saturations at relatively longer time scales. The effects are seen to be more
pronounced with magnetic field fluxes where the noise cross-correlation
magnifies the strength of the field concerned.
