  In this paper we make an effort to understand the interaction of turbulence
generated by the magnetorotational instability (MRI) with turbulence from other
sources, such as supernova explosions (SNe) in galactic disks. First we perform
a linear stability analysis (LSA) of non-ideal MRI to derive the limiting value
of Ohmic diffusion that is needed to inhibit the growth of the instability for
different types of rotation laws. With the help of a simple analytical
expression derived under first-order smoothing approximation (FOSA), an
estimate of the limiting turbulence level and hence the turbulent diffusion
needed to damp the MRI is derived. Secondly, we perform numerical simulations
in local cubes of isothermal nonstratified gas with external forcing of varying
strength to see whether the linear result holds for more complex systems.
Purely hydrodynamic calculations with forcing, rotation and shear are made for
reference purposes, and as expected, non-zero Reynolds stresses are found. In
the magnetohydrodynamic calculations, therefore, the total stresses generated
are a sum of the forcing and MRI contributions. To separate these
contributions, we perform reference runs with MRI-stable shear profiles
(angular velocity increasing outwards), which suggest that the MRI-generated
stresses indeed become strongly suppressed as function of the forcing. The
Maxwell to Reynolds stress ratio is observed to decrease by an order of
magnitude as the turbulence level due to external forcing exceeds the predicted
limiting value, which we interpret as a sign of MRI suppression. Finally, we
apply these results to estimate the limiting radius inside of which the SN
activity can suppress the MRI, arriving at a value of 14 kpc.
