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We investigate the evolution of hydromagnetic perturbations in a smallsection of accretion disks. It is known that molecular viscosity is negligiblein accretion disks. Hence, it has been argued that a mechanism, known asMagnetorotational Instability (MRI), is responsible for transporting matter inthe presence of weak magnetic field. However, there are some shortcomings,which question effectiveness of MRI. Now the question arises, whether otherhydromagnetic effects, e.g. transient growth (TG), can play important role tobring nonlinearity in the system, even at weak magnetic fields. Otherwise,whether MRI or TG, which is primarily responsible to reveal nonlinearity tomake the flow turbulent? Our results prove explicitly that the flows with highReynolds number (Re), which is the case of realistic astrophysical accretiondisks, exhibit nonlinearity by TG of perturbation modes faster than that bymodes producing MRI. For a fixed wave vector, MRI dominates over transienteffects, only at low Re, lower than its value expected to be in astrophysicalaccretion disks, and low magnetic fields. This seriously questions (overall)persuasiveness of MRI in astrophysical accretion disks.

physical review. e, statistical, nonlinear and soft matter physics

Origin of nonlinearity and plausible turbulence by hydromagnetic  transient growth in accretion disks: Faster growth rate than  magnetorotational instability