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Stability analyses for equilibria of the compressible reducedmagnetohydrodynamics (CRMHD) model are carried out by means of theEnergy-Casimir (EC) method. Stability results are compared with those obtainedfor ideal magnetohydrodynamics (MHD) from the classical {\delta}W criterion. Anidentification of the terms in the second variation of the free energyfunctional for CRMHD with those of {\delta}W is made: two destabilizing effectspresent for CRMHD turn out to correspond to the kink and interchangeinstabilities in usual MHD, while the stabilizing roles of field line bendingand compressibility are also identified in the reduced model. Also, using theEC method, stability conditions in the presence of toroidal flow are obtained.A formal analogy between CRMHD and a reduced incompressible model formagnetized rotating disks, due to Julien and Knobloch [EAS Pub. Series, 21, 81(2006)], is discovered. In light of this analogy, energy stability analysisshows that the condition for magnetorotational instability (MRI) for the lattermodel, corresponds to the condition for interchange instability in CRMHD, withthe Coriolis term and shear velocity playing the roles of the curvature termand pressure gradient, respectively. Using the EC method, stability conditionsfor the rotating disk model, for a large class of equilibria with possiblenon-uniform magnetic fields, are obtained. In particular, this shows it ispossible for the MRI system to undergo, in addition to the MRI, anotherinstability that is analogous to the kink instability. For vanishing magneticfield, the Rayleigh hydrodynamical stability condition is recovered.

Stability of compressible reduced magnetohydrodynamic equilibria - analogy with magnetorotational instability