INTERCHANGE METHOD IN INCOMPRESSIBLE MAGNETIZED COUETTE-FLOW - STRUCTURAL AND MAGNETOROTATIONAL INSTABILITIES

In view of its importance to astrophysical problems involving magnetiz ed accretion disks and outflows in stars, we analyze the stability of incompressible, magnetized Couette flow to axisymmetric perturbations. We use an energy variational principle, the so-called interchange or Chandrasekhar's method, to derive the relevant stability criteria. Thi s method is equivalent to the free-energy formalism that we have recen tly introduced to describe hydrodynamical instabilities in rotating, s elf-gravitating systems. In its implementation, all the applicable con servation laws are explicitly taken into account during the variations of the free-energy function. Thus we show that a purely toroidal magn etic field B-phi, which does not harm the conservation of circulation by imposing the additional conservation of azimuthal magnetic flux, le ads to structural stability in Couette flow: the stability properties of the unmagnetized flow are recovered in the limit B-phi --> 0. In co ntrast, an axial-field component B-z, however small, destroys the cons ervation laws of circulation and azimuthal magnetic flux by imposing i sorotation and conservation of the axial current along field lines. Th is radical change leads to a different stability criterion that implie s structural instability, i.e., the stability properties of the flow w ith B-z = 0 are not recovered in the limit B-z --> 0 irrespective of t he presence of rotation and/or a toroidal-field component. We discuss the relevance of our results for magnetized accretion flows and for ou tflows around stars and compact objects in active galactic nuclei. We also provide an application to thin accretion disks in Keplerian rotat ion.