Publikationsrepositorium - Helmholtz-Zentrum Dresden-Rossendorf

We present a study of destabilization of a rotating flow of an electrically conducting and viscous fluid in an external azimuthal magnetic field of arbitrary radial dependence.
With the use of the WKB approximation we obtain a dispersion relation which gives us the growth rates of the non-axisymmetric perturbation and conditions for the onset of the azimuthal magnetorotational instability in an explicit form.
We demonstrate that in the absence of the dissipation the flow is marginally stable if the ratio of the magnetic Rossby number and the hydrodynamic Rossby number is equal to the squared ration of the angular velocity of the fluid to the Alfven angular velocity.
In particular, this constraint contains the Chandrasekhar's equipartition solution - a special solution of ideal MHD equations for which the fluid velocity is parallel to the direction of the magnetic field and magnetic and kinetic energies are finite and equal.
With the use of the explicit expression for the onset of AMRI we demonstrate that AMRI is a destabilized by the electrical resistivity Chandrasekhar's equipartition solution that is marginally stable in the ideal MHD. Finally, we establish an expression that allows for a qualitative and quantitative analysis of the transition between the AMRI and Tayler instability.