Publikationsrepositorium - Helmholtz-Zentrum Dresden-Rossendorf

Magnetized shear flows are ubiquitous in nature and laboratory. The combined action of the magnetic field and velocity shear triggers various important instabilities and dynamical phenomena, ultimately determining transition to turbulence and global evolution of the flows. Here we focus on magnetorotational instability (MRI), and its non-ideal/resistive variants – helical and azimuthal magnetorotational instabilities (HMRI, AMRI) that arise as a result of combined action of magnetic field and differential rotation. It is one of the main instability responsible for turbulence and outward transport of angular momentum in magnetized astrophysical discs, which represent special case of shear flows. The discs are in Keplerian rotation with decreasing angular velocity and increasing angular momentum, which are Rayleigh-stable. However, it is well know that such spectrally stable hydrodynamical shear flows are non-normal or non-self-adjoint and as a consequence perturbations can undergo substantial transient, or non-modal (non-exponential) amplification in there. Since one of the main factors driving MRI in the magnetized case is also shear, the effects of non-normality inevitably influence the dynamics of MRI (i.e., the main linear equations describing MRI contain shear and are therefore non-normal) and should be taken into account. We investigate in detail the shear/non-normality-induced, or non-modal dynamics (growth) of HMRI/AMRI, which dominates at intermediate (dynamical/orbital) times, versus its modal growth that dominates at large times. We show that the non-modal growth of MRI can exceed its modal growth in a range of parameters. This can have implications for nonlinear transition. Interesting connection between the modal growth of HMRI and purely hydrodynamical non-modal growth was identified.