above the linear stability threshold, to strongly nonlinear, or turbulent regime occurs. We calculate the azimuthal and axial energy spectra corresponding to these two regimes and show that they differ qualitatively. Remarkably, the nonlinear state remains in all cases nearly axisymmetric suggesting that HMRI turbulence is quasi two-dimensional in nature. Although the contribution of non-axisymmetric modes increases moderately with the Elsasser number, their total energy remains much smaller than that of the axisymmetric ones.'
address: |
    $^1$Helmholtz-Zentrum Dresden-Rossendorf, Dresden 01328, Germany\
    $^2$Department of Physics, Faculty of Exact and Natural Sciences, Tbilisi State University, Tbilisi 0179, Georgia\
    $^3$Abastumani Astrophysical Observatory, Ilia State University, Tbilisi 0162, Georgia\
    $^4$University of Bremen, Center of Applied Space Technology and Microgravity (ZARM), Bremen 28359, Germany
author:
- 'G. Mamatsashvili$^{1,2,3}$, F. Stefani$^{1}$, A. Guseva$^{4}$ and M. Avila$^{4}$'
bibliography:
- 'biblio.bib'
title: 'Quasi-two-dimensional nonlinear evolution of helical magnetorotational instability in a magnetized Taylor-Couette flow'
---

Introduction
============

The magnetorotational instability (MRI, [@Velikhov59; @Balbus_Hawley98]) is one of the most important processes in magnetized differentially rotating conducting fluids, which largely determines their dynamics and evolution. It is a powerful linear instability arising as a result of the combined effect of weak magnetic field and radially decreasing angular velocity. The MRI 