Quasi-two-dimensional nonlinear evolution of helical magnetorotational instability in a magnetized Taylor-Couette flow

Magnetorotational instability (MRI) is one of the fundamental processes in astrophysics, driving angular momentum transport and mass accretion in a wide variety of cosmic objects. Despite a lot of theoretical, numerical and experimental efforts over the last decades, its saturation mechanism and amplitude, which sets angular momentum transport rate, remains not well understood, especially in the limit of high resistivity, or small magnetic Prandtl numbers typical to interiors of protoplanetary disks, liquid cores of planets and liquid metals in laboratory.
We investigate the nonlinear development and saturation properties of the helical magnetorotational instability (HMRI), a relative of standard magnetorotational instability with only axial magnetic field, in magnetized Taylor-Couette flow using direct numerical simulations. From the linear theory of HMRI, it is known that the Elsasser number, or interaction parameter plays a special role for its dynamics and determines the growth rate. We show that this parameter is also important in the present nonlinear problem. With increasing its value, a sudden transition (bifurcation) from weakly nonlinear, where the system is slightly above the linear stability threshold, to turbulent regime occurs. The energy spectra corresponding to these two regimes, also differ qualitatively. Remarkably, the nonlinear states in these cases remain mostly axisymmetric and in fact represents a type of sustained two-dimensional magnetohydrodynamic turbulence driven by HMRI. Although the contribution of non-axisymmetric modes increases with the Elsasser number, their total energy still remains more than order of magnitude smaller than that of the axisymmetric ones.