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

Abstract

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 much theoretical/numerical and experimental efforts over the last decades, its saturation mechanism and amplitude, which sets the angular momentum transport rate, remains not well understood, especially in the limit of high resistivity, or small magnetic Prandtl numbers typical to interiors (dead zones) of protoplanetary disks, liquid cores of planets and liquid metals in laboratory. Using direct numerical simulations, in this paper we investigate the nonlinear development and saturation properties of the helical magnetorotational instability (HMRI)-a relative of the standard MRI-in a magnetized Taylor-Couette flow at very low magnetic Prandtl number (correspondingly at low magnetic Reynolds number) relevant to liquid metals. For simplicity, the ratio of azimuthal field to axial field is kept fixed. From the linear theory of HMRI, it is known that the Elsasser number, or interaction parameter determines its growth rate and plays a special role in the dynamics. We show that this parameter is also important in the nonlinear problem. By increasing its value, a sudden transition from weakly nonlinear, where the system is slightly 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 this HMRI-driven 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.

Transport Properties of the Azimuthal Magnetorotational Instability

“…Mamatsashvili et al (2017) have observed the same correlation for the helical MRI. Hence, the results presented in the following can be seen as an upper bound on the angular momentum transport.…”

From helical to standard magnetorotational instability: predictions for upcoming liquid sodium experiments

“…However, either one of the two types of stresses is dominant for HMRI or (H-)SMRI. The Reynolds stress plays a main role in the energy supply for HMRI, in which velocity perturbations are much larger than magnetic field ones, because the latter, due to high resistivity Rm ≪ 1 in this regime, are proportional to Rm and are therefore quite small [10,26]. On the other hand, for SMRI that operates at much higher Rm 1, magnetic field perturbations are more important and hence Maxwell stress plays a major role [22].…”