Periodic magnetorotational dynamo action as a prototype of nonlinear magnetic-field generation in shear flows

Abstract

The nature of dynamo action in shear flows prone to magnetohydrodynamic instabilities is investigated using the magnetorotational dynamo in Keplerian shear flow as a prototype problem. Using direct numerical simulations and Newton's method, we compute an exact time-periodic magnetorotational dynamo solution to the three-dimensional dissipative incompressible magnetohydrodynamic equations with rotation and shear. We discuss the physical mechanism behind the cycle and show that it results from a combination of linear and nonlinear interactions between a large-scale axisymmetric toroidal magnetic field and non-axisymmetric perturbations amplified by the magnetorotational instability. We demonstrate that this large-scale dynamo mechanism is overall intrinsically nonlinear and not reducible to the standard mean-field dynamo formalism. Our results therefore provide clear evidence for a generic nonlinear generation mechanism of time-dependent coherent large-scale magnetic fields in shear flows and call for new theoretical dynamo models. These findings may offer important clues to understand the transitional and statistical properties of subcritical magnetorotational turbulence.

Nonlinear Transverse Cascade and Sustenance of MRI Turbulence in Keplerian Disks with an Azimuthal Magnetic Field

“…This feedback process is essentially 3D: we verified that modes with |k z | = 1, 2 give the largest contribution to the horizontal integral in the expression for the nonlinear term N (not shown here). It is appropriate here to give a comparative analysis of the dynamical processes investigated in this paper and those underlying sustained 3D MRI-dynamo cycles reported in Herault et al (2011) and Riols et al (2015Riols et al ( , 2017, despite the fact that these papers considered a magnetized Keplerian flow with different, zero net vertical flux, configuration and different values of parameters (smaller resolution, box aspect ratio, smaller Reynolds numbers) than those adopted here. These apparently resulted in the resistive processes penetrating into the vital area (in our terms) and reducing a number of active modes to only first non-axisymmetric ones (shearing waves) with the minimal azimuthal and vertical wavenumbers, k y = 2π/L y , k z = 0, 2π/L z , which un-dergo the transient MRI due to the mean axisymmetric azimuthal (dynamo) field.…”

“…The other modes with larger wavenumbers lie outside the vital area and always have energies and stresses less than 50% of the maximum value, therefore, not playing as much a role in the energy-exchange process between the background flow and turbulence. Note that the total number of the active modes (color dots) in Figure 7 is equal to 114, implying that the dynamics of the MRI-turbulence, strictly speaking, cannot be reduced to low-order models of the sustaining processes, involving only a small number of active modes (e.g., Herault et al 2011;Riols et al 2017). …”

“…Time integration is done by a standard explicit third-order Runge-Kutta scheme, except for viscous and resistive terms, which are integrated using an implicit scheme. The code has been extensively used in the shearing box studies of disk turbulence (e.g., Lesur & Ogilvie 2010;Lesur & Longaretti 2011;Herault et al 2011;Meheut et al 2015;Murphy & Pessah 2015;Riols et al 2017).…”

Local instabilities in magnetized rotational flows: a short-wavelength approach

“…In this case the magnetic field can only be produced in the disk itself, very likely by a periodic MRI dynamo process (Herault et al 2011) or some sort of an α − Ω dynamo (Brandenburg et al 1995), the α part of which relies on the turbulent flow structure arising due to the MRI. Such a closed loop of magnetic field self-excitation and MRI has attracted much attention in the past, though with many unsolved questions concerning numerical convergence (Fromang & Papaloizou 2007), the influence of disk stratification (Shi, Krolik & Hirose 2010), and the role of boundary conditions for the magnetic field (Käpylä & Korpi 2011).…”

Magnetorotational dynamo action in the shearing box

“…In this zero-net-flux case, a linear instability is not possible, but the flow may become unstable for a finite initial perturbation (subcritical instability) (Rincon et al 2007;Lesur & Ogilvie 2008;Herault et al 2011;Riols et al 2013;Squire & Bhattacharjee 2014;Riols et al 2016). Our recent high-resolution numerical simulations (Walker et al 2016) concentrated on the case of unit magnetic Prandtl number (Pm) and used the "long" shearing box (Lx : Ly : Lz = 2 : 4 : 1).…”