On the Nature of Magnetic Turbulence in Rotating, Shearing Flows

Abstract

The local properties of turbulence driven by the magnetorotational instability (MRI) in rotating, shearing flows are studied in the framework of a shearing-box model. Based on numerical simulations, we propose that the MRI-driven turbulence comprises two components: the large-scale shear-aligned strong magnetic field and the small-scale fluctuations resembling magnetohydrodynamic (MHD) turbulence. The energy spectrum of the large-scale component is close to $k^{-2}$, whereas the spectrum of the small-scale component agrees with the spectrum of strong MHD turbulence $k^{-3/2}$. While the spectrum of the fluctuations is universal, the outer-scale characteristics of the turbulence are not; they depend on the parameters of the system, such as the net magnetic flux. However, there is remarkable universality among the allowed turbulent states -- their intensity $v_0$ and their outer scale ${\lambda }_0$ satisfy the balance condition $v_0/{\lambda }_0\sim \mathrm{d}\Omega /\mathrm{d}\ln r$, where $\mathrm{d}\Omega /\mathrm{d}\ln r$ is the local orbital shearing rate of the flow. Finally, we find no sustained dynamo action in the $\mathrm{Pm}=1$ zero net-flux case for Reynolds numbers as high as $45000$, casting doubts on the existence of an MRI dynamo in the $\mathrm{Pm}\le 1$ regime.

5 pages, 6 figures, 1 table

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