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

References in corpus (33)

• Simulations of Incompressible MHD Turbulence
• Simulations of nonhelical hydromagnetic turbulence
• MHD simulations of the magnetorotational instability in a shearing box with zero net flux. II. The effect of transport coefficients
• Impact of dimensionless numbers on the efficiency of MRI-induced turbulent transport
• Experimental observation and characterization of the magnetorotational instability
• Spectral energy dynamics in magnetohydrodynamic turbulence
• Dynamic Alignment in Driven Magnetohydrodynamic Turbulence
• On magnetic field generation in Kolmogorov turbulence
• Numerical demonstration of fluctuation dynamo at low magnetic Prandtl numbers
• Anisotropy of Alfvénic Turbulence in the Solar Wind and Numerical Simulations
• Hydrodynamic stability of rotationally supported flows: Linear and nonlinear 2D shearing box results
• On the Magnetic Prandtl Number Behavior of Accretion Disks
• A self-sustaining nonlinear dynamo process in Keplerian shear flows
• Aspect ratio dependence in magnetorotational instability shearing box simulations
• Experimental evidence for non-axisymmetric magnetorotational instability in a rotating liquid metal exposed to an azimuthal magnetic field
• Numerical Measurements of the Spectrum in Magnetohydrodynamic Turbulence
• Global bifurcations to subcritical magnetorotational dynamo action in Keplerian shear flow
• Energy spectra stemming from interactions of Alfven waves and turbulent eddies
• MRI-driven turbulent transport: the role of dissipation, channel modes and their parasites
• Viscous, Resistive Magnetorotational Modes
• Instabilities in magnetized spherical Couette flow
• On the angular momentum transport due to vertical convection in accretion discs
• Strong magnetohydrodynamic turbulence with cross helicity
• Periodic magnetorotational dynamo action as a prototype of nonlinear magnetic field generation in shear flows
• MHD simulations of the magnetorotational instability in a shearing box with zero net flux: the case Pm=4
• Nonlinear energy transfers in accretion discs MRI turbulence. I-Net vertical field case
• Angular momentum transport and large eddy simulations in magnetorotational turbulence: the small Pm limit
• Magnetic dynamo action at low magnetic Prandtl numbers
• Numerical simulations of strong incompressible magnetohydrodynamic turbulence
• Dissipative effects on the sustainment of a magnetorotational dynamo in Keplerian shear flow
• Magnetostrophic MRI in the Earth's Outer Core
• The Role of the Magnetorotational Instability in the Sun
• Local and global aspects of the linear MRI in accretion disks

Cited by in corpus (31)

• Dynamo theories
• Role of magnetic reconnection in MHD turbulence
• Magnetorotational Turbulence and Dynamo in a Collisionless Plasma
• On the maximum magnetic field amplification by the magnetorotational instability in core-collapse supernovae
• Resolution Dependence of Magnetorotational Turbulence in the Isothermal Stratified Shearing Box
• MHD instabilities in accretion disks and their implications in driving fast magnetic reconnection
• Supergranulation and multiscale flows in the solar photosphere: Global observations vs. a theory of anisotropic turbulent convection
• Magnetorotational dynamo chimeras. The missing link to turbulent accretion disk dynamo models?
• Turbulence in Magnetized Pair Plasmas
• Particle Diffusion and Acceleration in Magnetorotational Instability Turbulence
• Zero net flux MRI-turbulence in disks $-$ sustenance scheme and magnetic Prandtl number dependence
• Impact of magneto-rotational instability on grain growth in protoplanetary disks: I. Relevant turbulence properties
• Nonlinear transverse cascade and sustenance of MRI-turbulence in Keplerian disks with an azimuthal magnetic field
• Active modes and dynamical balances in MRI-turbulence of Keplerian disks with a net vertical magnetic field
• Magnetorotational Dynamo Action in the Shearing Box
• Energy partition between Alfvénic and compressive fluctuations in magnetorotational turbulence with near-azimuthal mean magnetic field
• Universal small-scale structure in turbulence driven by magnetorotational instability
• Sustained Turbulence in Differentially Rotating Magnetized Fluids at Low Magnetic Prandtl Number
• Dissipative structures in magnetorotational turbulence
• MRI turbulence in vertically stratified accretion discs at large magnetic Prandtl numbers
• Nonaxisymmetric MHD instabilities of Chandrasekhar states in Taylor-Couette geometry
• High-speed shear driven dynamos. Part 2. Numerical analysis
• Calliope: Pseudospectral shearing magnetohydrodynamics code with a pencil decomposition
• Inertial range of magnetorotational turbulence
• The evolution of a circumplanetary disc with a dead zone
• Origin of hydrodynamic instability from noise: from laboratory flow to accretion disk
• First-principles measurement of ion and electron energization in collisionless accretion flow
• Studying black holes on horizon scales with space-VLBI
• Gravitoturbulent dynamo in global simulations of gaseous disks
• Transport of electrons in tangled magnetic fields
• Fully kinetic shearing-box simulations of magnetorotational turbulence in 2D and 3D. I. Pair plasmas