Transport properties of the Azimuthal Magnetorotational Instability

Abstract

The magnetorotational instability (MRI) is thought to be a powerful source of turbulence in Keplerian accretion disks. Motivated by recent laboratory experiments, we study the MRI driven by an azimuthal magnetic field in an electrically conducting fluid sheared between two concentric rotating cylinders. By adjusting the rotation rates of the cylinders, we approximate angular velocity profiles $\omega \propto r^q$. We perform direct numerical simulations of a steep profile close to the Rayleigh line $q\gtrsim -2$ and a quasi-Keplerian profile $q\approx -3/2$ and cover wide ranges of Reynolds ($Re\le 4\cdot 10^4$) and magnetic Prandtl numbers ($0\le Pm\le 1$). In the quasi-Keplerian case, the onset of instability depends on the magnetic Reynolds number, with $R{m}_c\approx 50$, and angular momentum transport scales as $\sqrt{Pm}R{e}^2$ in the turbulent regime. The ratio of Maxwell to Reynolds stresses is set by $Rm$. At the onset of instability both stresses have similar magnitude, whereas the Reynolds stress vanishes or becomes even negative as $Rm$ increases. For the profile close to the Rayleigh line, the instability shares these properties as long as $Pm\gtrsim 0.1$, but exhibits a markedly different character if $Pm\to 0$, where the onset of instability is governed by the Reynolds number, with $R{e}_c\approx 1250$, transport is via Reynolds stresses and scales as $R{e}^2$. At intermediate $Pm=0.01$ we observe a continuous transition from one regime to the other, with a crossover at $Rm=\mathcal{O}(100)$. Our results give a comprehensive picture of angular momentum transport of the MRI with an imposed azimuthal field.

References in corpus (17)

• Impact of dimensionless numbers on the efficiency of MRI-induced turbulent transport
• Magnetorotational Instability in a Rotating Liquid Metal Annulus
• Measurement of angular momentum transport in turbulent flow between independently rotating cylinders
• Non-axisymmetric Magnetorotational Instabilities in Cylindrical Taylor-Couette Flow
• Experimental evidence for non-axisymmetric magnetorotational instability in a rotating liquid metal exposed to an azimuthal magnetic field
• MHD instability in differentially rotating cylindric flows
• Observation of magnetocoriolis waves in a liquid metal Taylor-Couette experiment
• On the viability of the shearing box approximation for numerical studies of MHD turbulence in accretion disks
• The angular momentum transport by unstable toroidal magnetic fields
• Angular momentum transport and large eddy simulations in magnetorotational turbulence: the small Pm limit
• Boundary-layer turbulence in experiments of quasi-Keplerian flows
• On the relation of standard and helical magnetorotational instability
• Transition to magnetorotational turbulence in Taylor--Couette flow with imposed azimuthal magnetic field
• Dynamo Action in a Quasi-Keplerian Taylor-Couette Flow
• Reynolds number scaling of influence of boundary layers on the global behavior of laboratory quasi-Keplerian flows
• The angular momentum transport by standard MRI in quasi-Kepler cylindric Taylor-Couette flows
• Nonaxisymmetric MHD instabilities of Chandrasekhar states in Taylor-Couette geometry

Cited by in corpus (7)

• Stability and instability of hydromagnetic Taylor-Couette flows
• Asteroseismology of evolved stars to constrain the internal transport of angular momentum. VI. Testing a parametric formulation for the azimuthal magneto-rotational instability
• Fully nonlinear mode competitions in magnetised Taylor-Couette flow
• Interplay between tidal flows and magnetic fields in nonlinear simulations of stellar and planetary convective envelopes
• Quasi-two-dimensional nonlinear evolution of helical magnetorotational instability in a magnetized Taylor-Couette flow
• Transport properties of Keplerian flows in extended local domains with no imposed field
• Transition to chaos and modal structure of magnetized Taylor-Couette flow