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Register a new userDissipative effects on the sustainment of a magnetorotational dynamo in Keplerian shear flow
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Added by
Antoine Riols-Fonclare
Publication date
2014
fields
Physics
and research's language is
English
Authors
A. Riols
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The magnetorotational (MRI) dynamo has long been considered one of the possible drivers of turbulent angular momentum transport in astrophysical accretion disks. However, various numerical results suggest that this dynamo may be difficult to excite in the astrophysically relevant regime of magnetic Prandtl number (Pm) significantly smaller than unity, for reasons currently not well understood. The aim of this article is to present the first results of an ongoing numerical investigation of the role of both linear and nonlinear dissipative effects in this problem. Combining a parametric exploration and an energy analysis of incompressible nonlinear MRI dynamo cycles representative of the transitional dynamics in large aspect ratio shearing boxes, we find that turbulent magnetic diffusion makes the excitation and sustainment of this dynamo at moderate magnetic Reynolds number (Rm) increasingly difficult for decreasing Pm. This results in an increase in the critical Rm of the dynamo for increasing kinematic Reynolds number (Re), in agreement with earlier numerical results. Given its very generic nature, we argue that turbulent magnetic diffusion could be an important determinant of MRI dynamo excitation in disks, and may also limit the efficiency of angular momentum transport by MRI turbulence in low Pm regimes.
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Though usually treated in isolation, the magnetorotational and gravitational instabilities (MRI and GI) may coincide at certain radii and evolutionary stages of protoplanetary discs and active galactic nuclei. Their mutual interactions could profoundly influence several important processes, such as accretion variability and outbursts, fragmentation and disc truncation, or large-scale magnetic field production. Direct numerical simulations of both instabilities are computationally challenging and remain relatively unexplored. In this paper, we aim to redress this neglect via a set of 3D vertically stratified shearing-box simulations, combining self-gravity and magnetic fields. We show that gravito-turbulence greatly weakens the zero-net-flux MRI. In the limit of efficient cooling (and thus enhanced GI), the MRI is completely suppressed, and yet strong magnetic fields are sustained by the gravitoturbulence. This turbulent `spiral wave dynamo may have widespread application, especially in galactic discs. Finally, we present preliminary work showing that a strong net-vertical-flux revives the MRI and supports a magnetically dominated state, in which the GI is secondary.
We reveal and investigate a new type of linear axisymmetric helical magnetorotational instability which is capable of destabilizing viscous and resistive rotational flows with radially increasing angular velocity, or positive shear. This instability is double-diffusive by nature and is different from the more familiar helical magnetorotational instability, operating at positive shear above the Liu limit, in that it works instead for a wide range of the positive shear when ${rm (i)}$ a combination of axial/poloidal and azimuthal/toroidal magnetic fields is applied and ${rm (ii)}$ the magnetic Prandtl number is not too close to unity. We study this instability first with radially local WKB analysis and then confirm its existence using a global stability analysis of the magnetized flow between two rotating cylinders with conducting or insulating boundaries. From an experimental point of view, we also demonstrate the presence of the new instability in a magnetized viscous and resistive Taylor-Couette flow with positive shear for such values of the flow parameters, which can be realized in upcoming experiments at the DRESDYN facility. Finally, this instability might have implications for the dynamics of the equatorial parts of the solar tachocline and dynamo action there, since the above two necessary conditions for the instability to take place are satisfied in this region. Our global stability calculations for the tachocline-like configuration, representing a thin rotating cylindrical layer with the appropriate boundary conditions -- conducting inner and insulating outer cylinders -- and the values of the flow parameters, indicate that it can indeed arise in this case with a characteristic growth time comparable to the solar cycle period.
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 HMRI 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.
We present results from the first 3D kinetic numerical simulation of magnetorotational turbulence and dynamo, using the local shearing-box model of a collisionless accretion disc. The kinetic magnetorotational instability grows from a subthermal magnetic field having zero net flux over the computational domain to generate self-sustained turbulence and outward angular-momentum transport. Significant Maxwell and Reynolds stresses are accompanied by comparable viscous stresses produced by field-aligned ion pressure anisotropy, which is regulated primarily by the mirror and ion-cyclotron instabilities through particle trapping and pitch-angle scattering. The latter endow the plasma with an effective viscosity that is biased with respect to the magnetic-field direction and spatio-temporally variable. Energy spectra suggest an Alfven-wave cascade at large scales and a kinetic-Alfven-wave cascade at small scales, with strong small-scale density fluctuations and weak non-axisymmetric density waves. Ions undergo non-thermal particle acceleration, their distribution accurately described by a kappa distribution. These results have implications for the properties of low-collisionality accretion flows, such as that near the black hole at the Galactic center.
A three-dimensional nonlinear dynamo process is identified in rotating plane Couette flow in the Keplerian regime. It is analogous to the hydrodynamic self-sustaining process in non-rotating shear flows and relies on the magneto-rotational instability of a toroidal magnetic field. Steady nonlinear solutions are computed numerically for a wide range of magnetic Reynolds numbers but are restricted to low Reynolds numbers. This process may be important to explain the sustenance of coherent fields and turbulent motions in Keplerian accretion disks, where all its basic ingredients are present.
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