Shearing-box simulations of MRI-driven turbulence in weakly collisional accretion discs
ABSTRACT We present a systematic shearing-box investigation of magnetorotational instability (MRI)-driven turbulence in a weakly collisional plasma by including the effects of an anisotropic pressure stress, i.e. anisotropic (Braginskii) viscosity. We constrain the pressure anisotropy (Δp) to lie within the stability bounds that would be otherwise imposed by kinetic microinstabilities. We explore a broad region of parameter space by considering different Reynolds numbers and magnetic-field configurations, including net vertical flux, net toroidal-vertical flux, and zero net flux. Remarkably, we find that the level of turbulence and angular-momentum transport are not greatly affected by large anisotropic viscosities: the Maxwell and Reynolds stresses do not differ much from the MHD result. Angular-momentum transport in Braginskii MHD still depends strongly on isotropic dissipation, e.g. the isotropic magnetic Prandtl number, even when the anisotropic viscosity is orders of magnitude larger than the isotropic diffusivities. Braginskii viscosity nevertheless changes the flow structure, rearranging the turbulence to largely counter the parallel rate of strain from the background shear. We also show that the volume-averaged pressure anisotropy and anisotropic viscous transport decrease with increasing isotropic Reynolds number (Re); e.g. in simulations with net vertical field, the ratio of anisotropic to Maxwell stress (αA/αM) decreases from ∼0.5 to more »
Authors:
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Award ID(s):
Publication Date:
NSF-PAR ID:
10204599
Journal Name:
Monthly Notices of the Royal Astronomical Society
Volume:
486
Issue:
3
Page Range or eLocation-ID:
4013 to 4029
ISSN:
0035-8711
5. We propose that pressure anisotropy causes weakly collisional turbulent plasmas to self-organize so as to resist changes in magnetic-field strength. We term this effect ‘magneto-immutability’ by analogy with incompressibility (resistance to changes in pressure). The effect is important when the pressure anisotropy becomes comparable to the magnetic pressure, suggesting that in collisionless, weakly magnetized (high- $\unicode[STIX]{x1D6FD}$ ) plasmas its dynamical relevance is similar to that of incompressibility. Simulations of magnetized turbulence using the weakly collisional Braginskii model show that magneto-immutable turbulence is surprisingly similar, in most statistical measures, to critically balanced magnetohydrodynamic turbulence. However, in order to minimize magnetic-field variation, the flow direction becomes more constrained than in magnetohydrodynamics, and the turbulence is more strongly dominated by magnetic energy (a non-zero ‘residual energy’). These effects represent key differences between pressure-anisotropic and fluid turbulence, and should be observable in the $\unicode[STIX]{x1D6FD}\gtrsim 1$ turbulent solar wind.