Kempski Philipp, Quataert Eliot, Squire Jonathan, Kunz Matthew W
Department of Astronomy and Theoretical Astrophysics Center, University of California, Berkeley, Berkeley, CA 94720, USA.
Department of Physics, University of Otago, 730 Cumberland St, North Dunedin, Dunedin 9016, New Zealand.
Mon Not R Astron Soc. 2019 Jul;486(3):4013-4029. doi: 10.1093/mnras/stz1111. Epub 2019 May 3.
We present a systematic shearing-box investigation of 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 (Δ) 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 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 ( / ) decreases from ~ 0.5 to ~ 0.1 as we move from Re ~ 10 to Re ~ 10, while 〈4Δ/ 〉 → 0. Anisotropic transport may thus become negligible at high Re. Anisotropic viscosity nevertheless becomes the dominant source of heating at large Re, accounting for ≳50% of the plasma heating. We conclude by briefly discussing the implications of our results for RIAFs onto black holes.
我们通过纳入各向异性压力应力（即各向异性（布拉金斯基）粘性）的影响，对弱碰撞等离子体中由磁流体动力学驱动的湍流进行了系统的剪切盒研究。我们将压力各向异性（Δ）限制在由动力学微观不稳定性否则会施加的稳定性界限内。通过考虑不同的雷诺数和磁场配置，包括净垂直通量、净环形 - 垂直通量和零净通量，我们探索了一个广阔的参数空间区域。值得注意的是，我们发现湍流水平和角动量传输受大的各向异性粘性影响不大：麦克斯韦应力和雷诺应力与磁流体动力学结果相差不大。即使各向异性粘性比各向同性扩散率大几个数量级，布拉金斯基磁流体动力学中的角动量传输仍然强烈依赖于耗散，例如各向同性磁普朗特数。然而，布拉金斯基粘性改变了流动结构，重新排列了湍流，以在很大程度上抵消背景剪切的平行应变率。我们还表明，体积平均压力各向异性和各向异性粘性传输随着各向同性雷诺数（Re）的增加而减小；例如，在具有净垂直场的模拟中，当我们从Re ~ 10移动到Re ~ 10时，各向异性与麦克斯韦应力的比值（ / ）从~ 0.5降至~ 0.1，而〈4Δ/ 〉→ 0。因此，在高Re时各向异性传输可能变得可以忽略不计。然而，在大Re时各向异性粘性成为加热的主要来源，占等离子体加热的≳50%。我们通过简要讨论我们的结果对黑洞吸积流的影响来结束本文。
