无外加场的扩展局域Keplerian流的输运性质
Transport properties of Keplerian flows in extended local domains with no imposed field
摘要：
我们比较运输统计的细长不可压缩剪切盒不同的雷诺数和磁普朗特数，$Re$和$Pm$，和纵横比，$L_z/L_x$。我们发现，在固定的展弦比$L_z/L_x=4$和$Re = 10,000$下，$Pm \lesssim 1$的湍流应力变化不大，对$Pm > 1$遵循$\sim Pm^{3/2}$的幂律。这与以前基于净施加通量和小盒子$L_z/L_x \sim 1$模拟的结果定性一致，但幂律指数不同。随着$L_z/L_x$的增加，应力的饱和水平、麦克斯韦应力与磁能的比值以及雷诺应力与麦克斯韦应力的比值大致不变。对于盒子在方位角和垂直方向上都伸长的情况，传输系数$α\in [0.1,1.0]$是具有$L_y/L_x = 2$和大$L_z/L_x$的情况的$10-100$倍。总体而言，我们的研究结果表明，湍流的饱和状态是敏感的耗散系数和纵横比（都$L_z/L_x$，$L_y/L_x$）激励进一步的工作在这个问题上。
英文摘要：
We compare transport statistics of elongated incompressible shearing boxes for different Reynolds and magnetic Prandtl numbers, $Re$ and $Pm$, and aspect ratios, $L_z/L_x$. We find that at fixed aspect ratio $L_z/L_x=4$ and $Re = 10,000$, the turbulent stresses for $Pm \lesssim 1$ do not show considerable variation and follow a power law $\sim Pm^{3/2}$ for $Pm > 1$. This is qualitatively consistent with previous results based on net imposed flux and small box $L_z/L_x \sim 1$ simulations but the power law exponent is different. The saturated level of stresses, the ratio of Maxwell stress to the magnetic energy and Reynolds to Maxwell stress ratio are roughly invariant as $L_z/L_x$ is increased. For cases where the boxes are elongated in both the azimuth and vertical direction, the transport coefficient $α\in [0.1,1.0]$ that is $10-100$ times larger than the case with $L_y/L_x = 2$ and large $L_z/L_x$. Overall, our results suggest that the saturated state of turbulence is sensitive to both dissipation coefficients and aspect ratio (both $L_z/L_x$, $L_y/L_x$) motivating further work on this problem.
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