Transport properties of Keplerian flows in extended local domains with no imposed field

TL;DR

This study investigates how the transport properties of Keplerian flows in elongated shearing boxes depend on Reynolds number, magnetic Prandtl number, and aspect ratios, revealing that turbulence saturation is sensitive to these parameters.

Contribution

It provides new insights into the dependence of turbulent transport on aspect ratio and dissipation coefficients in extended local domains without imposed magnetic fields.

Findings

Transport coefficients vary with aspect ratio and dissipation parameters.

Turbulent stresses follow a power law with magnetic Prandtl number for Pm > 1.

Saturated turbulence levels are roughly invariant with aspect ratio changes.

Abstract

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 $\alpha \in [0.1,1.0]$ 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.