Scaling of Turbulent Viscosity and Resistivity: Extracting a Scale-dependent Turbulent Magnetic Prandtl Number

Bian, Xin; Shang, Jessica K.; Blackman, Eric G.; Collins, Gilbert W.; Aluie, Hussein

doi:10.3847/2041-8213/ac0fe5

Title: Scaling of Turbulent Viscosity and Resistivity: Extracting a Scale-dependent Turbulent Magnetic Prandtl Number

Journal Article · Mon Aug 09 00:00:00 EDT 2021 · The Astrophysical Journal. Letters

DOI:https://doi.org/10.3847/2041-8213/ac0fe5· OSTI ID:1814595

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Univ. of Rochester, NY (United States)

Turbulent viscosity $$\nu_t$$ and resistivity $$\eta_t$$ are perhaps the simplest models for turbulent transport of angular momentum and magnetic fields, respectively. The associated turbulent magnetic Prandtl number $$Pr_t\equiv \nu_t/\eta_t$$ has been well recognized to determine the final magnetic configuration of accretion disks. Here, we present an approach to determining these ``effective transport'' coefficients acting at different length-scales using coarse-graining and recent results on decoupled kinetic and magnetic energy cascades. By analyzing the kinetic and magnetic energy cascades from a suite of high-resolution simulations, we show that our definitions of $$\nu_t$$, $$\eta_t$$, and $$Pr_t$$ have power-law scalings in the ``decoupled range.'' We observe that $$Pr_t\approx1 \text{~to~}2$$ at the smallest inertial-inductive scales, increasing to $$\approx 5$$ at the largest scales. However, based on physical considerations, our analysis suggests that $$Pr_t$$ has to become scale-independent and of order unity in the decoupled range at sufficiently high Reynolds numbers (or grid-resolution), and that the power-law scaling exponents of velocity and magnetic spectra become equal. In addition to implications to astrophysical systems, the scale-dependent turbulent transport coefficients offer a guide for large eddy simulation modeling.

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Research Organization:: Univ. of Rochester, NY (United States)

Sponsoring Organization:: USDOE Office of Science (SC), Fusion Energy Sciences (FES); USDOE National Nuclear Security Administration (NNSA)

Grant/Contract Number:: NA0003856; SC0014318; SC0001063; SC0020229; SC0019329; NA0003914; SC0020432; SC0020103; AC02-05CH11231; AC02-06CH11357

OSTI ID:: 1814595

Alternate ID(s):: OSTI ID: 1871434

Journal Information:: The Astrophysical Journal. Letters, Vol. 917, Issue 1; ISSN 2041-8205

Publisher:: IOP PublishingCopyright Statement

Country of Publication:: United States

Language:: English

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