Coarsegrained incompressible magnetohydrodynamics: Analyzing the turbulent cascades
Abstract
Here, we formulate a coarsegraining approach to the dynamics of magnetohydrodynamic (MHD) fluids at a continuum of lengthscales. In this methodology, effective equations are derived for the observable velocity and magnetic fields spatiallyaveraged at an arbitrary scale of resolution. The microscopic equations for the bare velocity and magnetic fields are renormalized by coarsegraining to yield macroscopic effective equations that contain both a subscale stress and a subscale electromotive force (EMF) generated by nonlinear interaction of eliminated fields and plasma motions. At large coarsegraining lengthscales, the direct dissipation of invariants by microscopic mechanisms (such as molecular viscosity and Spitzer resistivity) is shown to be negligible. The balance at large scales is dominated instead by the subscale nonlinear terms, which can transfer invariants across scales, and are interpreted in terms of work concepts for energy and in terms of topological fluxlinkage for the two helicities. An important application of this approach is to MHD turbulence, where the coarsegraining length ℓ lies in the inertial cascade range. We show that in the case of sufficiently rough velocity and/or magnetic fields, the nonlinear interscale transfer need not vanish and can persist to arbitrarily small scales. Although closed expressions are not available for subscale stressmore »
 Authors:
 Univ. of Rochester, Rochester, NY (United States)
 Publication Date:
 Research Org.:
 Univ. of Rochester, Rochester, NY (United States); Univ. of Rochester, NY (United States)
 Sponsoring Org.:
 USDOE Office of Science (SC), Fusion Energy Sciences (FES) (SC24); USDOE Office of Science (SC), High Energy Physics (HEP) (SC25); USDOE National Nuclear Security Administration (NNSA), Office of Defense Nuclear Security (NA70)
 OSTI Identifier:
 1437700
 Alternate Identifier(s):
 OSTI ID: 1356076; OSTI ID: 1358358
 Grant/Contract Number:
 SC0014318; NA0001944; 20150568ER
 Resource Type:
 Journal Article: Published Article
 Journal Name:
 New Journal of Physics
 Additional Journal Information:
 Journal Volume: 19; Journal Issue: 2; Journal ID: ISSN 13672630
 Publisher:
 IOP Publishing
 Country of Publication:
 United States
 Language:
 English
 Subject:
 22 GENERAL STUDIES OF NUCLEAR REACTORS; energydissipation rate; largeeddy simulation; free magneticfields; isotropic turbulence; hydromagnetic turbulence; ideal hydrodynamics; inverse cascade; inertialrange; helicity; flows; magnetohydrodynamics; turbulence; coarsegraining; cascade
Citation Formats
Aluie, Hussein. Coarsegrained incompressible magnetohydrodynamics: Analyzing the turbulent cascades. United States: N. p., 2017.
Web. doi:10.1088/13672630/aa5d2f.
Aluie, Hussein. Coarsegrained incompressible magnetohydrodynamics: Analyzing the turbulent cascades. United States. doi:10.1088/13672630/aa5d2f.
Aluie, Hussein. Tue .
"Coarsegrained incompressible magnetohydrodynamics: Analyzing the turbulent cascades". United States.
doi:10.1088/13672630/aa5d2f.
@article{osti_1437700,
title = {Coarsegrained incompressible magnetohydrodynamics: Analyzing the turbulent cascades},
author = {Aluie, Hussein},
abstractNote = {Here, we formulate a coarsegraining approach to the dynamics of magnetohydrodynamic (MHD) fluids at a continuum of lengthscales. In this methodology, effective equations are derived for the observable velocity and magnetic fields spatiallyaveraged at an arbitrary scale of resolution. The microscopic equations for the bare velocity and magnetic fields are renormalized by coarsegraining to yield macroscopic effective equations that contain both a subscale stress and a subscale electromotive force (EMF) generated by nonlinear interaction of eliminated fields and plasma motions. At large coarsegraining lengthscales, the direct dissipation of invariants by microscopic mechanisms (such as molecular viscosity and Spitzer resistivity) is shown to be negligible. The balance at large scales is dominated instead by the subscale nonlinear terms, which can transfer invariants across scales, and are interpreted in terms of work concepts for energy and in terms of topological fluxlinkage for the two helicities. An important application of this approach is to MHD turbulence, where the coarsegraining length ℓ lies in the inertial cascade range. We show that in the case of sufficiently rough velocity and/or magnetic fields, the nonlinear interscale transfer need not vanish and can persist to arbitrarily small scales. Although closed expressions are not available for subscale stress and subscale EMF, we derive rigorous upper bounds on the effective dissipation they produce in terms of scaling exponents of the velocity and magnetic fields. These bounds provide exact constraints on phenomenological theories of MHD turbulence in order to allow the nonlinear cascade of energy and crosshelicity. On the other hand, we show that the forward cascade of magnetic helicity to asymptotically small scales is impossible unless 3rdorder moments of either velocity or magnetic field become infinite.},
doi = {10.1088/13672630/aa5d2f},
journal = {New Journal of Physics},
number = 2,
volume = 19,
place = {United States},
year = {Tue Feb 21 00:00:00 EST 2017},
month = {Tue Feb 21 00:00:00 EST 2017}
}
Web of Science

Here, we formulate a coarsegraining approach to the dynamics of magnetohydrodynamic (MHD) fluids at a continuum of lengthscales. In this methodology, effective equations are derived for the observable velocity and magnetic fields spatiallyaveraged at an arbitrary scale of resolution. The microscopic equations for the bare velocity and magnetic fields are renormalized by coarsegraining to yield macroscopic effective equations that contain both a subscale stress and a subscale electromotive force (EMF) generated by nonlinear interaction of eliminated fields and plasma motions. At large coarsegraining lengthscales, the direct dissipation of invariants by microscopic mechanisms (such as molecular viscosity and Spitzer resistivity) ismore »Cited by 3

Coarsegrained incompressible magnetohydrodynamics: analyzing the turbulent cascades
We formulate a coarsegraining approach to the dynamics of magnetohydrodynamic (MHD) fluids at a continuum of lengthscales. In this methodology, effective equations are derived for the observable velocity and magnetic fields spatiallyaveraged at an arbitrary scale of resolution. The microscopic equations for the bare velocity and magnetic fields are renormalized by coarsegraining to yield macroscopic effective equations that contain both a subscale stress and a subscale electromotive force (EMF) generated by nonlinear interaction of eliminated fields and plasma motions. At large coarsegraining lengthscales, the direct dissipation of invariants by microscopic mechanisms (such as molecular viscosity and Spitzer resistivity) is shownmore »Cited by 3 
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The transport of neutral particles in turbulent plasmas is addressed from the prospect of developing coarsegrained transport models which can be implemented in code suites like B2EIRENE, currently used for designing the ITER divertor. The statistical properties of turbulent fluctuations are described by a multivariate Gamma distribution able to retain space and time correlations through a proper choice of covariance function. We show that in the scattering free case, relevant for molecules and impurity atoms, the average neutral particle density obeys a Boltzmann equation with an ionization rate renormalized by fluctuations. This result lends itself to a straightforward implementation inmore »