Lagrangian-averaged model for magnetohydrodynamic turbulence and the absence of bottlenecks

AMS Citation:
Graham, J. P., P. D. Mininni, and A. Pouquet, 2009: Lagrangian-averaged model for magnetohydrodynamic turbulence and the absence of bottlenecks. Physical Review E, 80, 016313, doi:10.1103/PhysRevE.80.016313.
Date:2009-07-22
Resource Type:article
Title:Lagrangian-averaged model for magnetohydrodynamic turbulence and the absence of bottlenecks
Abstract: We demonstrate that, for the case of quasiequipartition between the velocity and the magnetic field, the Lagrangian-averaged magnetohydrodynamics (LAMHD) α model reproduces well both the large-scale and the small-scale properties of turbulent flows; in particular, it displays no increased (superfilter) bottleneck effect with its ensuing enhanced energy spectrum at the onset of the subfilter scales. This is in contrast to the case of the neutral fluid in which the Lagrangian-averaged Navier-Stokes α model is somewhat limited in its applications because of the formation of spatial regions with no internal degrees of freedom and subsequent contamination of superfilter-scale spectral properties. We argue that, as the Lorentz force breaks the conservation of circulation and enables spectrally nonlocal energy transfer (associated with Alfvén waves), it is responsible for the absence of a viscous bottleneck in magnetohydrodynamics (MHD), as compared to the fluid case. As LAMHD preserves Alfvén waves and the circulation properties of MHD, there is also no (superfilter) bottleneck found in LAMHD, making this method capable of large reductions in required numerical degrees of freedom; specifically, we find a reduction factor of ≈200 when compared to a direct numerical simulation on a large grid of 1536³ points at the same Reynolds number.
Peer Review:Refereed
Copyright Information:Copyright 2009 American Physical Society.
OpenSky citable URL: ark:/85065/d7rx9db4
Publisher's Version: 10.1103/PhysRevE.80.016313
Author(s):
  • Jonathan Graham
  • Pablo Mininni - NCAR/UCAR
  • Annick Pouquet - NCAR/UCAR
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