Depletion of nonlinearity in magnetohydrodynamic turbulence: Insights from analysis and simulations

AMS Citation:
Gibbon, J. D., and Coauthors, 2016: Depletion of nonlinearity in magnetohydrodynamic turbulence: Insights from analysis and simulations. Physical Review E, 93, 043104, doi:10.1103/PhysRevE.93.043104.
Date:2016-04-01
Resource Type:article
Title:Depletion of nonlinearity in magnetohydrodynamic turbulence: Insights from analysis and simulations
Abstract: It is shown how suitably scaled, order-m moments, D±m, of the Elsässer vorticity fields in three-dimensional magnetohydrodynamics (MHD) can be used to identify three possible regimes for solutions of the MHD equations with magnetic Prandtl number PM=1. These vorticity fields are defined by ω±=curlz±=ω±j, where z± are Elsässer variables, and where ω and j are, respectively, the fluid vorticity and current density. This study follows recent developments in the study of three-dimensional Navier-Stokes fluid turbulence [Gibbon et al., Nonlinearity 27, 2605 (2014)]. Our mathematical results are then compared with those from a variety of direct numerical simulations, which demonstrate that all solutions that have been investigated remain in only one of these regimes which has depleted nonlinearity. The exponents q± that characterize the inertial range power-law dependencies of the z± energy spectra, E±(k), are then examined, and bounds are obtained. Comments are also made on (a) the generalization of our results to the case PM≠1 and (b) the relation between D±m and the order-m moments of gradients of magnetohydrodynamic fields, which are used to characterize intermittency in turbulent flows.
Peer Review:Refereed
Copyright Information:Copyright 2016 American Physical Society.
OpenSky citable URL: ark:/85065/d79k4cv2
Publisher's Version: 10.1103/PhysRevE.93.043104
Author(s):
  • J. Gibbon
  • A. Gupta
  • G. Krstulovic
  • R. Pandit
  • H. Politano
  • Y. Ponty
  • Annick Pouquet - NCAR/UCAR
  • G. Sahoo
  • J. Stawarz
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