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 P_{M}=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)NONLE50951-771510.1088/0951-7715/27/10/2605]. 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 P_{M}≠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.
authors.affiliation: Department of Mathematics, Imperial College London, London SW7 2AZ, United Kingdom.
authors.forename: J D
authors.initials: JD
authors.lastname: Gibbon
authors.affiliation: Department of Physics, University of Rome "Tor Vergata," 00133 Rome, Italy.
authors.forename: A
authors.initials: A
authors.lastname: Gupta
authors.affiliation: Laboratoire Lagrange, Université Côte d'Azur, Observatoire de la Côte d'Azur, CNRS, Blvd de l'Observatoire, CS 34229, 06304 Nice cedex 4, France.
authors.forename: G
authors.initials: G
authors.lastname: Krstulovic
authors.affiliation: Centre for Condensed Matter Theory, Indian Institute of Science, Bangalore, 560 012, India.
authors.forename: R
authors.initials: R
authors.lastname: Pandit
authors.affiliation: Laboratoire Dieudonné, Université de Nice Sophia-Antipolis, France.
authors.forename: H
authors.initials: H
authors.lastname: Politano
authors.affiliation: Laboratoire Lagrange, Université Côte d'Azur, Observatoire de la Côte d'Azur, CNRS, Blvd de l'Observatoire, CS 34229, 06304 Nice cedex 4, France.
authors.forename: Y
authors.initials: Y
authors.lastname: Ponty
authors.affiliation: National Center for Atmospheric Research, P.O. Box 3000, Boulder, Colorado 80307, USA.|Laboratory for Atmospheric and Space Physics, University of Colorado, Boulder, Colorado 80303, USA.
authors.forename: A
authors.initials: A
authors.lastname: Pouquet
authors.affiliation: Department of Physics, University of Rome "Tor Vergata," 00133 Rome, Italy.
authors.forename: G
authors.initials: G
authors.lastname: Sahoo
authors.affiliation: Laboratory for Atmospheric and Space Physics, University of Colorado, Boulder, Colorado 80303, USA.
authors.forename: J
authors.initials: J
authors.lastname: Stawarz