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

• Published in: Physical review. E 2016-04, Vol.93 (4), p.043104-043104, Article 043104
• Main Authors: Gibbon, J D, Gupta, A, Krstulovic, G, Pandit, R, Politano, H, Ponty, Y, Pouquet, A, Sahoo, G, Stawarz, J
• Format: Article
• Language: English
• ISSN: 2470-0045; 2470-0053
• DOI: 10.1103/PhysRevE.93.043104

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.