2015/08/31 by John Gibbon, J. D. Gibbon, A. Gupta +13
Biochemistry, Genetics and Molecular Biology · Engineering · Physics and Astronomy · #Convection #Fluid Dynamics and Turbulent Flows #Geomagnetism and Paleomagnetism Studies #Intermittency #Magnetic field #Magnetohydrodynamic drive #Magnetohydrodynamic turbulence #Magnetohydrodynamics #Mechanics #Nonlinear system #Physics #Prandtl number #Quantum mechanics #Solar and Space Plasma Dynamics #Statistical physics #Turbulence #Vortex #Vorticity #nlin.CD #physics.flu-dyn
paper · pdf · doi:10.1103/physreve.93.043104
published as Phys. Rev. E 93, 043104 (2016) · 14 pages, 3 figures
openalex publication_date 2016/04/04 · arxiv created 2016/05/26 · arxiv updated 2016/05/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06
It is shown how suitably scaled, order-m moments, Dm^\ifmmode±\else\textpm\fi, of the Els"asser 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 \mathbf\ensuremathω^\ifmmode±\else\textpm\fi=curl\phantom\rule0.16em0exz^\ifmmode±\else\textpm\fi=\mathbf\ensuremathω\ifmmode±\else\textpm\fi\mathbitj, where z^\ifmmode±\else\textpm\fi are Els"asser variables, and where \mathbf\ensuremathω and \mathbitj 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^\ifmmode±\else\textpm\fi that characterize the inertial range power-law dependencies of the z^\ifmmode±\else\textpm\fi energy spectra, E^\ifmmode±\else\textpm\fi(k), are then examined, and bounds are obtained. Comments are also made on (a) the generalization of our results to the case PM\ensuremath≠1 and (b) the relation between Dm^\ifmmode±\else\textpm\fi and the order-m moments of gradients of magnetohydrodynamic fields, which are used to characterize intermittency in turbulent flows.