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- W2215743493 abstract "It is shown how suitably scaled, order-$m$ moments, ${D}_{m}^{ifmmodepmelsetextpmfi{}}$, of the Elsasser 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 ${mathbf{ensuremath{omega}}}^{ifmmodepmelsetextpmfi{}}=text{curl}phantom{rule{0.16em}{0ex}}{z}^{ifmmodepmelsetextpmfi{}}=mathbf{ensuremath{omega}}ifmmodepmelsetextpmfi{}mathbit{j}$, where ${z}^{ifmmodepmelsetextpmfi{}}$ are Elsasser variables, and where $mathbf{ensuremath{omega}}$ and $mathbit{j}$ 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 ${q}^{ifmmodepmelsetextpmfi{}}$ that characterize the inertial range power-law dependencies of the ${z}^{ifmmodepmelsetextpmfi{}}$ energy spectra, ${mathcal{E}}^{ifmmodepmelsetextpmfi{}}(k)$, are then examined, and bounds are obtained. Comments are also made on (a) the generalization of our results to the case ${P}_{M}ensuremath{ne}1$ and (b) the relation between ${D}_{m}^{ifmmodepmelsetextpmfi{}}$ and the order-$m$ moments of gradients of magnetohydrodynamic fields, which are used to characterize intermittency in turbulent flows." @default.
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- W2215743493 date "2016-04-04" @default.
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- W2215743493 title "Depletion of nonlinearity in magnetohydrodynamic turbulence: Insights from analysis and simulations" @default.
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- W2215743493 doi "https://doi.org/10.1103/physreve.93.043104" @default.
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