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# Depletion of Nonlinearity in Magnetohydrodynamic Turbulence: Insights from Analysis and Simulations

Abstract : We build on recent developments in the study of fluid turbulence [Gibbon \textit{et al.} Nonlinearity 27, 2605 (2014)] to define suitably scaled, order-$m$ moments, $D_m^{\pm}$, of $\omega^\pm= \omega \pm j$, where $\omega$ and $j$ are, respectively, the vorticity and current density in three-dimensional magnetohydrodynamics (MHD). We show by mathematical analysis, for unit magnetic Prandtl number $P_M$, how these moments can be used to identify three possible regimes for solutions of the MHD equations; these regimes are specified by inequalities for $D_m^{\pm}$ and $D_1^{\pm}$. We then compare our mathematical results with those from our direct numerical simulations (DNSs) and thus demonstrate that 3D MHD turbulence is like its fluid-turbulence counterpart insofar as all solutions, which we have investigated, remain in \textit{only one of these regimes}; this regime has depleted nonlinearity. We examine the implications of our results for the exponents $q^{\pm}$ that characterize the power-law dependences of the energy spectra $\mathcal{E}^{\pm}(k)$ on the wave number $k$, in the inertial range of scales. We also comment on (a) the generalization of our results to the case $P_M \neq 1$ and (b) the relation between $D_m^{\pm}$ and the order-$m$ moments of gradients of hydrodynamic fields, which are used in characterizing intermittency in turbulent flows.
Document type :
Journal articles

https://hal.archives-ouvertes.fr/hal-01288496
Contributor : Hélène Politano Connect in order to contact the contributor
Submitted on : Thursday, March 10, 2022 - 2:50:03 PM
Last modification on : Thursday, March 10, 2022 - 2:50:05 PM

### File

gibbon2016.pdf
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### Citation

John D. Gibbon, Anupam Gupta, Giorgio Krstulovic, Rahul Pandit, Hélène Politano, et al.. Depletion of Nonlinearity in Magnetohydrodynamic Turbulence: Insights from Analysis and Simulations. Physical Review E : Statistical, Nonlinear, and Soft Matter Physics, American Physical Society, 2016, 93 (4), pp.043104. ⟨10.1103/PhysRevE.93.043104⟩. ⟨hal-01288496⟩

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