dorsal/arxiv
View SchemaSpectral energy dynamics in magnetohydrodynamic turbulence
| Authors | Wolf-Christian Mueller, Roland Grappin |
|---|---|
| Categories | |
| ArXiv ID | physics/0509019 |
| URL | https://arxiv.org/abs/physics/0509019 |
| DOI | 10.1103/PhysRevLett.95.114502 |
Abstract
Spectral direct numerical simulations of incompressible MHD turbulence at a resolution of up to $1024^3$ collocation points are presented for a statistically isotropic system as well as for a setup with an imposed strong mean magnetic field. The spectra of residual energy, $E_k^\mathrm{R}=|E_k^\mathrm{M}-E_k^\mathrm{K}|$, and total energy, $E_k=E^\mathrm{K}_k+E^\mathrm{M}_k$, are observed to scale self-similarly in the inertial range as $E_k^\mathrm{R}\sim k^{-7/3}$, $E_k\sim k^{-5/3}$ (isotropic case) and $E^\mathrm{R}_{k_\perp}\sim k_\perp^{-2}$, $E_{k_\perp}\sim k_\perp^{-3/2}$ (anisotropic case, perpendicular to the mean field direction). A model of dynamic equilibrium between kinetic and magnetic energy, based on the corresponding evolution equations of the eddy-damped quasi-normal Markovian (EDQNM) closure approximation, explains the findings. The assumed interplay of turbulent dynamo and Alfv\'en effect yields $E_k^\mathrm{R}\sim k E^2_k$ which is confirmed by the simulations.
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"date_created": "2026-03-02T18:01:00.691000Z",
"date_modified": "2026-03-02T18:01:00.691000Z",
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"abstract": "Spectral direct numerical simulations of incompressible MHD turbulence at a\nresolution of up to $1024^3$ collocation points are presented for a\nstatistically isotropic system as well as for a setup with an imposed strong\nmean magnetic field. The spectra of residual energy,\n$E_k^\\mathrm{R}=|E_k^\\mathrm{M}-E_k^\\mathrm{K}|$, and total energy,\n$E_k=E^\\mathrm{K}_k+E^\\mathrm{M}_k$, are observed to scale self-similarly in\nthe inertial range as $E_k^\\mathrm{R}\\sim k^{-7/3}$, $E_k\\sim k^{-5/3}$\n(isotropic case) and $E^\\mathrm{R}_{k_\\perp}\\sim k_\\perp^{-2}$,\n$E_{k_\\perp}\\sim k_\\perp^{-3/2}$ (anisotropic case, perpendicular to the mean\nfield direction). A model of dynamic equilibrium between kinetic and magnetic\nenergy, based on the corresponding evolution equations of the eddy-damped\nquasi-normal Markovian (EDQNM) closure approximation, explains the findings.\nThe assumed interplay of turbulent dynamo and Alfv\\\u0027en effect yields\n$E_k^\\mathrm{R}\\sim k E^2_k$ which is confirmed by the simulations.",
"arxiv_id": "physics/0509019",
"authors": [
"Wolf-Christian Mueller",
"Roland Grappin"
],
"categories": [
"physics.flu-dyn",
"physics.plasm-ph"
],
"doi": "10.1103/PhysRevLett.95.114502",
"title": "Spectral energy dynamics in magnetohydrodynamic turbulence",
"url": "https://arxiv.org/abs/physics/0509019"
},
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