dorsal/arxiv
View SchemaThe scaling properties of dissipation in incompressible isotropic three-dimensional magnetohydrodynamic turbulence
| Authors | J. A. Merrifield, W. -C. Muller, S. C. Chapman, R. O. Dendy |
|---|---|
| Categories | |
| ArXiv ID | physics/0412014 |
| URL | https://arxiv.org/abs/physics/0412014 |
| DOI | 10.1063/1.1842133 |
| Journal | Phys. Plasmas 12, 022301 (2005) |
Abstract
The statistical properties of the dissipation process constrain the analysis of large scale numerical simulations of three dimensional incompressible magnetohydrodynamic (MHD) turbulence, such as those of Biskamp and Muller [Phys. Plasmas 7, 4889 (2000)]. The structure functions of the turbulent flow are expected to display statistical self-similarity, but the relatively low Reynolds numbers attainable by direct numerical simulation, combined with the finite size of the system, make this difficult to measure directly. However, it is known that extended self-similarity, which constrains the ratio of scaling exponents of structure functions of different orders, is well satisfied. This implies the extension of physical scaling arguments beyond the inertial range into the dissipation range. The present work focuses on the scaling properties of the dissipation process itself. This provides an important consistency check in that we find that the ratio of dissipation structure function exponents is that predicted by the She and Leveque [Phys. Rev. Lett 72, 336 (1994)] theory proposed by Biskamp and Muller. This supplies further evidence that the cascade mechanism in three dimensional MHD turbulence is non-linear random eddy scrambling, with the level of intermittency determined by dissipation through the formation of current sheets.
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"abstract": "The statistical properties of the dissipation process constrain the analysis\nof large scale numerical simulations of three dimensional incompressible\nmagnetohydrodynamic (MHD) turbulence, such as those of Biskamp and Muller\n[Phys. Plasmas 7, 4889 (2000)]. The structure functions of the turbulent flow\nare expected to display statistical self-similarity, but the relatively low\nReynolds numbers attainable by direct numerical simulation, combined with the\nfinite size of the system, make this difficult to measure directly. However, it\nis known that extended self-similarity, which constrains the ratio of scaling\nexponents of structure functions of different orders, is well satisfied. This\nimplies the extension of physical scaling arguments beyond the inertial range\ninto the dissipation range. The present work focuses on the scaling properties\nof the dissipation process itself. This provides an important consistency check\nin that we find that the ratio of dissipation structure function exponents is\nthat predicted by the She and Leveque [Phys. Rev. Lett 72, 336 (1994)] theory\nproposed by Biskamp and Muller. This supplies further evidence that the cascade\nmechanism in three dimensional MHD turbulence is non-linear random eddy\nscrambling, with the level of intermittency determined by dissipation through\nthe formation of current sheets.",
"arxiv_id": "physics/0412014",
"authors": [
"J. A. Merrifield",
"W. -C. Muller",
"S. C. Chapman",
"R. O. Dendy"
],
"categories": [
"physics.plasm-ph",
"physics.space-ph"
],
"doi": "10.1063/1.1842133",
"journal_ref": "Phys. Plasmas 12, 022301 (2005)",
"title": "The scaling properties of dissipation in incompressible isotropic three-dimensional magnetohydrodynamic turbulence",
"url": "https://arxiv.org/abs/physics/0412014"
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