dorsal/arxiv
View SchemaA numerical study of the alpha model for two-dimensional magnetohydrodynamic turbulent flows
| Authors | P. D. Mininni, D. C. Montgomery, A. G. Pouquet |
|---|---|
| Categories | |
| ArXiv ID | physics/0410159 |
| URL | https://arxiv.org/abs/physics/0410159 |
| DOI | 10.1063/1.1863260 |
Abstract
We explore some consequences of the ``alpha model,'' also called the ``Lagrangian-averaged'' model, for two-dimensional incompressible magnetohydrodynamic (MHD) turbulence. This model is an extension of the smoothing procedure in fluid dynamics which filters velocity fields locally while leaving their associated vorticities unsmoothed, and has proved useful for high Reynolds number turbulence computations. We consider several known effects (selective decay, dynamic alignment, inverse cascades, and the probability distribution functions of fluctuating turbulent quantities) in magnetofluid turbulence and compare the results of numerical solutions of the primitive MHD equations with their alpha-model counterparts' performance for the same flows, in regimes where available resolution is adequate to explore both. The hope is to justify the use of the alpha model in regimes that lie outside currently available resolution, as will be the case in particular in three-dimensional geometry or for magnetic Prandtl numbers differing significantly from unity. We focus our investigation, using direct numerical simulations with a standard and fully parallelized pseudo-spectral method and periodic boundary conditions in two space dimensions, on the role that such a modeling of the small scales using the Lagrangian-averaged framework plays in the large-scale dynamics of MHD turbulence. Several flows are examined, and for all of them one can conclude that the statistical properties of the large-scale spectra are recovered, whereas small-scale detailed phase information (such as e.g. the location of structures) is lost.
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"abstract": "We explore some consequences of the ``alpha model,\u0027\u0027 also called the\n``Lagrangian-averaged\u0027\u0027 model, for two-dimensional incompressible\nmagnetohydrodynamic (MHD) turbulence. This model is an extension of the\nsmoothing procedure in fluid dynamics which filters velocity fields locally\nwhile leaving their associated vorticities unsmoothed, and has proved useful\nfor high Reynolds number turbulence computations. We consider several known\neffects (selective decay, dynamic alignment, inverse cascades, and the\nprobability distribution functions of fluctuating turbulent quantities) in\nmagnetofluid turbulence and compare the results of numerical solutions of the\nprimitive MHD equations with their alpha-model counterparts\u0027 performance for\nthe same flows, in regimes where available resolution is adequate to explore\nboth. The hope is to justify the use of the alpha model in regimes that lie\noutside currently available resolution, as will be the case in particular in\nthree-dimensional geometry or for magnetic Prandtl numbers differing\nsignificantly from unity. We focus our investigation, using direct numerical\nsimulations with a standard and fully parallelized pseudo-spectral method and\nperiodic boundary conditions in two space dimensions, on the role that such a\nmodeling of the small scales using the Lagrangian-averaged framework plays in\nthe large-scale dynamics of MHD turbulence. Several flows are examined, and for\nall of them one can conclude that the statistical properties of the large-scale\nspectra are recovered, whereas small-scale detailed phase information (such as\ne.g. the location of structures) is lost.",
"arxiv_id": "physics/0410159",
"authors": [
"P. D. Mininni",
"D. C. Montgomery",
"A. G. Pouquet"
],
"categories": [
"physics.flu-dyn",
"physics.plasm-ph"
],
"doi": "10.1063/1.1863260",
"title": "A numerical study of the alpha model for two-dimensional magnetohydrodynamic turbulent flows",
"url": "https://arxiv.org/abs/physics/0410159"
},
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