Structure information in rapid distortion analysis and one-point modeling of axisymmetric magnetohydrodynamic turbulence

• It has recently been suggested that dimensionality information, as carried by the Reynolds dimensionality tensor, should be included in an extended Reynolds stress closure for modeling of magnetohydrodynamic (MHD) turbulence at low magnetic Reynolds numbers. This would enable more accurate modeling of the Joule dissipation, and capture the length-scale anisotropies and tendencies towards two-dimensionality characteristic of MHD turbulence. In the present work, an evolution equation for the Reynolds dimensionality tensor is derived, based on the spectral formulation of the Navier-Stokes equations. Most of the terms in the equation require modeling. Rapid distortion theory (RDT) is applied to study the behavior of the different magnetic terms of the dimensionality and Reynolds stress tensor equations; a variety of different anisotropy states could be examined by letting magnetic forcing act on a number of initial spectral energy distributions obtained from axisymmetric strain. The properties and limitations of linear or bilinear invariant tensor models for the magnetic terms are evaluated. In the limit of large interaction numbers (where Joule dissipation dominates), the resulting model equations for the energy decay have analytic solutions. By choosing one model constant appropriately, these are made consistent with the asymptotic energy decay K similar to t(-1/2) predicted earlier by Moffatt. The long-term objective of these efforts is the development of an effective second-moment closure for engineering applications.

Nyckelord

reynolds-stress closures

mhd turbulence

numerical-simulation

number

flows

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