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 Re ynolds 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 ten dencies 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 equatio ns. Most of the terms in the equation require modeling. Rapid distortion th eory (RDT) is applied to study the behavior of the different magnetic terms of the dimensionality and Reynolds stress tensor equations; a variety of d ifferent anisotropy states could be examined by letting magnetic forcing ac t on a number of initial spectral energy distributions obtained from axisym metric strain. The properties and limitations of linear or bilinear invaria nt tensor models for the magnetic terms are evaluated. In the limit of larg e interaction numbers (where Joule dissipation dominates), the resulting mo del equations for the energy decay have analytic solutions. By choosing one model constant appropriately, these are made consistent with the asymptoti c 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-m oment closure for engineering applications. (C) 2000 American Institute of Physics. [S1070-6631(00)50110-X].