Phenomenology for the decay of energy-containing eddies in homogeneous MHD turbulence

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Abstract
We evaluate a number of simple, one-point phenomenological models for the decay of energy-containing eddies in magnetohydrodynamic (MHD) and hydrodynamic turbulence. The MHD models include effects of cross helicity and Alfvénic couplings associated with a constant mean magnetic field, based on physical effects well-described in the literature. The analytic structure of three separate MHD models is discussed. The single hydrodynamic model and several MHD models are compared against results from spectral-method simulations. The hydrodynamic model phenomenology has been previously verified against experiments in wind tunnels, and certain experimentally determined parameters in the model are satisfactorily reproduced by the present simulation. This agreement supports the suitability of our numerical calculations for examining MHD turbulence, where practical difficulties make it more difficult to study physical examples. When the triple-decorrelation time and effects of spectral anisotropy are properly taken into account, particular MHD models give decay rates that remain correct to within a factor of 2 for several energy-halving times. A simple model of this type is likely to be useful in a number of applications in space physics, astrophysics, and laboratory plasma physics where the approximate effects of turbulence need to be included.