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

We evaluate a number of simple, one‐point phenomenological models for the decay of energy‐containing eddies in magnetohydrodynamic(MHD) and hydrodynamicturbulence. The MHDmodels 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 MHDmodels is discussed. The single hydrodynamic model and several MHDmodels 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 MHDturbulence, 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 MHDmodels 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

Evolution of energy-containing turbulent eddies in the solar wind

Previous theoretical treatments of fluid-scale turbulence in the solar wind have concentrated on describing the state and dynamical evolution of fluctuations in the inertial range, which are characterized by power law energy spectra. In the present paper a model for the evolution of somewhat larger, more energetic magnetohydrodynamic (MHD) fluctuations is developed by analogy with classical hydrodynamic turbulence in the quasi-equilibrium range. The model is constructed by assembling and extending existing phenomenologies of homogeneous MHD turbulence, as well as simple two-length-scale models for transport of MHD turbulence in a weakly inhomogeneous medium. A set of equations is presented for the evolution of the turbulence, including the transport and nonlinear evolution of magnetic and kinetic energy, cross helicity, and their correlation scales. Two versions of the model are derived, depending on whether the fluctuations are distributed isotropically in three dimensions or restricted to the two-dimensional plane perpendicular to the mean magnetic field. This model includes a number of potentially important physical effects that have been neglected in previous discussions of transport of solar wind turbulence. Numerical solutions are shown for several cases of interest that demonstrate the advantages of this approach. We suggest that this model may prove useful in studies of solar wind heating and acceleration, as well as in describing the response of interplanetary turbulence to wave energy injected by pickup ions and planetary upstream waves

Reply to “Comment on ‘Evolution of energy-containing turbulent eddies in the solar wind’ by W. H. Matthaeus, S. Oughton, D. H. Pontius Jr., and Y. Zhou”

In their preceding comment on our paper [Matthaeus et al., 1994] (hereinafter reffered to as paper 1), Tu and Marsh [this issue] object vehemently to what they perceive as undeserved criticism of the class of solar wind turbulence models developed by Tu and coworkers[Tu et al., 1984, Tu, 1987, 1988]. Our intent was not to slight the valuable contributions made in those groundbreaking theories for incorporating turbulence into models for spatial transport. Rather, we wished to point out certain shortcomings in existing theories and suggest how they might be improved