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

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 Alfvdnic 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.

von Kármán self-preservation hypothesis for magnetohydrodynamic turbulence and its consequences for universality

“…Simulations support this view (e.g. Oughton et al 1994;Hossain et al 1995) and suggest that non-zero B 0 reduces energy decay relative to the isotropic case, but that the effect saturates at strong B 0 (Hossain et al 1995). On the other hand, it is not difficult to show that a uniform B 0 does not enter into the (second-order) von Kármán-Howarth equations for MHD, as is evident from the derivation of (2.5).…”

“…Much later, Politano & Pouquet (1998a,b) derived the appropriate equations in terms of Elsässer variables, and also determined the associated third-order ('4/5') law for MHD. Energy decay laws based on simple (dimensional) analysis have been offered for MHD (Biskamp 1994;Hossain et al 1995) and subjected to some numerical testing (Hossain et al 1995;Politano, Pouquet & Sulem 1995). Additional analysis along these lines has suggested dependence of energy decay on the lowwavenumber form of the spectrum (Galtier, Politano & Pouquet 1997) and associated conservation laws for linear or angular momentum and self-similarity of the large scales (Davidson 2009(Davidson , 2010.…”

“…In fact, the same or comparable equations for MHD energy decay have been written previously (Dobrowolny, Mangeney & Veltri 1980;Hossain et al 1995) on the basis of dimensional analysis or via modelling, sometimes motivated by similar approaches in hydrodynamics (e.g. Kolmogorov 1941b;Dryden 1943).…”

Transport of solar wind fluctuations: A two-component model

“…This involves treating Z + ≈ Z − , i.e., assuming small cross helicity. Extensions that support arbitrary cross helicity and a mean magnetic field B 0 have been proposed [Dobrowolny et al, 1980;Hossain et al, 1995;Matthaeus et al, 1994].…”

Kinetic helicity and MHD turbulence

“…of the magnetic energy spectra. It is clear that much of the decay is self-similar (Hossain et al 1995;Galtier et al 1997), even though there is no well-defined (powerlaw) inertial range present. Also evident is a slight but progressive build-up of kinetic and magnetic energy at the (two) smallest wavenumbers.…”