Showing papers by "William H. Matthaeus published in 1995"

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 Alfvenic 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 i...

Unquiet on any front: Anisotropic turbulence in the solar wind

Abstract: Detailed models of turbulence enter into space physics in a number of ways, through descriptions of power law spectra, through estimates of heating rates, correlation scales, time scales of nonlinear interactions, and through other statistical characterizations. These turbulence properties, which are also of great interest to theorists studying plasma turbulence in the magnetohydrodynamic (MHD) approximation, are quite likely sensitively dependent upon the rotational symmetry of the turbulent fluctuations. In the past few years, advances in several areas of solar wind research suggest a change in how the community may look at the symmetries of solar wind turbulence. This should influence the standard simple turbulence models used in space physics and related areas. At issue is the gradual uncovering, through studies of several types, of the possibility that the rotational symmetry of solar wind turbulent fluctuations may be very different from that advocated traditionally. In addition, and most importantly, this suggested change of perspective on the "standard solar wind turbulence model" is seen to have quite significant and quantitative impact on diverse problems, such as cosmic ray transport, solar wind radial evolution, the coronal and solar wind heating problems, and the interpretation of particle and field data from spacecraft. These recent developments are reviewed here. Statistical isotropy is frequently a convenient assumption in describing homogeneous turbulence in an ordinary fluid. For example, the Kolmogoroff description [Batchelor, 1970] is relevant when the spectral density of energy is invariant under arbitrary rotations, even when the turbulence coexists with a uniform background flow. Such a mean flow is eliminated by a Galilean transformation, leading to the conclusion that hydrodynamic anisotropies are connected with initial data, boundary or driving effects, or inhomogeneities such as large scale gradients. In the absence of these effects, or sufficiently far from their influence in space or time, it is possible to argue convincingly that hydrodynamics tends to become isotropic. Magnetohydrodynamics (MHD) stands in sharp contrast to hydrodynamics in this regard. Even when the statistics of MHD turbulence are homogeneous (or, translationally invariant), the effects of a 10-~

Linear transport of solar wind fluctuations

Abstract: Numerical solutions for the linear transport of solar wind fluctuations are presented. The model used takes into account the effects of advection, expansion, and wave propagation, as well as the recently illuminated effects of (non-WKB) “mixing” terms. The radial evolution of the fluctuating kinetic and magnetic energies and of the cross helicity is computed, and it is demonstrated that in appropriate limits the solutions converge to the WKB forms. In more general cases, however, where the fluctuations consist of a superposition of various types of turbulence, mixing leads to solutions which differ substantially from those predicted by WKB theory. The degree of mixing shows considerable dependence on the nature of the turbulence, giving rise to varying levels, at 1 ∼ AU, of the ratio of “inward” and “outward” fluctuation energies and the ratio of kinetic and magnetic fluctuation energies. The transport properties described here may provide a partial explanation for the observed decrease of cross helicity with increasing heliocentric distance in the solar wind.

Magnetic helicity in magnetohydrodynamic turbulence with a mean magnetic field

Abstract: A computational investigation of magnetic helicity of the fluctuating magnetic field Hm in ideal and freely decaying three‐dimensional (3‐D) magnetohydrodynamics (MHD) in the presence of a uniform mean magnetic field is performed. It is shown that for ideal 3‐D MHD Hm, which is a rugged invariant in the absence of a mean magnetic field [Frisch et al., J. Fluid Mech. 77, 796 (1975)], decays from its initial value and proceeds to oscillate about zero. The decay of Hm is shown to result from the presence of a new ‘‘generalized’’ helicity invariant, which includes contributions from the uniform magnetic field. The loss of invariance of Hm will diminish the effects of inverse transfer of Hm on freely decaying turbulence. This is demonstrated in a discussion of the selective decay relaxation process.

Anisotropy in incompressible and compressible 3D MHD turbulence

Abstract: Using direct numerical simulation results we discuss how the presence of a dc magnetic field (B0) in initially isotropic turbulent magnetohydrodynamic (MHD) flows leads to anisotropy in the small-scale velocity and magnetic fields. In such cases, the small-scale vorticity and current structures tend to elongate and align with B0.

Dominant 2D magnetic turbulence in the solar wind

Abstract: There have been recent suggestions that solar wind magnetic turbulence may be a composite of slab geometry (wavevector aligned with the mean magnetic field) and 2D geometry (wavevectors perpendicular to the mean field). We report results of two new tests of this hypothesis using Helios measurements of inertial ranged magnetic spectra in the solar wind. The first test is based upon a characteristic difference between perpendicular and parallel reduced power spectra which is expected for the 2D component but not for the slab component. The second test examines the dependence of power spectrum density upon the magnetic field angle (i.e., the angle between the mean magnetic field and the radial direction), a relationship which is expected to be in opposite directions for the slab and 2D components. Both tests support the presence of a dominant (approximately 85 percent by energy) 2D component in solar wind magnetic turbulence.

Anisotropic turbulence in the solar wind

Abstract: Recent investigations indicate that the solar wind turbulence spectrum may contain a significant admixture of two dimensional fluctuations, having variations mainly perpendicular to the local magnetic field. These indications come from simulations, from the theory of nearly incompressible MHD, from cosmic ray transport studies and from transport theory for solar wind turbulence, and from interpretations of direct observations.