Engineering topics
Publications and source records attributed to Matthaeus, W. H..
A technique for the measurement of magnetic helicity from values of the two point magnetic field correlation matrix under the assumption of spatial homogeneity is presented. Knowledge of a single scalar function of space, derivable from the correlation matrix, suffices to determine the magnetic helicity. The technique is illustrated by reporting the first measurement of the magnetic helicity of the solar wind.
The mean value of the correlation between local magnetic field and vector potential, known as the magnetic helicity, is a measure of the lack of mirror reflection symmetry of magnetic covariances in a turbulent medium. A method is presented for extraction of helicity spectra from magnetometer data, and applied to an evaluation of the magnetic helicity of interplanetary magnetic fluctuations.
The pitch angle scattering of cosmic ray is modified greatly if the medium through which they propagate contains significant amounts of magnetic helicity. When helicity is present in the medium, the often used expression for the pitch angle diffusion coefficient derived from quasilinear theory must be modified. These modifications are illustrated for slab and isotropic symmetries. Using measurements of helicity in the solar wind determined from single point measurements of the correlation tensor of magnetic fluctuations obtained from Voyager 2, the effects of the observed helicity on both the pitch angle and spatial diffusion coefficients are estimated.
An incompressible, dissipative numerical code of the spectral type is used to follow the nonlinear evolution of a magnetohydrodynamic sheet pinch in two spatial dimensions. The evolution involves considerable turbulent activity in the electric current field, with the excited spatial scales ranging from the size of the containing volume down to the dissipation lengths of the magnetic and velocity fields. Strong current filamentation near magnetic X-points is observed, as is 'jetting', or expulsion of magnetofluid from the vicinity of the X-point parallel to the current sheet.
It has been found that the computed values of the mean free path for pitch angle scattering of low rigidity cosmic rays computed from weak turbulence theory are systematically larger than the values inferred from analyses of solar particle events. Reasons for this discrepancy are considered, taking into account components of the spectral tensor of the magnetic field fluctuations which can contribute to pitch angle scattering. The contributions of the additional terms can be estimated from the interplanetary magnetic field. It is shown that these additional contributions can be significant. A description is given of a formalism which includes the possibility that the field magnitude is constant. The formalism provides a formal basis for the heuristic arguments made by Goldstein (1980).
Implications of certain applications of turbulence theory to two-dimensional turbulence and magnetohydrodynamic flow are discussed. It is shown that the use of the Navier-Stokes equation (NSE) for measurements of turbulent fluctuations has been effective only for three-dimensional flows. For two-dimensional flows, used for the study of large-scale motions in the atmosphere or ocean, enstrophy is cascaded to high wave numbers and dissipated at a finite rate even at infinite Re. MHD flows are numerically calculated for the two-dimensional case and analytically for the three-dimensional case, for which discrepancies in the relative rates of energy and cross helicity decay lead to a recommendation that numerical calculations for the three-dimensional case be carried out to determine the precise decayed states.
The study of turbulence with spatially homogeneous but anisotropic statistical properties has applications in space physics and laboratory plasma physics. The first step in the systematic study of such fluctuations is the elucidation of the kinematic properties of the relevant statistical objects, which are the correlation tensors. The theory of isotropic tensors, developed by Robertson, Chandrasekhar and others, is reviewed and extended to cover the general case of turbulence with a pseudo-vector preferred direction, without assuming mirror reflection invariance. Attention is focused on two point correlation functions and it is shown that the form of the decomposition into proper and pseudo-tensor contributions is restricted by the homogeneity requirement. It is also shown that the vector and pseudo-vector preferred direction cases yield different results. An explicit form of the two point correlation tensor is presented which is appropriate for analyzing interplanetary magnetic fluctuations. A procedure for determining the magnetic helicity from experimental data is presented.