Anisotropy of the Taylor scale and the correlation scale in plasma sheet and solar wind magnetic field fluctuations

Abstract

Magnetic field data from nine spacecraft in the magnetospheric plasma sheet and the solar wind are employed to determine the correlation scale and the magnetic Taylor microscale from simultaneous multiple‐point measurements for multiple intervals with a range of mean magnetic field directions. We have determined that in the solar wind the Taylor scale is independent of direction relative to the mean magnetic field, but the correlation scale along the mean magnetic field (2.7 × 106 ± 0.2 × 106 km) is longer than along the perpendicular direction (1.5 × 106 ± 0.1 × 106 km). Within the plasma sheet we found that the correlation scale varies from 16,400 ± 1000 km along the mean magnetic field direction to 9200 ± 600 km in the perpendicular direction. The Taylor scale is also longer parallel to the magnetic field (2900 ± 100 km) than perpendicular to it (1100 ± 100 km). In the solar wind the ratio of the parallel correlation scale to the perpendicular correlation scale is 2.62 ± 0.79; in the plasma sheet the ratio is 1.78 ± 0.16, which indicates that the turbulence in both regions is anisotropic. The correlation and Taylor scales may be used to estimate effective magnetic Reynolds numbers separately for each angular channel. Reynolds numbers were found to be approximately independent of the angle relative to the mean magnetic field. These results may be useful in magnetohydrodynamic modeling of the solar wind and the magnetosphere and can contribute to our understanding of solar and galactic cosmic ray diffusion in the heliosphere.

Transport of solar wind fluctuations: A two-component model

“…We thus attempt to adjust the boundary conditions so that the solutions are also consistent with 1 AU data. For example, Weygand et al [2009] used Cluster data sets to estimate perpendicular and parallel magnetic correlation lengths in slow wind, obtaining 0.014 AU and 0.037 AU, respectively.…”

“…, and (right) l res (dotted curve) and observational estimates of the perpendicular and parallel magnetic correlation length at 1 AU (plus sign and diamond [Weygand et al, 2009]). …”

“…Instead, estimates for the length scales at 1 AU are taken from an analysis of Cluster data: ' = l = 0.014 AU, l k = 0.037 AU [Weygand et al, 2009]. We choose s c =~c = 0.5, although the model is rather insensitive to the choice since the cross helicities both approach zero by about 10 AU (see Figure 2c).…”

Technique for measuring and correcting the Taylor microscale

“…We then determine the radius of curvature from correlation function and an estimate of the Taylor microscale. In the following section, we will demonstrate an extrapolation technique [Weygand et al, , 2009[Weygand et al, , 2010[Weygand et al, , 2011] to estimate Taylor microscale from a series of parabolic fits of the correlation function near the origin. The details of the method we use are given in the following subsections.…”

“…The motivation of this study comes from recent efforts to measure the Taylor microscale in solar wind turbulence calculated using multispacecraft techniques [Matthaeus et al, 2005;Weygand et al, 2007Weygand et al, , 2009Weygand et al, , 2010Weygand et al, , 2011Gurgiolo et al, 2013]. The Taylor scale is related to the second derivatives of the data [Batchelor, 1970] (also see below); therefore, it is inherently sensitive to the high-frequency spectral content of the signal.…”