Measurement of the Taylor Microscale and the Effective Magnetic Reynolds Number in the Solar Wind With Cluster

Abstract

We use magnetic field data from the Cluster mission to estimate the value of the Taylor microscale and the effective magnetic Reynolds number in the interplanetary solar wind. Turbulent cascades can be characterized by the spatial scale at which dissipation begins to impact the local energy transfer, estimated by the Taylor microscale, as well as the separation between the injection and dissipation scales, estimated by the effective magnetic Reynolds number. Estimating the Taylor microscale requires measurements of the autocorrelation function at small separations. The Cluster spacecraft have exceptionally sensitive search coil magnetometers with high time resolution, making them ideal for measuring the Taylor microscale. We obtain a value of $430\pm 20$ km; smaller than most previous measurements. We interpret this value as being smaller due to the higher time resolution, enabling the curvature of the autocorrelation function to be measured closer to the origin, giving a more accurate measurement. Combining the Taylor Microscale's computed value with concurrent correlation length measurements, we obtain a value of $150,000\pm 10,000$ for the effective magnetic Reynolds number, which compares well to other observations. The four spacecraft of Cluster also allow directions transverse to the flow to be surveyed. The small separations (7 km) of Clusters 3 and 4 show that the Taylor microscale may vary as a function of direction to the mean magnetic field direction. The observed differences are small, requiring more observations to confirm this anisotropy.