Evaluation of the turbulent energy cascade rates from the upper inertial range in the solar wind at 1 AU

Abstract

We construct a database from ACE spacecraft measurements of solar wind magnetic field fluctuations at 1 AU which resolves ∼2 decades in frequency at the high end of the inertial range. Using magnetic field measurements outside of magnetic clouds in combination with plasma measurements, we evaluate expressions for the Kolmogorov and Kraichnan cascade rates at 0.01 Hz from magnetic field power spectra and consider both isotropic and cross‐field rates. We examine these rates as functions of proton temperature and solar wind speed, comparing them to the expected rate based on the heating of protons at 1 AU. The average Kolmogorov rate is consistently more than a factor of 10 greater than expected. We conclude that the cascade rate cannot be estimated using the Kolmogorov prescription and power spectra. The Kraichnan rate is close to the expected rate and is potentially a good way to estimate the cascade rate. No distinction is found between the isotropic and cross‐field rates at 1 AU. However, consideration of the likely dependence of cascade rates with distance from the Sun shows that a distinction should exist at distances closer than 1 AU but not outside 1 AU. Moreover, we find that inside 1 AU, the cross‐field Kraichnan prediction can maintain agreement with the expected heating rate whereas the isotropic prediction cannot.