Power spectrum of small‐scale turbulent velocity fluctuations in the solar wind

Abstract

It is well known that the power spectrum of magnetic field fluctuations in the solar wind exhibits a Kolmogorov spectrum f−α in the inertial range of the turbulence with a power law exponent α near 5/3. The power spectrum of velocity fluctuations has not been as well studied, partly because of the lack of high time resolution measurements needed to resolve a significant fraction of the inertial range. In situ measurements in the ecliptic plane at 1 AU acquired by the 3DP instrument on board the Wind spacecraft near solar minimum in 1995 are used to determine power spectra of the proton bulk velocity fluctuations between 10−5 and 10−1 Hz. The spectrum for the proton kinetic energy (the sum of the spectra for the individual components Vx, Vy, and Vz) obtained using 3‐s velocity data is found to possess the spectral exponent α = 1.50 in the inertial range of the turbulence. A similar calculation of the magnetic energy spectrum yields the exponent α = 1.67. The Alfvén ratio, the ratio of the kinetic to magnetic energy spectrum, is a slowly increasing function of frequency throughout the inertial range increasing from approximately 0.5 to 1 in the frequency interval from 10−4 to 10−2 Hz. This indicates that the partition of energy between small‐scale velocity and magnetic field fluctuations is frequency‐dependent, contrary to some theories. The total energy spectrum (kinetic plus magnetic) has the power law exponent 3/2. A brief investigation of high‐ and low‐speed solar wind streams is also performed, which shows that different spectral exponents for velocity and magnetic field fluctuations are observed in both high‐ and low‐speed wind.