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.