The Evolution of the Spectrum of Velocity Fluctuations in the Solar Wind
Recent work has shown that at 1AU from the Sun the power spectrum of the solar wind magnetic field has the -5/3 spectral slope expected for Kolmogorov turbulence, but that the velocity has closer to a -3/2 spectrum. This paper traces the changes in solar wind velocity spectra from 0.3 to 5 AU using data from the Helios and Ulysses spacecraft to show that this is a transient stage in the evolution. The spectrum of the velocity is found to be flatter than that of the magnetic field for the higher frequencies examined for all cases until the slopes become equal (at -5/3) well past 1 AU when the wind is relatively nonAlfvenic. In some respects, in particular in the evolution of the frequency at which the spectrum changes from flatter at larger scales to a traditionally turbulent spectrum at smaller scales, the velocity field evolves more rapidly that the magnetic, and this is associated with the dominance of the magnetic energy over the kinetic at "inertial range" scales. The Alfvenicity of the fluctuations, not the speed of the flow, is shown to control the rate of the spectral evolution. This study shows that, for the solar wind ., the idea of a simple "inertial range" with uniform spectral properties is not realistic, and new phenomenologies will be needed to capture the true situation. In addition a flattening of the velocity spectrum persists at times for small scales, which may provide a clue to the nature of the small-scale interactions.