The Development of Kolmogoroff-Like Power Spectra in the Expanding Solar Wind

Power spectra of the solar wind fluctuations consistently exhibit a -5/3 power-law slope consistent with the idea that the medium is undergoing a turbulent cascade as seen in ordinary fluids. This is surprising both because the radial streams and the magnetic field threading the plasma will induce anisotropies and because the expansion of the wind will tend to lead to the suppression of nonlinear cascades. These conditions violate the assumptions used by Kolmogoroff to derive the -5/3 law. We have studied this issue using a compressible IMHD code in spherical coordinates and have shown that a -5/3 spectrum results from a broad-band flat-spectrum input condition that is sheared and distorted by a current sheet as the wind expands. We determine spectra from time series taken at selected points in the domain as is done with observational spacecraft data. The spectra are very like those we have seen in nonexpanding runs and exhibit evolution and compressive characteristics very similar to those seen in observations. We will report on these results in addition to a new set of runs intended to constrain the necessary and sufficient conditions for the spectra to have this form. The simulation also allows us to examine the anisotropy for the spectra to attempt to determine why the result of an isotropic magnetofluid is obtained in a highly anisotropic situation.