Evolution of the spectrum of solar wind velocity fluctuations from 0.3 to 5 AU

Abstract

[1] Recent work has shown that at 1 AU 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 solar wind 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 non-Alfvénic. In some respects, in particular in the evolution of the frequency at which the spectrum changes from flatter at larger scales to a "turbulent" spectrum at smaller scales, the velocity field evolves more rapidly than the magnetic, and this is associated with the dominance of the magnetic energy over the kinetic at "inertial range" scales. The speed of the flow is argued to be largely unrelated to the spectral slopes, consistent with previous work, whereas high Alfvénicity appears to slow the spectral evolution, as expected from theory. 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. It is also noted that a flattening of the velocity spectrum often occurs at small scales.

The Solar Wind as a Turbulence Laboratory

“…The general trend shown in Figure 23 is towards −5/3 as the distance increases. Lower values are due to the highly Alfvénic fast polar wind while higher values, around 2, are mainly due to the jumps at the stream fronts as previously shown by Roberts (2007). Thus, Living Reviews in Solar Physics http://www.livingreviews.org/lrsp-2013-2…”

“…These results are clearly opposite to the expected scaling for kinetic and magnetic fluctuations which should follow Kolmogorov and Kraichnan scaling, respectively (see Section 2.8). However, as remarked by Roberts (2007), Voyager observations of the velocity spectrum have demonstrated a likely asymptotic state in which the spectrum steepens towards a spectral index of −5/3, finally matching the magnetic spectrum and the theoretical expectation of Kolmogorov turbulence. Moreover, the same authors examined Ulysses spectra to determine if the Voyager result, based on a very few sufficiently complete intervals, were correct.…”

“…Preliminary results confirmed the −5/3 slope for velocity fluctuations at ∼ 5 AU from the Sun in the ecliptic. Figure 23, taken from Roberts (2007), shows the evolution of the spectral index during the radial excursion of Ulysses. These authors examined many intervals in order to develop a more general picture of the spectral evolution in various conditions, and how magnetic and velocity spectra differ in these cases.…”

On the cross-helicity dependence of the energy spectrum in magnetohydrodynamic turbulence

“…10͒ and ͉ c ͉ is known to increase, on average, as the heliocentric distance decreases. 43,44 The generalization of the GS theory derived here contains the LGS theory 27 as a special case and shows that there exist other generalizations of the GS theory, other than the LGS theory, that also obey the condition ͑w + / w − ͒ 2 = ͑ + / − ͒ 2 . Interestingly, these alternatives to the LGS theory have a different functional dependence on the normalized cross-helicity c .…”

Electron-ion Coulomb scattering and the electron Landau damping of Alfvén waves in the solar wind

“…For convenience it will be assumed that the functional form of the velocity (= electric field) spectrum of the solar wind is the same as the functional form of the magnetic field spectrum, which is in fact not really true for the inertial subrange: The velocity spectra tends to have a shallower spectral index than the magnetic field, and the energy density of the magnetic field fluctuations exceeds the energy density of the velocity fluctuations [cf. Podesta et al , 2007; Roberts , 2010; Podesta , 2011; J. E. Borovsky, The velocity and magnetic field fluctuations of the solar wind at 1 AU: Statistical analysis of Fourier spectra, unpublished manuscript, 2011; S. Boldyrev et al, Spectral scaling laws in MHD turbulence simulations and in the solar wind, submitted to Physical Review Letters , 2011].…”