Roberts (Aaron) talk on inertial range spectral evolution

For a while it seemed like a simple fluid-like, self-similar, Kolmogoroff
cascade was the easy explanation for the nature and evolution of the
majority of solar wind fluctuations.
More recently we have found that:
• the cascade is not stirred at large scales, and the large scales present a number
of puzzles;
• the velocity and magnetic spectra evolve differently with different “inertial
ranges” in both slope (until far from the Sun) and wavenumber range
• anisotropy in both variances and spectral characteristics are the order of the day
and are strongly scale dependent; and
• it is not clear what fraction of the fluctuations should be considered to be
“turbulent” as opposed to, for example, convected structures or discontinuities.
This talk will review some recent results in these areas, and attempt to
characterize where we are in our understanding.
Large scale transverse fluctuations are more equipartioned
than expected from a “quasi-static” regime
Pvr / Pbr
Solar rotation
Pvn / Pbn
Pvt / Pbt
Shear in V (Vr(q)) is
the dominant energy in
fluctuations at large
Helios 2, 0.3 AU
f –1
f –5/3
f –1
f –3/2
Note the curious flattening—seen, at times in v, density,
|B|, and z –, and more prevalently closer to the Sun. It is
not an artifact, but a real feature.
Velocity (black) and Magnetic (red) spectra
1 AU (Helios 2; same streams)
Note again the flattening of the V spectrum
Velocity (black/green) and Magnetic (red) spectra
~4.5 AU (Ulysses)
Velocity spectral slope is
clearly –5/3, not –3/2
Still a flattening in V
(N.B. change in f range)
Velocity (black) and Magnetic (red) spectra
4.7 AU (ecliptic, Ulysses pre-Jupiter)
B is flat (f –1) while V is
already in an “inertial
The low-f and high-f
spectra can have a
transition that may indicate a
lack of cascade from large to small
scales. The turbulence is decaying,
not driven.
f –5/3
f –5/3
Velocity Spectral Slope vs radial distance,
speed, latitude, and Alfvénicity (Ulysses)
Near ecliptic (<20°)
0.5 > |σc| > 0.33
+ > 675 km/s
|σc| > 0.5
• Don’t trust 1 AU – spectra are rapidly evolving, and eventually
reach a “Kolmogoroff” spectrum for both velocity and magnetic
field, which take different paths to get there.
• The only really Alfvénic fluctuations (both in correlation and in
amplitude) are in “smooth” streams nearer the Sun.
• The large-scale fluctuations are not well understood, and there does
not seem to be a simple “non-WKB” or “quasi-static” regime.
• We need to rethink the idea of “the inertial range” for the solar wind.
• Cross-helicity strongly determines the rate of evolution (as
• In the inner heliosphere, the evolution of velocity fluctuations is
often energetically more important that of the magnetic field.
• Turbulence in the solar wind is decaying rather than driven.
• We still don’t know whether low cross-helicity regions near the Sun
represent “older turbulence” or a different origin—they do have
more “evolved” spectra, but we await new missions to determine the
origin of the spectrum nearer the Sun.

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