A New Look at Some Solar Wind Turbulence Puzzles

D. Aaron RobertsNASA GSFC

(SHINE, 2006)

The Puzzles

• Magnetic vs. velocity spectra; why are they different?

• Origin of the anisotropic variance of B

• Large-scale fluctuations; reason for the “Alfvén ratio” ~ 1

• Origin of k-space anisotropy

• How can various quantities turn with the Parker field?

Spectrum of B; 1AU, many days

Spectrum of V; 1AU, many days

Spectrum of V; 0.3 AU, Helios 2, 6 days40.5 sec data. Slope = 1 (green)

Spectrum of V; 2 AU, Voyager 2, 8.3 hrs12 sec data; Slope = 1.5 (red), = 1.67 (green)

Spectrum of sqrt(rho)V, SW frame; 5 AU, Voyager 2, 44 days,96 sec data; Slope = 1.5 (red), = 1.67 (green)

Br vs Bt, 0.3 AU, 1 day, Alfvénic

Br vs Bt, 1 AU, 1 day, Alfvénic

Br vs Bt, 4 AU, 1 day, (less) Alfvénic

Br vs Bt, 0.3 AU, 1 day, Alfvénic (Slow Wind)

Br vs Bt, 0.3 AU, 1 day, nonAlfvénic

Pmax/Pmin (0.3 AU, Alfvénic) vs interval duration

cos(B, min var); 0.3 AU, Alfvénic

cos(B, min var); 0.3 AU, nonAlfvénic

Vsw

Vsw

Currentsheet

r

B

InflowBoundary B(,,t) &v(, ,t) areapplied

Flux tubes: Br(,);Velocity shear: vr()Waves: B(t) v(t)

“Virtual Sun”

The solutions described below were obtained in spherical coordinates in three dimensions, and at a resolution of 150150150 for r, , and

Br vs Bt simulated; 0.5 AU, initially Alfvénic but quickly evolving

Br vs Bt simulated; ~1 AU

Br vs Bt simulated; ~3 AU

Background

• We use the "OMNI" 1-AU, combined hour-averaged solar wind dataset from J. King (NSSDC/SECAA)

• 40 years of data exist, with 30 years complete enough for spectral analysis (~1/4 million points)

• Here we examine magnetic and plasma quantities (B, V, B, n)

Overview

• There is significant power at all scales from hours to 30 years, with high-frequency power laws and many spectral features at solar rotation, annual, and solar cycle frequencies.

• The radial component of V dominates except at the smallest scales.

|B|: 11-year cycle; little 27-day power; multiple high-f power laws (Blue => 50pt smoothing)

+

–

Vr: 11-year and 27 day cycles; broad, high low-f power; -2 spectrum break to -5/3

++

B

Vn: Relatively featureless power laws; low power at low f

Vt: Strong annual peak, little 27-day power

+

Bt: Strong annual and 27-day peaks and harmonics (due to sectors); high-f power laws.

+ +++++

Bn: Similar to Vn; very little low-f power

Br: 27-day and modulated (split) annual peak. Modulation is from 11/22-year cycle.

++

Ratio of energy in V to B; Dominant Vr, but all --> 0.5-1 at high-f; no “quasi-static” (“nonWKB”)

region

R

N

T

PVr/PVt; PVn/PVt; PBn/PBt: Dominant Vr and ~isotropic transverse components

Vr/Vt

Vn/Vt

Bn/Bt

Alfvénicity, 1 AU

ISEE-3, IMP-8, Interball

B

3-D, Q-2D + Slab, k-space; Fourier code initial condition

ky

kx“Slab”

kz

3-D, Q-2D + Slab, k-space; Fourier code later condition

r (AU)

0.5 1.82

-180

180

Correlation function

Power Spectrum

B

Shear produced2-D correlationfunction, similarto solar windobservations

Conclusions (1 of 2)• The minimum variance of B is nearly along B in

highly Alfvénic regions; turbulence tends to decrease both effects.

• |B| ~ const key to min variance (Barnes, 1981), and the “spherical polarization” follows the field. How?

• WKB and simulations have failed to produce this effect; transverse variability is required, but how?

• Compressive effects don’t help (Hollweg & Lilliequist, 1978).

• The dominant energy in fluctuations from the scale of years to a fraction of a day is contained in the variation in the radial flow speed;

Conclusions (2 of 2)• There is no "quasi-static" regime for solar wind

fluctuations but rather the transverse magnetic and velocity fluctuations are comparable in energy at essentially all scales. Why?

• Neither quasi-2-D turbulence or slab waves will turn with the Parker field; only a nonlinear coupling of the two (or other means) will accomplish this. The “two component” model does not reflect this.

• Shear can easily turn k, but not B.• Velocity and magnetic fluctuations evolve at different

rates, and with different spectra. Turbulence theory?