Spectral Distribution of the Cross Helicity in the Solar Wind

There are a variety of theoretical and observational indications that fluctuation energy in astrophysical and space plasma turbulence is distributed anisotropically in space relative to the magnetic field direction. The cross helicity, represented by correlations between velocity and magnetic field fluctuations, enters a magnetohydrodynamic description on equal footing with the energy, but its anisotropy has not been examined in the same degree of detail. Here we employ Advanced Coronal Explorer data to examine the rotational symmetry of the cross helicity. We find that the normalized cross helicity is associated more or less equally with all angular components of the fluctuations. This favors turbulence models that allow for cross communication between parallel and perpendicular wave numbers, suggesting that “wavelike” and “turbulencelike” fluctuations are strongly coupled.

Figure 1

Magnetic field self-correlation function $R_{bb}(r)$, computed at different angles $\theta$ between the direction of the mean magnetic field and the displacement vector $\mathbf{r}$. Error bars are shown beside the legends. They represent the statistical error, evaluated at a separation $r$ equal to the correlation length. The largest scale shown corresponds to $\sim 0.1\mathrm{A}\mathrm{U}$.

Figure 2

Cross-helicity correlation function $R_{vb}=(R_{\mathrm{o}\mathrm{u}\mathrm{t}}-R_{\mathrm{i}\mathrm{n}})/4$, computed at different ranges of $\theta$ as in Fig. 1. Error bars have the same meaning as in Fig. 1.

Figure 3

Reduced power spectrum of the normalized cross helicity [${\sigma }_c(k)$], for different values of $\theta$, as in Fig. 1.