Nonaxisymmetric Anisotropy of Solar Wind Turbulence

A key prediction of turbulence theories is frame-invariance, and in magnetohydrodynamic (MHD) turbulence, axisymmetry of fluctuations with respect to the background magnetic field. Paradoxically the power in fluctuations in the turbulent solar wind are observed to be ordered with respect to the bulk macroscopic flow as well as the background magnetic field. Here, nonaxisymmetry across the inertial and dissipation ranges is quantified using in situ observations from Cluster. The observed inertial range nonaxisymmetry is reproduced by a “fly through” sampling of a direct numerical simulation of MHD turbulence. Furthermore, fly through sampling of a linear superposition of transverse waves with axisymmetric fluctuations generates the trend in nonaxisymmetry with power spectral exponent. The observed nonaxisymmetric anisotropy may thus simply arise as a sampling effect related to Taylor’s hypothesis and is not related to the plasma dynamics itself.

Figure 1

PSDs of magnetic field components (from bottom to top) ${\mathrm{PSD}}_z$ (black), ${\mathrm{PSD}}_y$ (red), and ${\mathrm{PSD}}_x$ (blue), where ${\mathbf{e}}_z=\overline{\mathbf{B}}/|\overline{\mathbf{B}}|,{\mathbf{e}}_x={\mathbf{e}}_z\times \widehat{\mathbf{V}}/|{\mathbf{e}}_z\times \widehat{\mathbf{V}}|$ and ${\mathbf{e}}_y={\mathbf{e}}_z\times {\mathbf{e}}_x$. Error bars are always smaller than 4% and are usually smaller than the linewidth. The inset shows the ratio of perpendicular PSDs ${\mathrm{PSD}}_y/{\mathrm{PSD}}_x$.

Figure 2

The ratio $E_y/E_x$, where ${\mathbf{e}}_x$ and ${\mathbf{e}}_y$ refer to a field aligned coordinate system as in Fig. 1, for the solar wind data (blue dotted line), the range of values obtained from a number of simulation fly throughs for case I (crosshatched area) and case II (hatched area), as well as predictions of Eq. (8) for the spectral indices $\gamma =5/3$ (black solid line), $\gamma =1.5$ (red dashed line), $\gamma =1.5\pm 0.1$ (left gray area) and $\gamma =2.76\pm 0.05$ (right gray area).