Anisotropic Scaling of Magnetohydrodynamic Turbulence

We present a quantitative estimate of the anisotropic power and scaling of magnetic field fluctuations in inertial range magnetohydrodynamic turbulence, using a novel wavelet technique applied to spacecraft measurements in the solar wind. We show for the first time that, when the local magnetic field direction is parallel to the flow, the spacecraft-frame spectrum has a spectral index near 2. This can be interpreted as the signature of a population of fluctuations in field-parallel wave numbers with a $k_{\parallel }^{-2}$ spectrum but is also consistent with the presence of a “critical balance” style turbulent cascade. We also find, in common with previous studies, that most of the power is contained in wave vectors at large angles to the local magnetic field and that this component of the turbulence has a spectral index of $5/3$.

Figure 1

Magnetic power spectra at two different angle ranges of the local magnetic field to the flow: 0°–10° (circles) and 80°–90° (diamonds). Note the reduced power levels and steeper slope associated with the smaller angle. Guide lines with slopes of $5/3$ and 2 are shown above and below the data. Spectral indices in Fig. 2 are calculated over the scales between the dotted vertical lines.

Figure 2

Top: Trace of power in the magnetic field as a function of the angle between the local magnetic field and the sampling direction at a spacecraft frequency of 61 mHz. The larger scatter for ${\theta }_B>90°$ is the result of fewer data points at these angles. Bottom: Spectral index of the trace, fitted over spacecraft frequencies from 15–98 mHz.