The local Galactic HI gas was found to contain cold neutral medium (CNM) filaments that are aligned with polarized dust emission. These filaments appear to be dominated by the magnetic field and in this case turbulence is expected to show distinct anisotropies. We use the Galactic Effelsberg--Bonn HI Survey (EBHIS) to derive 2D turbulence spectra for the HI distribution in direction to 3C196 and two more comparison fields. Prior to Fourier transform we apply a rotational symmetric 50% Tukey window to apodize the data. We derive average as well as position angle dependent power spectra. Anisotropies in the power distribution are defined as the ratio of the spectral power in orthogonal directions. We find strong anisotropies. For a narrow range in position angle, in direction perpendicular to the filaments and the magnetic field, the spectral power is on average more than an order of magnitude larger than parallel. In the most extreme case the anisotropy reaches locally a factor of 130. Anisotropies increase on average with spatial frequency as predicted by Goldreich and Sridhar, at the same time the Kolmogorov spectral index remains almost unchanged. The strongest anisotropies are observable for a narrow range in velocity and decay with a power law index close to --8/3, almost identical to the average isotropic spectral index of $-2.9 < gamma < -2.6$. HI filaments, associated with linear polarization structures in LOFAR observations in direction to 3C196, show turbulence spectra with marked anisotropies. Decaying anisotropies appear to indicate that we witness an ongoing shock passing the HI and affecting the observed Faraday depth.
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