LOFAR detected toward 3C 196 linear polarization structures which were found subsequently to be closely correlated with cold filamentary HI structures. The derived direction-dependent HI power spectra revealed marked anisotropies for narrow ranges in velocity, sharing the orientation of the magnetic field as expected for magneto hydrodynamical turbulence. Using the Galactic portion of the Effelsberg-Bonn HI Survey we continue our study of such anisotropies in the HI distribution in direction of two WSRT fields, Horologium and Auriga; both are well known for their prominent radio-polarimetric depolarization canals. At 349 MHz the observed pattern in total intensity is insignificant but polarized intensity and polarization angle show prominent ubiquitous structures with so far unknown origin. Apodizing the HI survey data by applying a rotational symmetric 50 percent Tukey window, we derive average and position angle dependent power spectra. We fit power laws and characterize anisotropies in the power distribution. We use a Gaussian analysis to determine relative abundances for the cold and warm neutral medium. For the analyzed radio-polarimetric targets significant anisotropies are detected in the HI power spectra; their position angles are aligned to the prominent depolarization canals, initially detected by WSRT. HI anisotropies are associated with steep power spectra. Steep power spectra, associated with cold gas, are detected also in other fields. Radio-polarimetric depolarization canals are associated with filamentary HI structures that belong to the cold neutral medium (CNM). Anisotropies in the CNM are in this case linked to a steepening of the power-spectrum spectral index, indicating that phase transitions in a turbulent medium occur on all scales. Filamentary HI structures, driven by thermal instabilities, and radio-polarimetric filaments are associated with each other.
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