  We propose a new multiscale method to calculate the amplitude of the gradient
of the linear polarisation vector using a wavelet-based formalism. We
demonstrate this method using a field of the Canadian Galactic Plane Survey
(CGPS) and show that the filamentary structure typically seen in gradients of
linear polarisation maps depends strongly on the instrumental resolution. Our
analysis reveals that different networks of filaments are present on different
angular scales. The wavelet formalism allows us to calculate the power spectrum
of the fluctuations seen in gradients of linear polarisation maps and to
determine the scaling behaviour of this quantity. The power spectrum is found
to follow a power law with gamma ~ 2.1. We identify a small drop in power
between scales of 80 < l < 300 arcmin, which corresponds well to the overlap in
the u-v plane between the Effelsberg 100-m telescope and the DRAO 26-m
telescope data. We suggest that this drop is due to undersampling present in
the 26-m telescope data. In addition, the wavelet coefficient distributions
show higher skewness on smaller scales than at larger scales. The spatial
distribution of the outliers in the tails of these distributions creates a
coherent subset of filaments correlated across multiple scales, which trace the
sharpest changes in the polarisation vector P within the field. We suggest that
these structures may be associated with highly compressive shocks in the
medium. The power spectrum of the field excluding these outliers shows a
steeper power law with gamma ~ 2.5.
