Geometrical alignment properties in Fourier- and wavelet-filtered statistically stationary two-dimensional turbulence

In this paper we compare the geometrical alignment properties of Fourier- and wavelet-filtered statistically stationary two-dimensional turbulence. The goal is to study the preferential alignment angle of vorticity gradient with respect to the compressing eigenvector of the rate-of-strain tensor, and use this quantity as a measure of how the two filtering methods affect the small scale geometric structure of the flow. The principal result is that for the case of the incoherent part obtained through wavelet filtering the probability density function of this angle is flat, meaning that this field is effectively unstructured and therefore dynamically passive. On the contrary, the corresponding field obtained through Fourier filtering reveals a bump at the angle pi/4, which indicates the presence of dynamically active filament-type structures. These results provide evidence that, unlike the wavelet filtering, the Fourier filtering does remove dynamically important information from the flow.