Correlation between large- and small-scale velocity components under Fourier filters

By introducing the Fourier filters, we analyse the correlation between large- and small-scale velocity components in homogeneous isotropic turbulence theoretically. We show that different Fourier filters act similarly on this multi-scale correlation with a “natural” mechanism of removing the physical correlations between large- and small-scale velocity components. This conclusion calls for the further investigation on the Hilbert—Huang decomposition to investigate the mechanism of Marusic et al (2008).