What does the amplitude modulation coefficient actually measure?

The amplitude modulation coefficient, R, that is widely used to characterize non-linear interactions between large- and small-scale motions in wall-bounded turbulence is not actually compatible with detecting the convective non-linearity of the Navier-Stokes equations. Through a spectral decomposition of R and a simplified model of triadic convective interactions, we show that R actually suppresses the signature of convective scale interactions, and we suggest that what R likely measures is linear interactions between large-scale motions and the background mean flow. From this perspective, R represents the relative difference in convective velocities between large-scale motions and the local mean velocity and is related to the violation of Taylor's frozen turbulence hypothesis.