Quantifying the interaction between large and small scales in wall-bounded turbulent flows: A note of caution

Turbulent flow close to solid walls is dominated by an ensemble of fluctuations of large and small spatial scales. Recent work by Mathis [ J. Fluid Mech. 628 , 311 ( 2009 ) ; Phys. Fluids 21 , 111703 ( 2009 )] introduced and used a decoupling procedure based on the Hilbert transformation applied to the filtered small-scale component of the fluctuating streamwise velocity. This method is employed as a robust tool to quantify a dominant amplitude modulation of the small scales by the large scales found in the outer part of the boundary layer. In the present study, however, we demonstrate by means of experimental and synthetic signals that the correlation coefficient used to quantify the amplitude modulation is related to the skewness of the original signal, and hence, for the Reynolds numbers considered here, may not be an independent tool to unambiguously detect or quantify the effect of large-scale amplitude modulation of the small scales.