The relationship between the velocity skewness and the amplitude modulation of the small scale by the large scale in turbulent boundary layers

A defining feature of the inner-outer interactions in wall-bounded turbulent flows is the imprint of the outer large-scale motions on the inner small scale. Recently, Mathis et al. ["Large-scale amplitude modulation of the small-scale structures in turbulent boundary layers," J. Fluid Mech. 628, 311 (2009)] quantified this imprint by applying the Hilbert transform to small-scale components of the fluctuating streamwise velocity, u. They found that the wall-normal profile of the amplitude modulation between the large scale and the envelope of the small scale exhibits strong resemblance to the skewness profile of u. In this study, we assess this apparent relationship and show that the Reynolds number trend in the skewness profile of u is strongly related to the amplitude modulation effect of the small scales by the large. This observation also leads to an alternative diagnostic for the amplitude modulation effect, which is one component of the skewness factor based on a scale decomposition.