Inner/outer layer interactions in turbulent boundary layers: A refined measure for the large-scale amplitude modulation mechanism

The amplitude modulation (AM) imparted by the outer layer large-scale motions on the near-wall turbulence is studied through direct numerical simulation of compressible boundary layer flow at moderate Reynolds number. Mathis et al. [J. Fluid Mech. 628, 311 (2009)] introduced an amplitude modulation coefficient to quantify this effect, whereby carrier and modulated signals are decoupled through a procedure based on the Hilbert transform of the streamwise velocity signals. However, Schlatter and Örlü [Phys. Fluids 22, 051704 (2010)] have recently shown that a non-zero amplitude modulation coefficient is closely associated to a non-zero value of the velocity skewness, and therefore, it does not necessarily reflect genuine physics. In this paper, the analysis is extended through systematic use of the two-point amplitude modulation correlation, which is shown to be a refined measure of the top-down influence of large-scale outer events on the inner part of the boundary layer.