Phase relationships between large and small scales in the turbulent boundary layer
The apparent amplitude modulation effect between large- and small-scale motions in the turbulent boundary layer, including both streamwise and wall-normal velocity components, is explored by cross-correlation techniques. Single-point hotwire and planar PIV measurements are employed to consider the envelopes of small-scale fluctuations in both directions and their correlation with the fluctuations of large-scale motions in the streamwise direction. The degree of correlation is interpreted as a measure of phase lag between the different scale motions, and these phase measurements are used to demonstrate that the fluctuations in the envelope of small-scale motions in both directions tend to lead corresponding fluctuations in the large scales in the streamwise direction. The cospectral density of the cross-correlation between the different scales is used to identify the particular large-scale motions dominant in the modulation effect, and it is shown that the dominant interacting (or 'modulating') scale corresponds in size to the very large-scale motions observed in internal flows but not normally observed in the outer region of the boundary layer.
© 2013 Springer-Verlag Berlin Heidelberg. Received: 16 November 2012. Revised: 6 February 2013. Accepted: 8 February 2013. Published online: 27 February 2013. This work was supported by the Air Force Office of Scientific Research Hypersonics and Turbulence portfolio, under grant #FA9550-09-1-0701 (Program Manager John Schmisseur).