A wavelet-based detector function for characterizing intermittent velocity signals

In this work, we propose a new detector function based on wavelet transform to discriminate between turbulent and non-turbulent regions in an intermittent velocity signal. The traditional detector functions based on first or second derivative of velocity signal, which are commonly used in intermittency calculation schemes, show large fluctuations within turbulent parts of the signal and require averaging over a certain “smoothing period” to remove the fake dropouts, introducing subjectivity in calculating intermittency. The new detector function proposed here is obtained by averaging the “pre-multiplied wavelet energy” over the entire frequency range, which can be interpreted as wavelet energy contained in the first derivative of the velocity signal. We demonstrate the effectiveness of our detector within the framework of the widely used method by Hedley and Keffer (J Fluid Mech 64:625, 1974), for a range of velocity signals representing the different stages of roughness-induced transition. We show that the wavelet detector is much smoother than the double-derivative-based detector of Hedley and Keffer, and at the same time has a good discriminatory property (due to pre-multiplication by frequency). This makes the choice of the smoothing period unnecessary and removes the subjectivity associated with it. The wavelet detector function works equally well in detecting the edge intermittency of a canonical turbulent boundary layer, thereby highlighting its generality. The performance of the proposed detector to calculate edge intermittency is compared with a recent energy-based method by Chauhan et al. (J Fluid Mech 742:119, 2014), showing a favorable match. Our detector can, in principle, be used with any of the methods used for specifying threshold for obtaining an indicator function.