A wavelet-based detector function for characterizing intermittent velocity signals

TL;DR

This paper introduces a wavelet-based detector function for identifying turbulent regions in velocity signals, offering a smoother and more objective alternative to traditional derivative-based methods, applicable across various turbulent flow scenarios.

Contribution

A novel wavelet energy averaging method for detector functions that eliminates the need for smoothing parameters and subjectivity in intermittency analysis.

Findings

Wavelet detector effectively discriminates turbulent and non-turbulent regions.

The method removes the subjectivity associated with smoothing periods.

Demonstrated success across different turbulent flow conditions.

Abstract

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 derivative-based detector function, which is commonly used in intermittency calculation schemes, shows large fluctuations within turbulent parts of the signal and requires averaging over a certain ``smoothing period'' to remove the fake drop-outs, 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, resulting in a function that is much smoother than the derivative-based detector and at the same time has a good discriminatory property. This makes the choice of the smoothing period unnecessary and removes the subjectivity associated with it. We demonstrate the effectiveness of the wavelet detector within the framework of the widely-used method by Hedley and Keffer (1974, J. Fluid Mech., V64, pp625), for a range of velocity signals representing the different stages of roughness-induced transition. The wavelet detector function works well in detecting the edge intermittency of a canonical turbulent boundary layer as well, thereby highlighting its generality. Our detector can, in principle, be used with any method of specifying threshold for obtaining an indicator function.