A Practical Method for Integral Time Scale Estimation in the Presence of Spectral Distortions

The integral time scale serves as a key indicator of the smallest measurement time unit and the largest energy-containing time scale in turbulent flows. The integral scales are typically estimated by integrating the auto-correlation function of the velocity signal up to its first zero-crossing. However, the presence of spectral peaks due to unsteady coherent structures and high-frequency noise can distort the power spectrum and lead to inaccurate estimation of the integral time scale. Therefore, this study proposes a practical method that identifies and removes spectral peaks and noise from the power spectrum. To justify this method, a theoretical spectrum model containing peaks and noise allows analysis of their impacts on the estimated integral time scale. Based on the analysis, the spectrum is interpolated and extrapolated to recover unmeasured or distorted regions of the spectrum and improve the reliability of integral scale estimation. The proposed method is validated using DNS data and provides a physically consistent strategy for accurate integral time scale estimation in the presence of undesired spectral features.