Denoising of time-resolved PIV for accurate measurement of turbulence spectra and reduced error in derivatives

The accuracy of time-resolved PIV (TRPIV) turbulence measurements is limited by white noise, which reduces the signal-to-noise ratio (SNR) of small-scale velocity fluctuations. This paper demonstrates a novel energy filter that extends the concept of spectral noise subtraction to the time domain. The filter is equivalent to the spectral subtraction of white noise energy, and therefore it can recover the true signal energy. Its effectiveness is evaluated by comparing two-component (2C) TRPIV and constant temperature anemometry (CTA) measurements performed in grid-generated turbulence (Reλ = 90). The denoised PIV measurements exhibit a SNR equivalent to those of a high-performance CTA system. The temporal spectra of velocity fluctuations and derivatives are accurately recovered, with an improvement in dynamic range by a factor of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\fancyscript{O}(10^3)$$\end{document}. The error in dissipation estimates derived from the frequency spectrum is reduced to approximately 2 %. The correlation coefficient between spatial gradients computed directly and those computed via Taylor’s hypothesis improves from 0.83 to 0.95. The mean-square error reduction is found to be equivalent in the frequency and wavenumber domains, although we observe that frequency domain filtering has a limited ability to improve the SNR of spatial spectra at high wavenumbers. The performance of the energy filter is shown to be sensitive to the convergence of the measured spectra; therefore, we provide sampling criteria to ensure optimal implementation in measurements of turbulent flows.