Reynolds stress estimation up to single-pixel resolution using PIV-measurements

This article derives a theory for estimating Reynolds normal and shear stresses from PIV images with single-pixel resolution. The main idea is the analysis of the correlation function to identify the probability density function from which the Reynolds stresses can be derived in a 2-D regime. The work establishes a theoretical framework including the influence of the particle image diameter and the velocity gradients on the shape of the correlation function. Synthetic data sets are used for the validation of the proposed method. The application of the evaluation method on two experimental data sets shows that high resolution and accuracy are also obtained with experimental data. The approach is very general and can also be applied to correlation peaks that are obtained from sum-of-correlation PIV evaluations.