Assessing The Potential Of PIV Data To Resolve Hidden Frequency Scales

The present work investigates the performance of an advection-based flow reconstruction model to increase the temporal resolution of PIV measurements recorded in a turbulent, planar jet. Using a semi-Lagrangian technique in combination with Rapid Distortion Theory, a modified trajectory tracking procedure is implemented. The method introduces a specification for a two-dimensional convective velocity based on the least squares minimization of the linearized advection equation, in contrast to the previously introduced one-dimensional mean velocity profile outlined in Vocke et al. (2023). The new implementation is based on local flow measurements, making it well-suited towards streamwise heterogeneity and spatially developing flows. With this, the flow at some unknown time can be estimated from the know flow measurements at the forward and backward time. Spectral analysis illustrates the model's proficiency in recovering spatiotemporal information far exceeding the Nyquist frequency, with spectral reconstruction errors of less than 5% for the most extreme case. It is demonstrated that the spectral content can be estimated at least two orders of magnitude beyond the sampling frequency of the original recording. Improved performance compared to alternative methods is demonstrated with only minor impact on computational time. This indicates the approach may be used as a tool for experimental researchers a) having no access to a high-speed PIV or b) with high-speed PIV to increase the spectral resolution even further.