This article presents a reconstruction of the unsteady behaviour of a round jet at a Reynolds number equal to 3300, from the sole knowledge of the time-averaged flow field and one pointwise unsteady measurement. The reconstruction approach is an application of the work of Beneddine et al. (J. Fluid Mech., vol. 798, 2016, pp. 485-504) and relies on the computation of the dominant resolvent modes of the flow, using a parabolised stability equations analysis. To validate the procedure, the unsteady velocity field of the jet has been characterised by time-resolved particle image velocimetry (TR-PIV), yielding an experimental reference. We first show that the dominant resolvent modes are proportional to the experimental Fourier modes, as predicted by Beneddine et al. (J. Fluid Mech., vol. 798, 2016, pp. 485-504). From these results, it is then possible to fully reconstruct the unsteady velocity and pressure fluctuation fields, yielding a flow field that displays good agreement with the experimental reference. Finally, it is found that the robustness of the reconstruction mainly depends on the location of the pointwise unsteady measurement, which should be within energetic regions of the flow, and this robustness as well as the quality of the reconstruction can be greatly improved by considering a few pointwise measurements instead of a single one. The effects of other experimental parameters on the reconstruction, such as the size of the interrogation window used for the TR-PIV processing and the accuracy of the positioning of the sensors, are also investigated in this paper.

We introduce a new method for estimating fluid trajectories in time-resolved PIV. It relies on a Lucas–Kanade paradigm and consists in a simple and direct extension of a two-frame estimation with FOLKI-PIV (Champagnat et al 2011 Exp. Fluids 50 1169–82). The so-called Lucas–Kanade Fluid Trajectories (LKFT) are assumed to be polynomial in time, and are found as the minimizer of a global functional, in which displacements are sought so as to match the intensities of a series of images pairs in the sequence, in the least-squares sense. All pairs involve the central image, similar to other recent time-resolved approaches (FTC (Lynch and Scarano 2013 Meas. Sci. Technol. 24 035305) and FTEE (Jeon et al 2014 Exp. Fluids 55 1–16)). As switching from a two-frame to a time-resolved objective simply amounts to adding terms in a functional, no significant additional algorithmic element is required. Similar to FOLKI-PIV the method is very well suited for GPU acceleration, which is an important feature as computational complexity increases with the image sequence size. Tests on synthetic data exhibiting peak-locking show that increasing the image sequence size strongly reduces both associated bias and random error, and that LKFT has a remaining total error comparable to that of FTEE on this case. Results on case B of the third PIV challenge (Stanislas et al 2008 Exp. Fluids 45 27–71) also show its ability to drastically reduce the error in situations with low signal-to-noise ratio. These results are finally confirmed on experimental images acquired in the near-field of a low Reynolds number jet. Strong reductions in peak-locking, spatial and temporal noise compared to two-frame estimation are also observed, on the displacement components themselves, as well as on spatial or temporal derivatives, such as vorticity and material acceleration.