Investigation of Fluid Structures in a Smooth Open-Channel Flow Using Proper Orthogonal Decomposition

This paper reports particle image velocimetry (PIV) measurements of the instantaneous velocity fields in a smooth open-channel flow. The Reynolds number of the flow based on the water depth was 21,000. The instantaneous velocity fields were analyzed using proper orthogonal decomposition (POD) to expose the vortical structures. The velocity fields were reconstructed using different combination of modes; the first 12 modes to expose the energetic structures, and from Modes 13 to 100 to expose the less energetic structures. The first set recovered about 50% of the turbulent kinetic energy while the second group of modes recovered about 33% of the energy. The POD results were further combined with the results from the momentum analysis as well as with the conditional quadrant analysis performed at three different threshold levels. The POD results revealed the existence of hairpin vortices of different sizes and energy levels. Most of the large eddies are elongated and inclined toward the boundaries in the streamwise direction. The results also revealed patterns of strong ejection and sweep events which are common features in wall-bounded flows. Closer to the free surface $\left(y/d>0.6\right)$ , it was observed that the existence of hairpin vortices with legs possibly extended upward toward the free surface. As well, the distribution of the uniform momentum zones was consistent with the location of the vortices and their induced flow. While POD exposes the large- and small-scale structures based on the amount of turbulent kinetic energy, the quadrant analysis performed on the PIV maps shows the spatial distribution of the events related to the momentum transport.