Particle Tracking in a Shallow Mixing Layer: A Fluid Dynamics Laboratory in the Field

Abstract

At locations where two natural streams of different velocity come together, a mixing layer develops. In this free shear flow, the velocity difference between the two streams is gradually reduced through the exchange of lateral momentum. This involves different forms of turbulent phenomena. If the width of the flow domain is large compared to the water depth, as is often the case in rivers, the mixing layer is shallow. This shallowness further complicates the flow patterns. In this thesis the development of shallow mixing layers is studied using Particle Tracking in a field study in a natural river. The aim is to improve our understanding of shallow mixing layers and hence to contribute to improvements of computational models of these flows. Field measurements were performed in a lowland section of the river Spree (width 30m, depth 1m) near Berlin, in collaboration with the Leibniz-Institute of Freshwater Ecology and Inland Fisheries (IGB). A 30m long splitter plate was constructed in the middle of the river, parallel to the banks, with an upstream weir on one side to control the discharge. A large shear layer developed with noticeable coherent structures. Three setups were created with varying velocity differences across the splitter. Both single point measurements (Acoustic Doppler Velocimetry, ADV) and whole field measurements (Particle Tracking Velocimetry, PTV) were done. The Particle Tracking consisted of the interval release of floating particles in the beginning of the mixing layer, from the end of the splitter. These measurements were done at night using small tea candle lights, providing sufficient contrast with the water surface. Three runs were filmed from a camera fixed in a tree at 10m above the water surface. A special point of interest in the data processing, which was done using custom-made Matlab programming, was the perspective transformation of the camera images. The analysis of the Particle Tracking data focused on: - mean velocity profiles in the horizontal plane - visualisation of particle streaklines - Lagrangian single particle and two-particle statistics Using Particle Tracking as a whole-field velocimetry tool proved difficult. The particle density was too low and the area of interest was not completely covered. Nevertheless, the characteristic tangential mean velocity profiles were found. The streakline plots proved the existence of large two-dimensional coherent structures at the low-velocity edge of the mixing layer in the two setups with the highest shear. The use of Lagrangian statistics proved a particularly valuable tool for acquiring information on particle dispersion. Moreover the Lagrangian analysis matched well with the Particle Tracking data. It yielded information on the spreading rate of the particle cloud and the ensemble averaged separation in time of initially close particle pairs. Most notably, the result of the latter was identification of two distinct separating regimes using Batchelor time scaling. Lastly, the ADV analysis, performed by IGB in Berlin, showed that the advective stresses of the horizontal velocities were an order of magnitude higher than the plane Reynolds stresses. The ADV analysis, which is not completed yet, will help to gain insight into the role of the composite bed friction on the lateral momentum exchange; thus complementing previous laboratory research at TU Delft.Civil Engineering and Geoscience