Turbulent characteristics and Lagrangian Coherent Structures (LCS) in uniform compound channels

A great variety of natural water streams and artificial channels can be classified as “shallow compound channels” since their cross-stream section can be assumed to be characterized by a main central channel and shallow floodplains with a marked separation in the typical length scales involved, since their horizontal dimensions exceed the vertical dimension, see Jirka & Uijttewaal (2004). In the case of shallow free surface flows, two-dimensional coherent structures with length scales greater than the water depth are often observed in a wide range applications, Socolofsky & Jirka (2004). The typical geometry of the compound channels are such that the topography has a sharp discontinuity in the boundary between the main channel and the flood plains. As a result, the flow velocity in the floodplains is lower than in the main channel, due to the water shallowness and to the high bed roughness (e.g. presence of vegetation). The consequent shearing is a source of vorticity that is transported along the longitudinal direction. Moreover, the flow depth gradient along the cross section is indeed another fundamental source of vorticity that produces large scale vertical structures, as shown in (Soldini et al, 2004). Such turbulent structures are liable of the transfer of momentum and mass between the central main channel and floodplains. The present study is focused on the description of the dynamics undergone by macrovortices in a compound channel under statistically steady condition of flow. We show experimentally how the large scale vortical structures, after an initial grows starting from the inlet, reach a constant typical dimensions that remains unchanged along the streamwise direction. The typical vortex dimensions scale with the flow depth jump between the main channel and the floodplains. Further, the mixing processes associated to the above turbulent structures are analyzed in details with the aid of different mixing measures, such as the Hua and Klein criterion (Hua & Kein, 1998), the Finite Time Lyapunov Exponents (FTLE) and the absolute and relative statistics. If, on one hand, the mean particle statistics are able to discriminate the overall mixing regime, according to the classical Taylor theory, on the other hand, different measures as the FTLE are able to identify Lagrangian Coherent Structures (LCS) inside the Eulerian flow fields, enlightening the presence of transport barriers (Boffetta et al. 2001) that may prevent the exchange of mass between the main channel and the flood plains.