Linear Stability Analysis of Open- channel Flow with Two-Sided Bank Vegetation

The overgrowth of vegetation in constructed floodplains of river channels is commonly observed in Japan. Vegetation in watercourses is desirable in some cases, as it prevents bank erosion and provides habitat and food for numerous species. However, vegetation may also lead to problems, such as increase in channel resistance, reduction in the capacity of conveying water and generation of drift woods, exemplified in recent severe flood events in Japan (Hokkaido 2016, Kyushu 2017 and Western Japan 2018). Flood plain management and flood reduction measures thus may require precise estimations of discharge capacity, velocity distribution, and shear distribution in channels and rivers.
Vegetation in a part of a channel produces transverse shear flow, which may lead to flow instability and the generation of large-scale horizontal vortices. These horizontal vortices have a strong influence on the velocity distribution and the amount of discharge conveyed by a channel without overflow, and enhance the lateral mixing of not only the flow itself, but also the substances transported by the flow both inside and outside the vegetated area.
In this work, we study instability characteristics of an open-channel flow which is partially covered with vegetation on both of its sides. The basic flow velocity profile resembles that of a confined jet flow. Distinct from previous formulations, the base flow formulation is novel and consistently accounts for the distinction of two turbulence scales: 1) a large-scale turbulence which takes the form of the above-mentioned large-scale vortices and 2) a small-scale turbulence associated with bed friction. We analyse the effects of (1) bed friction, (2) kinematic eddy viscosity, (3) Froude number and (4) vegetation drag and density on the development of the large scale horizontal vortices, which appear near the edge of the vegetated zones. Our results indicate that two instability modes take place: a dominant mode, characterised by anti-phase vortex streets and a secondary mode characterized by in-phase vortex streets. The dominant mode is consistent with experiment observations whereas the secondary mode is overshadowed by the first mode.