Can meandering flows in shallow rectangular reservoir be modelled with the 2D shallow water equations?

In this article, the ability of the 2D shallow water equations to model meandering flows in shallow rectangular reservoirs is discussed. Four meandering flows, of various shallowness, were modelled using the academic flow model WOLF 2D, which includes a depth-averaged k- model accounting for the horizontal and vertical turbulent length-scales. The bottom friction was modelled with the Colebrook-White formula and different roughness heights were considered. A Proper Orthogonal Decomposition (POD) was applied to the simulation results to extract the behaviour of the main structures responsible for the meandering flow. The same POD analysis was also performed for the reference experimental flow fields, obtained by Large-Scale Particle Image Velocimetry. The first two POD modes obtained from the numerical simulations assuming a smooth bottom are in good agreement with the experimental modes in terms of energy, as well as temporal and spatial variations, whatever the shallowness. In contrast, the remaining simulated modes are not well rendered. The effect of an increased roughness height in the simulations is finally discussed. It leads to an improved reproduction of the first two modes and of the following modes, except when significant viscous effects govern in the flow.