Can Meandering Flows in Shallow Rectangular Reservoirs Be Modeled with the 2D Shallow Water Equations?

Abstract

AbstractThis paper discusses the ability of the two-dimensional (2D) shallow water equations to model meandering flows in shallow rectangular reservoirs. Four meandering flows of various shallowness were modeled using an academic flow model that includes a depth-averaged k-ϵ model accounting for the horizontal and vertical turbulent length-scales. Different roughness heights were considered for modeling the bottom friction. A proper orthogonal decomposition (POD) was applied to the simulation results to extract the behavior 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...