Maximum energy dissipation to explain velocity fields in shallow reservoirs

Shallow reservoirs are often used as sediment traps or storage basins, in which sedimentation depends on the flow pattern. Short rectangular reservoirs reveal a straight jet from inlet to outlet with identical recirculation zones on both sides. In longer reservoirs, the main jet reattaches to the side of the reservoir leading to small and large recirculation zones. Previous studies have found an empirical geometric relation describing the switch between these two flow patterns. In this study, we demonstrate, with a simple analytical model, that this switch coincides with a maximization of energy dissipation in the shear layer between the main jet and recirculation zones: short reservoirs dissipate more energy when the flow pattern is symmetric, while longer reservoirs dissipate more energy with an asymmetric pattern. This approach enables the prediction of the flow patterns without detailed knowledge of small scale processes, potentially useful in the early phase of reservoir design.