Upstream‐Migrating Bars in Partially Transporting Straight Channels: Numerical Simulation and Theoretical Interpretation

Abstract Alluvial bars in straight channels generally migrate downstream or can be non‐migrating but rarely migrate upstream. On the other hand, a recent long‐term field observation suggested a possibility of the upstream migration of bars. To understand this rare morphodynamic feature of alluvial bars, we herein perform non‐linear numerical simulations of alluvial bar formation and development in a straight channel. More specifically, we simulate alluvial bar dynamics under steady discharge and unsteady discharge (repeated hydrographs), wherein the bar regime retains super‐resonance condition. The result shows that initially formed, short downstream‐migrating free bars elongate, becoming much longer upstream migrating bars. The former bar elongation can be understood as a well‐observed non‐linear response of the bars, but much longer bar formation might originate from different morphodynamic features. The theoretical interpretation for this result using temporal and spatial mode linear analysis suggests a sort of forced bar formation in the upstream channel originating from nearly non‐migrating, slow‐movement bars. In other words, nearly non‐migration bars act as forcing factors, similar to an asymmetric obstacle in the channel, leading to an upstream morphodynamic influence observed under super‐resonance conditions. Subsequently, an interaction/coexistence of free‐migrating and forced‐steady bar responses may contribute to the formation of upstream‐migrating bars. These results provide new insights into the migration features of alluvial bars, but they still require a comprehensive theoretical framework to explain them. Additionally, observing upstream‐migrating bars will be an important future research, although it will be difficult due to the considerably slow migration speed predicted by the present numerical simulation.