Bifurcation Instability Modulated by a Connecting Channel Leads to Periodic Water Partitioning in a Simple Channel Network

Water and mass transport in distributary channel networks play an important role in nourishing fluvial and coastal wetlands, and are largely determined by the morphological configurations of channel bifurcations. While the morphological equilibrium of a single channel bifurcation has been extensively studied, the equilibrium configurations of channel networks with connecting channels linking the bifurcating branches, that is, the “bifurcation-connecting channel” units that are commonly found in rivers, deltas and estuaries, remain elusive. In this simple yet representative channel network of the “bifurcation-connecting channel” unit, we observed through numerical simulations an oscillatory water partitioning under moderate Shields stress and channel aspect ratio, in addition to the steady-state solutions reported in previous studies. The oscillatory water partitioning indicates a newly discovered periodic solution, which is an emergent behavior under constant boundary conditions. We found that the periodic solution is primarily due to the dynamic interactions between bifurcation instability and water surface slope advantage in the two branches modulated by the reversable discharges through the connecting channel, under moderate Shields stress and channel aspect ratio. In such cases, the developed slope advantage in the subordinate branch can suppress the deepening of the dominant branch and eventually lead to the shifting of the dominant branch. In contrast, the channel network attains a steady-state solution when the slope advantage or the bifurcation instability is dominant with relatively low and high Shields stress (or channel aspect ratio). Our results improve the understanding on the evolution and restoration of channel networks under increasing human interventions in global deltas.