Bifurcation dynamics and avulsion duration in meandering rivers by one-dimensional and three-dimensional models

At river bifurcations, water and sediment are divided over two branches. The dynamics of the bifurcation determine the long-term evolution (centuries) of the downstream branches, potentially leading to avulsion, but the dynamics are poorly understood. The long-term evolution can only be studied by one-dimensional models because of computational costs. For such models, a relation describing the sediment division is necessary, but only few relations are available and these remain poorly tested so far. We study the division of sediment and the morphodynamics on a timescale of decades to centuries by idealized three-dimensional modeling of bifurcations with upstream meanders and dominantly bed load transport. An upstream meander favors one bifurcate with more sediment and the other with more water, leading to destabilization. The bifurcations commonly attain a highly asymmetrical division of discharge and sediment after a few decades to a few centuries, depending on combinations of the relevant parameters. Although past work on avulsions focused on slope advantage, we found that bifurcations can be quasibalanced by opposing factors, such as a bifurcate connected to the inner bend with a downstream slope advantage. Nearly balanced bifurcations develop much slower than unbalanced bifurcations, which explains the observed variation in avulsion duration in natural systems. Which branch becomes dominant and the timescale to attain model equilibrium are determined by the length of the downstream bifurcates, the radius of the upstream bend, a possible gradient advantage for one bifurcate and, notably, the width -depth ratio. The latter determines the character of the bars which may result in overdeepening and unstable bars. The distance between the beginning of the upstream bend and the bifurcation determines the location of such bars and pools, which may switch the dominant bifurcate. In fact, when the bifurcation is quasibalanced by opposing factors, any minor disturbance or a different choice of roughness or sediment transport predictor may switch the dominant bifurcate. The division of sediment is nearly the same as the division of flow discharge in most runs until the discharge division becomes very asymmetrical, so that a bifurcate does not close off entirely. This partly explains the sustained existence of residual channels and existence of anastomosing rivers and the potential for reoccupation of old channel courses. We develop a new relation for sediment division at bifurcations in one-dimensional models incorporating the effect of meandering. The flow and sediment divisions predicted by two existing relations and the new relation for one-dimensional models are in qualitative agreement with the three-dimensional model. These one-dimensional relations are however of limited value for wider rivers because they lack the highly three-dimensional bar dynamics that may switch the direction of bifurcation evolution. The potential effects of bed sediment sorting, bank erosion, and levee formation on bifurcation stability and avulsion duration are discussed.