Pascal Pirlot

The mathematical model introduced by Bolla Pittaluga et al. in 2003 (BRT-model) allows finding equilibrium conditions for the discharge partition along the anabranches of a bifurcation, accounting only for the variation of bed elevation at the bifurcation head. In 2006, Miori et al. (MRT-model) accounted for the local channel width adjustment and in 2021, Ragno et al. considered the stabilising effect of a confluence at the example of channel loops (RRT-model). All three referenced models strongly interact with the geometrical configuration of the bifurcation. However, all geometrical parameters have not yet been investigated using the cited models, both in terms of equilibrium or transient modelling.

The variation of the bifurcation planimetry rises several key questions: - How does it affect the classic equilibria and thresholds? - What are the typical values for the geometric factors derived? - How are the field or experimental observations related to the theory developed?

The new planimetric parameters (enlargement and asymmetry) are isolated explicitly to produce pitchfork diagrams and a linear stability analysis was performed. After that, a primitive data collection was manually executed. The data set provided by Ragno et al. in 2022 furnishes information on the bankfull hydraulics of roughly 150 channel loops. The active width in the entering channel and the anabranches, at a single cross section was measured from satellite images for each loop. The observed asymmetry and enlargement were then related to their corresponding outputs, e.g. the observed asymmetry of a bifurcation is compared to the critical threshold that discriminates balanced (symmetric) from unbalanced (asymmetric) stable equilibrium.

The fixed bifurcation asymmetry imposes an unbalanced discharge stable equilibrium, but no specific change in the average downstream slope and water depth. As the bifurcation enlargement increases, so does the downstream kick in channel slope and the water depth decreases. Also, the stability of balanced configuration decreases. The observed asymmetry results in a bimodal distribution, sustaining a sense of symmetry versus decisive asymmetry. The observed enlargement is normally distributed around a mean value (1.4 for bed load and 1.25 for suspended load loops). Bolla Pittaluga, M., R. Repetto, and M. Tubino (2003), Channel bifurcation in braided rivers: Equilibrium configurations and stability, Water Resour. Res., 39(3), 1046 Miori, S., R. Repetto, and M. Tubino (2006), A one-dimensional model of bifurcations in gravel bed channels with erodible banks, Water Resour. Res., 42, W11413 Ragno, N., Redolfi, M., & Tubino, M. (2021). Coupled morphodynamics of river bifurcations and confluences. Water Resources Research, 57, e2020WR028515 Ragno, N., Redolfi, M., & Tubino, M. (2022). Quasi-universal length scale of river anabranches. Geophysical Research Letters, 49, e2022GL099928