A one‐dimensional model of bifurcations in gravel bed channels with erodible banks

Abstract

[1] In a recent paper, Bolla Pittaluga et al. proposed a physically based formulation for the nodal point conditions to be adopted at a channel bifurcation in the context of a onedimensional approach. They employed such conditions to study the equilibrium configurations of a simple bifurcation and their stability, assuming erodible bed and fixed banks. With the present work we extend the model proposed by Bolla Pittaluga et al. to the case of channels with erodible banks, i.e., channels which may adapt their width to the actual flow conditions. Such an extension is of a particular interest for river bifurcations in gravel bed braided streams, in which bed evolution and bank erosion processes occur over comparable timescales. Moreover, to study the morphological evolution of a bifurcation, we employ a different approach with respect to Bolla Pittaluga et al. and introduce a ''local analysis'' which does not account for the influence exerted on channel morphology by downstream conditions on longer timescales. For values of the controlling parameters typical of gravel bed braided streams, the model shows that the stable equilibrium solutions of a bifurcation are invariably characterized by a strongly unbalanced partition of water and sediment discharges in the two branches. Numerical simulations, based on a simplified model of the bifurcation evolution, allow us to investigate the role of the mechanism of generation of a bifurcation on its final equilibrium configurations. It is shown that bifurcations which form through the incision of a new, initially narrow, channel may lead to significantly different equilibrium configurations with respect to bifurcations which generate from a central deposition in a wide channel. In spite of its simplicity the model seems to retain the most relevant effects which govern the behavior of gravel bed channel bifurcations.

Response of river‐dominated delta channel networks to permanent changes in river discharge

“…This threshold for channel creation occurs because the existing network has some capacity to carry additional Q, and only when that capacity is exceeded is flooding sufficient to create new channels. Interestingly, during the approach to that threshold, increases in Q never cause the abandonment of bifurcations, even though theoretical work suggests that such an increase in Q could cause instability [Bolla Pittaluga et al, 2003;Miori et al, 2006;Edmonds and Slingerland, 2008].…”

“…The answer to this question, and the sensitivity of such delta networks, lies in the configurations of the bifurcate channels. Previous stability studies have focused on bifurcations that have symmetric downstream boundaries [Bolla Pittaluga et al, 2003;Miori et al, 2006;Edmonds and Slingerland, 2008], such as bifurcations with equal-length bifurcate channels that enter a lake. However, as will be shown for natural deltas, bifurcations in the numerical deltas respond to downstream boundary conditions that are asymmetric, with the ratio of average water-surface slopes between the two bifurcate channels in these experiments being 2.2 (n = 13), thus rendering comparisons to previous theory inappropriate.…”

“…Two distributaries with identical downstream boundary conditions and a given upstream Shields stress (Q) distribute water and sediment asymmetrically because this is a stable equilibrium configuration [Wang et al, 1995;Slingerland and Smith, 1998;Bolla Pittaluga et al, 2003;Miori et al, 2006;Zolezzi et al, 2006;Bertoldi and Tubino, 2007;Edmonds and Slingerland, 2008;Kleinhans et al, 2008]. For a given Q, upstream channel roughness, and channel aspect ratio, there exists only one asymmetric discharge ratio (Q r ) for which the downstream bifurcate channels are stable to small perturbations.…”

Bifurcation instability and chute cutoff development in meandering gravel-bed rivers

“…To evaluate the assumption in the 1D model of equilibrium flow and morphology in bends and to assess the bar regime, we determined the adaptation length of the bed (λ s ) and the adaptation length of the flow (λ w ; Table 3 based on Struiksma et al, 1985). The values for the River Allier predict that alternate bars should form in the channel, which would affect the division of water and sediment at the bifurcation (Miori et al, 2006;Kleinhans et al, 2008). This means that the migration of bars downstream affects the sediment transport division at the bifurcation ).…”

“…The division of water and sediment between both branches can change over time as a result of change of the downstream branches, for example channel widening (Miori et al, 2006) or lengthening. Also, conditions in the upstream channel affect the partitioning: particularly helical flow because of curvature, presence of bars , and inlet steps ) that cause gravity-driven sediment deflection on the transversely sloping bed (Bolla Pittaluga et al, 2003;Kleinhans et al, 2008).…”