## 1. Introduction

[2] Bifurcations are unit processes of fundamental importance for the behavior of braided river networks; in particular, weak variations of the geometry of a bifurcation may strongly affect water and sediment partition into the downstream branches, thus crucially controlling the development of braiding networks. The sensitive dependence of braided rivers on conditions at bifurcations has been highlighted in many contributions [e.g., *Hoey*, 1992]. In spite of their importance bifurcations have not been as widely studied as confluences, their counterpart processes [*Mosley*, 1976; *Ashmore and Parker*, 1983] and few experimental and field data are available in literature [*Dancy*, 1947; *Federici*, 1999].

[3] Bifurcations are common features of different fluvial systems, like braiding and anabranching river networks and river deltas. The morphology and development of a bifurcation is mainly governed by the dominant sediment transport mechanism, which determines the partitioning of sediment discharge into the two downstream branches. If suspended load is dominant, whatever the bed topography at the bifurcation, the sediment discharge rates into the downstream channels are closely related to the partition of water discharge. On the other hand, if bed load is dominant, the effect of local bed slope may play a crucial role in governing sediment partition, in particular at low values of Shields stress which typically characterize gravel braided rivers.

[4] In the present contribution we study the equilibrium configurations and the stability of gravel bed river bifurcations through a one-dimensional approach. The formulation of the problem is given in section 2. Though one-dimensional models do not allow a detailed description of flow field and bed topography, they are widely used in river engineering for long-term predictions of river morphological development. They also represent a useful tool for the investigation of complex systems, like braided networks, whose planimetric structure is extremely complex [*Howard et al.*, 1970; *Sapozhnikov and Foufoula-Georgiou*, 1996] and whose dynamics are highly unstable and characterized by many recurring processes [*Ashmore*, 1982, 1991]. In fact, several conceptual models have been proposed to describe the dynamics of braided rivers, which are able to reproduce the gross features of the network. They are based on simplified approaches whereby the network is schematized in terms of cells or channel units, which are subject to exchanges and dynamical rules based on experimental observations and theoretical models [*Murray and Paola*, 1994; *Satofuka*, 2001]. Numerical approaches have also been attempted in the context of two-dimensional shallow water models [*Enggrob and Tjerry*, 1999; *McArdell and Faeh*, 2001; *Kurabayashi and Shimizu*, 2001], however a fully mechanical description of braiding networks is still not available.

[5] In one-dimensional network confluences and bifurcations constitute nodal points where suitable internal conditions must be imposed. However, important differences exist in modeling the two processes as pointed out by *Wang et al.* [1995]: in the former case water and sediment discharges are known in both of the upstream branches, on the contrary a further relationship is required in the latter case, which governs water and sediment distribution in the two downstream channels.

[6] A first attempt to describe river bifurcations with movable bed through a one-dimensional model is due to *Wang et al.* [1995] who devoted particular attention to the case of river deltas; a brief overview of their work is reported in section 3. A further contribution, in the case of dominant suspended load, is due to *Slingerland and Smith* [1998] who investigated the conditions leading to avulsion of a meandering river.

[7] *Wang et al.* [1995] introduce an empirical nodal point condition which relates water and sediment discharges into the downstream branches. Their analysis suggests that such a condition plays a crucial role on the long-term evolution of the system. However, the nodal point condition depends on an empirical parameter which may vary significantly according to the estimates provided by the Authors; hence, the above approach can hardly be applied to predict the evolution of a real bifurcation.

[8] In order to overcome this difficulty an alternative formulation for the nodal point conditions, based on a quasi two-dimensional approach, is proposed in section 4 of the present paper. The equilibrium configurations of a simple channel loop are theoretically investigated in section 5. Section 6 is devoted to the linear stability analysis of the above solutions. Moreover theoretical results are compared with the full numerical solution of one-dimensional equations in section 7. Finally, section 8 is devoted to some concluding remarks.