Overview 

This work investigates the control of avulsions in bifurcated channel systems; a main channel splitting into 2 equal sub channels. Towards this end,  the authors build a mathematical/numerical model, extending the well known analysis presented by Bolla Pittaluga et al. (2003) (BRT). The proposed model can track the evolution of a perturbation at the branching point of the sub-channels. In the first place, the model recovers the regimes identified in BRT. At low channel aspect ratios, following a perturbation, the system recovers balanced flows in each of the sub-channels. Beyond a critical  aspect ratio Beta_c, however, the long term equilibrium of the flow in the system is unbalanced. This work show that as the aspect ratio is increased further, a second threshold Beta_TH is reached, here the sub channel, with the least flow, exhibits a partial-avulsion—where the channel still carries flow but ceases to transport sediment. Depending on the length of the sub channels, as the aspect ratio is increased even further, a point is reached where full avulsion occurs, i.e., the channel does not convey either water or sediment.

Comments

1. I think that the analysis in this paper is of sufficient interest to stand alone  but also feel that it  would be significantly enhanced,  if the authors can point toward experimental or field evidence of the behaviors predicted by the math.  For example, referring to Figure (9), it appears, by my calculations, that full avulsion would be reached in a system with channels of water depth of 2m, width 40 m, and length 1km+.

How common are such conditions in field settings? (eg. Wax Lake in Louisiana)?

Are records of permanently avulsed channels seen in such systems?

Are records of permanently avulsed channels seen in field systems with shorter channel lengths and smaller aspect ratios?

2. The addition of the analytical model (25) is a noteworthy and helpful. 

But so that others can explore the model, I would suggest explicitly writing out the transport models that are used in the last component.  The authors could also point towards what numerical method/tool they used to solve the system of nonlinear equations. 

3. Line 302:  It is not clear to me what is meant by Beta_NT is calculated analytically.  Is this arrived at by using the basic BRT analysis?

4. With reference to Fig 5. Why is there such an abrupt change (almost like a phase transition) at (or close to) Beta_NT.  Is such a jump exhibited in the analytical model in (25)? 

The study effectively overcomes the limit of the original BRT (2003) model for river bifurcation to account for the situation where one of the two branches reaches vanishing transport capacity. The finding of more asymmetrical flow distribution in those configurations agrees with what is commonly found through numerical simulations (i.e. Kleinhans et al., 2008). The numerical scheme presented is robust, however, it would be interesting to have some comments on how it responds to different kinds of perturbations (i.e. shape, position or magnitude) and, eventually, the effect in terms of morphodynamic timescales. The analytical model to study those conditions, even though strongly idealized, does its job in describing the configuration where the non-dominant branch is not able to adjust its riverbed anymore. It would be nice to see in future developments the inclusion of finer sediments to apply those considerations in low-land bifurcations.