the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 23 Aug 2023
Analysis of autogenic bifurcation processes resulting in river avulsion
Abstract. River bifurcations are constituent components of multi-thread fluvial systems, playing a crucial role in their morphodynamic evolution and the partitioning of water and sediment. Although many studies have been directed at exploring bifurcation dynamics, the conditions under which avulsions occur, resulting in the complete abandonment of one branch, are still not well understood. To address this knowledge gap, we develop a novel 1D numerical model, based on existing nodal point relations for sediment partitioning, which allows for the simulation of the morphodynamic evolution of a free bifurcation. Model results show that when the discharge asymmetry is so high that the shoaling branch does not transport sediments (partial avulsion conditions) the dominant branch undergoes significant degradation, leading to a higher inlet step between the bifurcates and further amplifying the discharge asymmetry. The degree of asymmetry is found to increase with the length of the downstream channels, to the point that when they are sufficiently long, the shoaling branch is completely abandoned (full avulsion conditions). To complement our numerical findings, we also formulate a new analytical model that is able to reproduce the essential characteristics of the partial avulsion equilibrium, which enables us to identify the key parameters that control the transition between different configurations. In summary, this research sheds light on the fundamental processes that drive avulsion through the abandonment of river bifurcations. The insights gained from this study provide a foundation for further investigations and may offer valuable information for the design of sustainable river restoration projects.
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Notice on discussion status
The requested preprint has a corresponding peer-reviewed final revised paper. You are encouraged to refer to the final revised version.
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Preprint
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The requested preprint has a corresponding peer-reviewed final revised paper. You are encouraged to refer to the final revised version.
- Preprint
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- BibTeX
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- Final revised paper
Journal article(s) based on this preprint
Interactive discussion
Status: closed
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RC1: 'Comment on egusphere-2023-1551', V. Voller, 29 Sep 2023
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)?
Citation: https://doi.org/10.5194/egusphere-2023-1551-RC1 - AC2: 'Reply on RC1', Gabriele Barile, 26 Oct 2023
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RC2: 'Comment on egusphere-2023-1551', Lorenzo Durante, 01 Oct 2023
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.
Citation: https://doi.org/10.5194/egusphere-2023-1551-RC2 -
AC1: 'Reply on RC2', Gabriele Barile, 26 Oct 2023
We thank the Reviewer for the insightful comments on our work. We agree with the Reviewer that the transient behaviour of the bifurcation may depend on the magnitude and shape of the initial perturbation. We did not perform a systematic analysis of the effect of the initial perturbation, but we expect the long-term equilibrium of the bifurcation - which is the main topic explored by our work - not to depend on it. As a matter of fact, the long-term discharge asymmetry displayed by numerical simulations matches that foreseen by the analytical models. In our work we focus on the behaviour of "free'' bifurcations and we do not model the generative processes that lead to their formation. Therefore, we assumed the simplest, less disturbed initial configuration, as needed to isolate the basic mechanisms. In this sense, our analysis is only telling part of the story, in which the bifurcation is unforced and weakly perturbed.
It is worth recalling that several previous works examined the role of various forcing factors, such as the curvature of the upstream channel (Kleinhans et al, 2008), branches progradation (Salter et al., 2018), tides (Ragno et al., 2020) and slope advantage in the downstream branches (Redolfi et al., 2019). Furthermore, Bertoldi et al. (2009) highlighted how cyclic discharge variations or the complete abandonment of one branch can be the consequence of the migration of bars in the upstream channel.We thank the Reviewer for the suggestion regarding the inclusion of finer sediment. We also believe that this would be an important future development. In the revised manuscript, we will therefore add the following paragraph at the end of Section 5.
The present formulation is valid under conditions where sediment is dominantly transported as bedload. Although some promising approaches have been proposed (Iwantoro et al., 2021),
a systematic understanding of the morphodynamics of channel bifurcations in suspension-dominated channels is still lacking, thus preventing a reliable extension of our model. However, we can expect that a similar scenario of transition to the avulsion condition also occurs for sand bed channels where most sediments are transported in suspension. In this case the higher values of the Shields stress are likely to be associated with an higher threshold βNT, so that larger values of the aspect ratio may be needed to reach avulsion conditions.Citation: https://doi.org/10.5194/egusphere-2023-1551-AC1
-
AC1: 'Reply on RC2', Gabriele Barile, 26 Oct 2023
Interactive discussion
Status: closed
-
RC1: 'Comment on egusphere-2023-1551', V. Voller, 29 Sep 2023
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)?
Citation: https://doi.org/10.5194/egusphere-2023-1551-RC1 - AC2: 'Reply on RC1', Gabriele Barile, 26 Oct 2023
-
RC2: 'Comment on egusphere-2023-1551', Lorenzo Durante, 01 Oct 2023
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.
Citation: https://doi.org/10.5194/egusphere-2023-1551-RC2 -
AC1: 'Reply on RC2', Gabriele Barile, 26 Oct 2023
We thank the Reviewer for the insightful comments on our work. We agree with the Reviewer that the transient behaviour of the bifurcation may depend on the magnitude and shape of the initial perturbation. We did not perform a systematic analysis of the effect of the initial perturbation, but we expect the long-term equilibrium of the bifurcation - which is the main topic explored by our work - not to depend on it. As a matter of fact, the long-term discharge asymmetry displayed by numerical simulations matches that foreseen by the analytical models. In our work we focus on the behaviour of "free'' bifurcations and we do not model the generative processes that lead to their formation. Therefore, we assumed the simplest, less disturbed initial configuration, as needed to isolate the basic mechanisms. In this sense, our analysis is only telling part of the story, in which the bifurcation is unforced and weakly perturbed.
It is worth recalling that several previous works examined the role of various forcing factors, such as the curvature of the upstream channel (Kleinhans et al, 2008), branches progradation (Salter et al., 2018), tides (Ragno et al., 2020) and slope advantage in the downstream branches (Redolfi et al., 2019). Furthermore, Bertoldi et al. (2009) highlighted how cyclic discharge variations or the complete abandonment of one branch can be the consequence of the migration of bars in the upstream channel.We thank the Reviewer for the suggestion regarding the inclusion of finer sediment. We also believe that this would be an important future development. In the revised manuscript, we will therefore add the following paragraph at the end of Section 5.
The present formulation is valid under conditions where sediment is dominantly transported as bedload. Although some promising approaches have been proposed (Iwantoro et al., 2021),
a systematic understanding of the morphodynamics of channel bifurcations in suspension-dominated channels is still lacking, thus preventing a reliable extension of our model. However, we can expect that a similar scenario of transition to the avulsion condition also occurs for sand bed channels where most sediments are transported in suspension. In this case the higher values of the Shields stress are likely to be associated with an higher threshold βNT, so that larger values of the aspect ratio may be needed to reach avulsion conditions.Citation: https://doi.org/10.5194/egusphere-2023-1551-AC1
-
AC1: 'Reply on RC2', Gabriele Barile, 26 Oct 2023
Peer review completion
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Marco Redolfi
Marco Tubino
The requested preprint has a corresponding peer-reviewed final revised paper. You are encouraged to refer to the final revised version.
- Preprint
(2728 KB) - Metadata XML