- A Comparison of the Planforms of Meandering Tidal and Fluvial Channels on the Ganges-Brahmaputra-Jamuna Delta, Bangladesh
U. of Minnesota thesis by Rachel L. Bain, 2014
This well written thesis starts with a thorough literature review on geometric models of meandering rivers.
Bain first shows the difference between with tidal and fluvial meandering.
After that she describes the two theories regarding the physics of meander formation: bar theory and bend theory.
Bain also states that in modern meander theory there are four key processes that must be incorporated into any physical model of meandering: flow-field hydrodynamics, sediment transport, bed morphodynamics and bank erosion.
In the research part of the thesis, Bains used Google Earth to digitize 130 meandering channels in the Ganges-B.-J. Delta in Bangladesh.
From this research, Bains concludes that tidal meanders are more symmetric and less sinuous than river meanders.
- River Meander Modeling and Confronting Uncertainty
U. of Arizona, Sandia report by Ari J. Posner, 2011
In his introduction, Posner states that meandering is an enigma within the scientific community, and that there still is no underlying theory for development and maintenance of meanders.
Reason for this is the dynamic nature of meanders: measuring geometric and hydraulic variables of these planiforms is "only a snapshot of time".
According to Posner, scientists therefore use the relationships between variables in an attempt to find some constants, a strategy that has led to the "Regime Theory", stating that each fluvial system has an equilibrium state that it tends toward.
In his study, Posner describes and analyses a laboratory experiment (Friedkin, 1945) with a 12 meter long river model and dozens of runs, starting with a sine-generated initial channel.
Each 32 hour run had 14 initial parameters.
Deterministic modeling
Posner then used two different deterministic models to simulate the 32 hour runs: the Ikeda et al. 1981 model and the Johanneson and Parker 1989b model.
In his study, he compares the results of these two models, finding the simpler Ikeda model giving better results than the more complex Johanneson and Parker model when computing power is considered.
Both models though, had center line errors large than 50%, suggesting the limitation and incapability of deterministic models.
Stochastic modelling
After that, Posner ran a Monte Carlo simulation of both models, using the bank erosion coefficient as a variable, running with 1000 iterations and he compared these results to the Friedkin, 1945 experiment.
The Monte Carlo simulations yielded a 95% confidence interval bound that bounds 90% of the observed channel centerline, with a mean centerline within 30% errors compared with observational data.
Conclusion
From this study, Posner concludes that the meandering migration process is a stochastic process that requires Monte Carlo simulation to realistically model its evolution process.
Posner also points to the fact that the planform takes a relative equilibrium quite fast, just after a 32 hour run, since longer runs up to 120 hours didn't show significant differences from shorter runs.
U. of Minnesota thesis by Rachel L. Bain, 2014
This well written thesis starts with a thorough literature review on geometric models of meandering rivers.
Bain first shows the difference between with tidal and fluvial meandering.
After that she describes the two theories regarding the physics of meander formation: bar theory and bend theory.
Bain also states that in modern meander theory there are four key processes that must be incorporated into any physical model of meandering: flow-field hydrodynamics, sediment transport, bed morphodynamics and bank erosion.
In the research part of the thesis, Bains used Google Earth to digitize 130 meandering channels in the Ganges-B.-J. Delta in Bangladesh.
From this research, Bains concludes that tidal meanders are more symmetric and less sinuous than river meanders.
- River Meander Modeling and Confronting Uncertainty
U. of Arizona, Sandia report by Ari J. Posner, 2011
In his introduction, Posner states that meandering is an enigma within the scientific community, and that there still is no underlying theory for development and maintenance of meanders.
Reason for this is the dynamic nature of meanders: measuring geometric and hydraulic variables of these planiforms is "only a snapshot of time".
According to Posner, scientists therefore use the relationships between variables in an attempt to find some constants, a strategy that has led to the "Regime Theory", stating that each fluvial system has an equilibrium state that it tends toward.
In his study, Posner describes and analyses a laboratory experiment (Friedkin, 1945) with a 12 meter long river model and dozens of runs, starting with a sine-generated initial channel.
Each 32 hour run had 14 initial parameters.
Deterministic modeling
Posner then used two different deterministic models to simulate the 32 hour runs: the Ikeda et al. 1981 model and the Johanneson and Parker 1989b model.
In his study, he compares the results of these two models, finding the simpler Ikeda model giving better results than the more complex Johanneson and Parker model when computing power is considered.
Both models though, had center line errors large than 50%, suggesting the limitation and incapability of deterministic models.
Stochastic modelling
After that, Posner ran a Monte Carlo simulation of both models, using the bank erosion coefficient as a variable, running with 1000 iterations and he compared these results to the Friedkin, 1945 experiment.
The Monte Carlo simulations yielded a 95% confidence interval bound that bounds 90% of the observed channel centerline, with a mean centerline within 30% errors compared with observational data.
Conclusion
From this study, Posner concludes that the meandering migration process is a stochastic process that requires Monte Carlo simulation to realistically model its evolution process.
Posner also points to the fact that the planform takes a relative equilibrium quite fast, just after a 32 hour run, since longer runs up to 120 hours didn't show significant differences from shorter runs.
