Meandering river dynamics

Meandering channels are dynamic landforms that arise as a result of fluid mechanic and sedimentary processes. Their evolution has been described by the meander morphodynamic equations, which dictate that channel curvature and bed topology give rise to local perturbations in streamwise fluid velocity, prompting the preferential erosion and sediment deposition that constitute meander behavior. Previous theoretical work has been based on simplified periodic systems. Here we determine the mathematical conditions required for unique solutions to the meander morphodynamics equations. Our predictions for non-periodic finite-domains constitute the first correct explanation of behavior observed in flumes, where a fixed inlet leads to the long-term decay of all meanders. We show that a continuous perturbation is required for sustained meandering. With a driven perturbation at the inlet, we find that high (low) frequency driving results in spatial decay (growth). We present original scaling arguments for the dependence of the meander migration rate on geological parameters, showing that the rate of migration increases with increased width, down-reach slope, and bank erodibility, and decreases with increased volumetric flow rate. The meander equations involve a single dimensionless parameter alpha, which characterizes the ratio of secondary to irrotational flow. We show that variations in alpha have significant impact on spatial and temporal scaling, and on the degree of upstream skewing in meander shapes. For numerical simulations, we develop a rigorous mathematical description of the relationship between spatial discretization schemes and numerical stability, and we present a robust, stable numerical algorithm. We introduce a parametric Lagrangian variable for improved stability and adaptive spatial resolution. Our implicit numerical solver facilitates a time-step size which is limited by accuracy instead of stability, leading to a significant improvement in computational speed. We present the first demonstrably accurate, converged solutions for the meander morphodynamics equations. Our nonlinear work has focused on the evolution of initially quiescent systems with boundary driving. We find that finite-domain theory accurately describes behavior close to the upstream boundary, whereas standard period-domain behavior dominates downstream. In the instance of clamped upstream boundaries, nonlinear simulation leads to a significantly longer progression of the initial disturbance relative to linear theory before subsiding into a straight channel. We find that upstream perturbations will cause the excitation of temporally growing waves downstream. Finally, we provide rigorous scaling analysis to determine the appropriate length of experimental flumes, the appropriate duration of experimental runs, and the necessary properties of sediment. We present simulations of previous experimental work and find good heuristic agreement, and we provide recommendations for experimental conditions for the observation of sustained meandering in laboratory flumes.

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Chemical Engineering

Grantor

University of Illinois at Urbana-Champaign

Year dc:date

2016

Author dc:creator

• Weiss, Samantha Freeman

Contributors dc:contributor

• Higdon, Jonathan J. L.
• Parker, Gary
• Rao, Christopher
• Schroeder, Charles

• Meandering
• morphodynamics
• channel
• meander
• uniqueness
• flume
• upstream
• perturbation
• geological scaling
• skewing
• hyberbolic differential equations
• nonlinear partial differential equations
• spatial discretization
• numerical stability
• parametric Lagrangian variable
• adaptive spatial resolution
• convergence
• boundary driving
• scaling analysis

Statement dc:rights

• Copyright 2016 Samantha Weiss

Language dc:language

en

Handle dc:identifier

http://hdl.handle.net/2142/92706

OAI identifier oai:identifier

oai:www.ideals.illinois.edu:2142/92706