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River channel response to changing governing conditions : rational regime models and experimental observations Eaton, Brett Curtis

Abstract

Rational regime models can be used to develop meaningful frameworks for understanding reach scale alluvial channel response to environmental changes. The key obstacle to their general acceptance is that they cannot be analytically closed, and they predict a range of solutions that are theoretically viable. As a result, modellers have had to invent some sort of optimality criterion, many of which are conceptually unsatisfactory, in order to isolate unique solutions. The optimality criterion described here is understood physically in terms of flow resistance maximization for the fluvial system, which produces the most nearly stable, hence most likely configuration. The flow resistance for the system comprises three components: grain-scale flow resistance, bedform-scale form resistance, and reach-scale form resistance. Analyses using various other proposed optimality criteria demonstrate that, for bedload dominated streams, the choice of optimization is not critical, since, for unique values of slope, discharge and characteristic grain size, they predict nearly identical channel configurations. In particular, when the reach-scale form resistance dominates the system adjustment, the maximum flow resistance criterion becomes theoretically equivalent to the previously proposed minimum slope hypothesis. The framework for evaluating channel response can be most generally represented as a series of three-dimensional surfaces in an alluvial state space defined by width/depth ratio, relative roughness and channel slope or - equivalently — dimensionless shear stress. Each surface represents the set of solutions for a unique value of bank strength. Experiments designed to test the theoretical implications associated with the maximum flow resistance criterion demonstrate that the system scale flow resistance responds as predicted. When the channel banks are as erodible as the bed, the reach-scale flow resistance is the dominant component of the system adjustment, resulting in a functional relation between the average water surface slope along the channel thalweg and the ratio of the sediment supply and the imposed discharge. This is equivalent to the well known and generally accepted graded relation between channel slope and sediment supply. When the banks are fixed, the channel slope remains nearly constant - as does the cross section shape - for a range of sediment supply rates. In this case, equilibrium seems to result from a textural modification of the bed surface and thus the grain scale or bedform flow resistance. These results are consistent with the concept of system-scale flow resistance being the key to understanding channel stability, and they indicate that the previous hypotheses, such as slope minimization, are too limited in the range of adjustments that they embrace. The maximum flow resistance criterion says nothing about the process-form interactions that produce the characteristic adjustment for the experimental channels, which comprises the development of a series of regular, alternating pools and riffles established within meander bends with constant meander amplitude. By reducing the scale of inquiry to that of individual morphologic units, such as riffles and pools, one arrives at a physically based understanding of the optimality criterion. A feedback mechanism between the local, cross sectional shear stress distribution, the local transport capacity, and the channel planform is presented. It predicts evolution of an initially straight channel toward a more sinuous path that stabilizes once the local transport capacity becomes equalized throughout the system (i.e. steady state fluid and sediment flux conditions are reached), and the cut banks at the meander apices reach a critically stable state. The longitudinal scale for this feedback process is related to the diffusion of a sediment wave across the channel, which sets a minimum wavelength for the resultant alternate bars. The regime model is re-formulated to characterize the individual morphologic units produced by the feedback process using two bounding geometries; a trapezoid, representing the typical riffle section, and an asymmetric triangle, representing the bar-pool sections at the meander apices. These two geometries correspond to the maximum and the minimum local shear stress variance, respectively. These solutions predict the theoretical limits for the slope and cross sectional shape for a given sediment supply and discharge. Comparisons between these predicted limits and the experimental data confirm the general applicability of this approach, despite the simplified model specification. Ultimately, then, the form of the lateral adjustment can be understood as the product of a metastable dynamic, wherein individual cross sections are only conditionally stable. Trapezoidal solutions are susceptible to perturbations in their nearly uniform cross sectional shear stress distributions, which causes an evolution toward an asymmetric, triangular section that can transport the same sediment supply at a lower channel slope. The triangular sections are stable, only so long as sufficient centripetal acceleration occurs, generating a secondary circulation that permits an asymmetric cross section to persist. More generally, the cause of meandering in bedload streams is the result of the oscillation between two conditionally stable states, and thus reach-scale stability is produced by the continual transition from one conditionally stable state to the next. The fundamental instability of straight channels with uniform cross sectional distributions results in a trajectory toward increased channel sinuosity and decreased channel slope, which produces an increase in the system scale flow resistance via the reach-scale flow resistance component. The maximum flow resistance criterion (and, by extension, all equivalent optimality criteria) represents a formalism that permits a ID model to describe a 3D reality, by encapsulating this dynamic.

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