| 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. (Abstract shortened by UMI.)... |
