Toward a theory of hydraulic geometry: the principle of flow resistance for the fluvial system

One of the primary obstacles to the development of a theoretically based expression of channel scaling, or hydraulic geometry, is the identification of an appropriate formalism to adapt one-dimensional models to the description of a three-dimensional phenomenon. Within the context of the fluvial system, the most nearly stable, hence most likely channel configuration is related to the principle of flow resistance maximization. The flow resistance for the system comprises three components: grain-scale flow resistance, bedform-scale form resistance, and lastly the reach-scale form resistance, which is the primary difference between system-scale flow resistance and the more usual representations. Stream table 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.