Minimum stream power and river channel patterns

Abstract

Channel patterns of sand-bed rivers have been analyzed using the concept of minimum stream power together with formulas for flow resistance and sediment transport. A diagram has been constructed, on the plane of water discharge vs. valley slope, dividing regime rivers into straight, meandering, and braided patterns in plan configuration. The analytical diagram is supported by river data and previous observations. For the given water discharge Q and sediment load Q s, the stable channel geometry and slope were obtained from the stream power analysis, wherein a stable configuration is assumed to correspond to a minimum stream power per unit channel length. For small values of Q and Q s, the analysis shows that a unique minimum exists, indicating a unique stable channel configuration and slope. With this unique stable channel slope equal to the valley slope, the channel pattern is straight. Above a certain threshold valley slope, the stream power actually has two minimums, indicating two possible stable channel configurations and slopes. Whenever multiple channel slopes exist on a uniform valley slope, the river must be sinuous. The reason for meandering development is attributed to minimum stream power per unit channel length for the river system, because with its multiple configurations and slopes, a meandering river may minimize its stream power expenditure as well as its sediment load for the river system subject to physical constraints. Analytical relations also predict that highly sinuous rivers which are small in width/depth ratio occur on flatter valley slopes and that they become more braided and less sinuous as the valley slope increases.