The Effect of Bed Roughness on Depth- Discharge Relations in Alluvial Channels

Alluvial channel stage-discharge and depth-discharge relations were studied in a large sand-bed recirculating flume. From this study, it was found that the form of these relations are intimately related to: 1. Regime of flow 2. Form of bed roughness a. Characteristics of the bed material b. Concentration of fine sediment c. Temperature 3. Rate of change of discharge with time In the range of shear where ripples and dunes develop on the bed, the stagedischarge curve for a rising stage is usually quite different from that for a falling stage. These curves are valid only for the conditions upon which they are based; no general solution is possible. In the range of shear which develops plane bed, standing sand and standing water waves that are in phase, and antidunes the risingand falling-stage curves coincide and hold for all values of discharge associated with these forms of bed roughness. When a shear stress in a channel forms dunes at small discharges and plane bed and perhaps standing waves and antidunes at larger discharges, there is a discontinuity in the stage-discharge or depth-discharge curves, particularly on the rising stage that occurs when the dunes wash out This is caused by the great reduction in resistance to flow which occurs when the bed form changes from ripples or dunes to plane bad, standing waves, or antidunes and the resultant reduction in depth, even though discharge is increasing. FORMS OF BED ROUGHNESS IN ALLUVIAL CHANNELS In a rigid channel a well-defined depth-discharge or stage-discharge curve can be developed that shows only minor scatter and generally no discontinuities. When plotting stage-discharge curves for alluvial streams, this ideal condition is not usual even when scour or fill do not occur. Because of the extreme variation in the resistance to flow as discharge and form of bed roughness vary and because of the effect of rate of change of discharge with time on the rate of development of the various forms of bed roughness, the stage-discharge relation for alluvial channels is not well defined. In fact, several different curves are possible at a single station unless the shear stress on the bed is always large enough that ripple and dunes do not form. If the possible changes in the form