Author(s): Zhang Li; Xudong Fu; Colin P. Stark; Roberto Fernandez Arrieta; Gary Parker
Keywords: Bedrock Rivers; Alluvial Waves; Bedrock Incision; Alluvial Cover
Abstract: We consider incising mixed bedrock-alluvial rivers in uplifting mountain regions. We study both the equilibrium state of the river profile, at which uplift and incision are in balance, and the evolution toward this state. The innovative feature of this research is the treatment of the effect of waves of alluvial sediment. To do this, we adapt the Sklar-Dietrich model of bedrock incision, according to which stones act as tools to abrade the bed. The Sklar-Dietrich model relates the fraction areal cover pc of the bedrock by alluvium to the ratio of sediment supply to the capacity sediment transport rate. It yields low incision at both low (pc ~ 0) and high (pc ~ 1) values of fraction areal cover, in the former case due to lack of tools, and in the latter case due to lack of exposed bedrock to abrade. The incision rate is optimized at an intermediate value of pc ~ 0. 5. The Sklar-Dietrich model cannot, however, handle the case of intermittent sediment supply, i. e. temporal cycling between high and low sediment input. Here we develop an extension of the formulation to treat cycled sediment supply, by specifically tracking waves of alluviation and cover rarification. During this cycling, the high-sediment supply crest of an alluvial wave may completely alluviate the bed, preventing incision, and the low-sediment supply trough of the wave may also cause little incision due to low pc. Incision is thus limited to the front and tail ends of the wave, where pc passes through values intermediate between 0 aand 1. We consider a periodic two-step “sedimentograph,” with a short period of high sediment supply and a long period of low supply. The supply rate averaged over the sedimentograph is equal to a reference value corresponding to constant sediment supply. We further vary the ratio rqh of the high feed rate to the reference feed rate between 1 (constant sediment supply) and 4, at which sediment feed vanishes during the period of low supply. For rqh ≤ 3, the final equilibrium bedrock slope does not differ strongly from the case rqh = 1 corresponding to constant feed rate. Increasing alternation between complete alluviation and rarification of sediment cover as rqh increases, however, reduces the efficiency of incision, so that the time to equilibrium increases dramatically as rqh increases. Around rqh = 3. 5, however, a sharp phase transition occurs, beyond which equilibrium bed slope increases by a factor of 2. 5, and the bed no longer undergoes periodic alluviation. This higher bed slope is close to the value attained when the feed rate corresponding to rqh = 4 is held constant throughout. Thus two phases are seen for the case of cyclically varying sediment input. In the mean-feed dominated phase, the bed equilibrates to a state not too different from that for constant feed rate equal to the mean value of the sedimentograph. In the peak-feed dominated phase, the bed equilibrates to a state near that which would prevail when the feed rate is held constant at peak feed value.