The Advective-Diffusive Morphodynamics of Mixed Bedrock-Alluvial Rivers Subjected to Spatiotemporally Varying Sediment Supply

Mountain rivers subject to earthquakes and intense precipitation have highly variable sediment supply rates. Here we consider the morphodynamics of 1-D mixed bedrock-alluvial rivers with temporally varying sediment supply rates. We use a periodic sedimentograph, characterized by short periods of high sediment feed rate and longer periods of low sediment feed rate. We study the problem with a corrected Macroroughness Saltation-Abrasion-Alluviation model. In this model, incision is driven by bedload colliding with bedrock, but incision can be turned off by either zero sediment transport or complete alluviation. The formulation is advective-diffusive, the former capturing upstream-migrating knickpoints and the latter capturing smearing of the sedimentograph downstream. The steady state balance between incision and uplift is characterized by a bedrock slope that varies downstream, exhibiting low values at the upstream end of the domain and higher values farther downstream. Sufficiently far downstream, the bedrock slope approaches that predicted for constant feed rates. The zone of low slope near the feed point corresponds to a pocket (zone of locally depressed bedrock slope) in the longitudinal profile, which is repeatedly drowned in and flushed of sediment. The steady state slope profile of a shorter reach is a truncated version of that of a longer reach. A limiting reach length including the pocket defines a sedimentograph boundary layer, where the effects of sediment feed fluctuation are felt.