Numerical Simulations Of Meanders Migrating Laterally As They Incise Into Bedrock

The problem of meandering in mixed bedrock-alluvial rivers is more challenging than that of purely alluvial streams, in that alluvial, bed incisional and bank incisional morphodynamics must be accounted for. Here we present a numerical formulation that addresses heretofore unanswered questions. Bed incision is based on abrasion due to saltating grains. The model satisfies mass conservation of alluvium over a partially covered bedrock surface. Bank incision is treated in terms of a measure of the incipient collision of bedload particles with the bank. It is assumed that land accretes along the inside of point bars when the water depth falls below a specified shallow value. All but one of the runs are performed with repetitive two-step hydrographs. Runs starting from a low-amplitude sine-generated curve indicate that sinuosities at least as high as 2.5 can be achieved. The rate of increase of sinuosity declines in time, but does not vanish. For the same hydrograph, increasing the initial thickness of alluvium on the bed causes the rate of vertical bedrock incision to decline, and bend sinuosity to increase at a faster rate. At a sufficiently high thickness, the channel migrates laterally without bed lowering. Bend shape can change dramatically with increasing alluvial thickness, with high thickness favoring more regular bend trains. For the same initial alluvial thickness, increasing the peak flow of the hydrograph causes the vertical incision rate and the rate of sinuosity growth to increase. The model thus captures a wide range of behavior associated with bedrock meandering.