Modeling the effects of bed topography on fluvial bedrock erosion by saltating bed load

摘要

Abrasion by saltation is an important mechanism of fluvial incision into bedrock. Sklar and Dietrich (2004) introduced an abrasion model in which the erosion rate of an "approximately planar" bed is linearly dependent on the kinetic energy transferred by the vertical velocity of saltating grains. However, most bedrock-floored channels exhibit topographic variations that yield deviations from a planar surface, referred to as "bed topography." Observations show that bed topography affects erosion. Here the saltation-abrasion model is extended for a nonplanar bed. A several-centimeter high bump, transverse to the flow, is repeated every 50 cm. The kinetic energy of grain impacts is calculated in two ways: (1) impact velocity normal to bed topography and (2) vertical impact velocity. By comparing the latter case with the planar model, it is possible to isolate the effects of topography on the interception of saltation trajectories. Incorporating bed topography changes erosion in three ways. First, erosion is 10 to 1000 times faster, depending upon transport stage and grain size. Enhanced erosion results from both the interception of grains by topography and the increased kinetic energy transfer associated with high-angle impacts on the stoss side of bumps. Second, erosion increases monotonically with transport stage, whereas maximum erosion occurs at low to intermediate transport stage with a planar bed. Third, erosion decreases monotonically with grain size, whereas maximum erosion occurs with intermediate-sized grains with a planar bed. Although the model is highly simplified, results show that bed topography should be considered when simulating erosion of bedrock.