Scales of boundary resistance in coarse-grained channels: turbulent velocity profiles and implications

Abstract

Gravel-bed surfaces are characterized by morphological features occurring at different roughness scales. The total shear stress generated by the flow above such surfaces is balanced by the sum of friction drag (grain stress) and form drag components (created by bed forms). To facilitate a better understanding of total resistance and bed load transport processes, there is a need to mathematically separate shear stress into its component parts. One way to do so is to examine the properties of vertical velocity profiles above such surfaces. These profiles are characterized by an inner layer that reflects grain resistance and an outer layer that reflects total resistance. A flume-based project was conducted to address these concerns through systematically comparing different roughness scales to ascertain how increased roughness affects the properties of vertical velocity profiles. Great care was taken to create natural roughness features and to obtain flow data at a high spatial and temporal resolution using an Acoustic Doppler Velocimeter. Average vertical velocity profiles above each roughness scale were clearly segmented. The vertical extent of the inner flow region was directly related to the scale of roughness present on the bed (and independent of flow depth), increasing with increased roughness. On a rough but rather uniform “plane” bed made of heterogeneous coarse sediments (with no bed forms), the shape of the velocity profile was clearly dominated by the local variations in grain characteristics. When pebble clusters were superimposed, the average shear stress in the outer flow region increased by 100% from the plane bed conditions. The ratio of inner grain shear stress to outer total shear stress for this pebble cluster experiment was 0.18 under shallow flow conditions and 0.3 under deep flow conditions. The grain stress component that should be used in bed load transport equations therefore appears to vary in these experiments between 15% and 30% of the total channel stress, increasing with decreased resistance. Roughness height ( K s/ D 50) values at the grain scale for the plane bed and pebble cluster experiments were 0.73 and 0.63, respectively. These are values that should be used in flow resistance equations to predict grain resistance and grain stress for bed load transport modeling.