Mechanics of headcut migration in rills

The proposed conceptual model relates two-dimensional headcut migration to sediment detachment upstream and downstream from a headcut. If upstream erosion dominates, the headcut tends to obliterate itself as it migrates upstream, approaching the eroding channel's bed slope. If downstream erosion dominates, the headcut face erodes from below and a near vertical face migrates upstream with time.;A criterion to determine which migration mode occurs is formulated from dimensional analysis and by equating hydraulic and sediment detachment equations. Dimensional analysis results in a time scale ratio of upstream to downstream erosion related to the upstream and downstream sediment detachment, bed slope, Reynolds number and a dimensionless headcut drop height. A physically based analysis of hydraulics and sediment detachment yields a relationship between the dimensionless terms. The resulting equation for headcut stability is favorably compared with a total of eleven laboratory measurements of headcut migration on cohesive soil.;The maximum scour depth and total volume of eroded material produced by the impinging jet just downstream from a headcut are analyzed. Previously developed methods for ultimate scour depth prediction in sand are modified to include cohesive soil. This method equates the sediment detachment potential of the bed material to jet diffusion. The same approach determines the time rate of maximum scour depth. Dimensional analysis relates scour depth normalized to ultimate depth to Reynolds number, Froude number and a dimensionless time scaled to jet properties. The change in scour depth is analytically shown to proceed as two distinct rates. Initially scour rate is independent of time because the bed is within the jet potential core. At greater times jet diffusion decreases the rate of scour and this rate decreases with increasing time and scour depth. In the limit the predicted ultimate scour depth is approached. The dimensional and physically based analyses for scour depth compare favorably with experimental data including measurements of the ultimate and change in scour depth for ten runs on cohesive soil, 14 runs on two different sand sizes.