Span shoulder migration in three-dimensional current-induced scour beneath submerged pipelines

New experiments involving the three-dimensional current-induced live-bed scour beneath submerged horizontal pipelines are presented, spanning larger Shields parameter and cylinder-to-sediment diameter ratio than previous studies. Specific emphasis is on gaining a better understanding of, and ability to predict, the span migration velocity during the initial and subsequent development of such a scour hole. Consistent with previous experimental observations, both a primary (faster) and secondary (slower) span migration are observed. Process visualization of suspended sediment patterns are in line with prior speculation that this transition coincides with reduced local bed shear stress amplifications as the scour hole both deepens and widens. Dimensional analysis and physical insight are combined, leading to a new rational model for predicting the span migration velocity in both live-bed and clear-water regimes, with predictions naturally coinciding at the limit of far field incipient motion conditions. In both regimes the data cluster as predicted, and fitted closed-form expressions are provided for predicting the span migration velocity. The rational approach likewise includes a new and simple criterion for the transition from primary to secondary migration in the live-bed regime. In the clear-water regime the model incorporates primary dependence on the ratio of the Shields parameter to its critical value, resolving apparent contradictions with a previous study which suggests that the depth-based Froude number is the most important governing parameter. The developed rational model can be used to quantitatively predict all known major features of the span migration velocity in the early stages of the three-dimensional (live-bed and clear-water) scour beneath submerged horizontal cylinders induced by perpendicular flow, and can hence be regarded as the first complete model for this evolution.