Flow dynamics and self-similar morphology of sand beds scoured by short-duration inclined submerged jets

The interaction between a submerged turbulent jet and an erodible granular bed is central to many geophysical and engineering flows. While long-duration jet scour has been extensively studied, the transient dynamics under short-duration oblique impingement remain poorly understood. Here, we use numerical simulations to investigate the scour mechanisms of a short-duration inclined submerged jet impinging on a uniform sand bed. We systematically examine the effects of the Froude number Fr, jet angle θ, and dimensionless nozzle height h on the evolving flow field and scour morphology. The results reveal that the late-stage flow structure is highly sensitive to these parameters: increasing Fr or θ intensifies local erosion, while a larger h weakens the impingement and reduces scour depth. A key finding is that the longitudinal scour-hole profiles, when normalized by the maximum depth and total length, collapse onto a single, non-symmetric master curve across all operating conditions—demonstrating strong spatial self-similarity. The horizontal expansion rate of the scour hole exceeds the vertical incision rate by nearly an order of magnitude in the early stage. The temporal evolution of both depth and length follows a self-similar exponential growth law. Based on the observed self-similarity and growth characteristics, we develop empirical scaling relationships that describe the final-time scour geometry in terms of Fr, θ, and h, thereby quantifying the self-similar nature of the process. These observations deepen the understanding of the mechanisms behind short-duration jet scour.