Experimental study of free-surface flow instability and bedforms in shallow flows

To test erosion and development of bed sculpture in unstable, pulsating shallow flow, three series of experiments were performed in a 10-m flume with flows of Reynolds Number (Re) up to 10³, Froude Number (Fr) up to 3.0, and slope up to 2%. In the first series of experiments (59 runs), the bed was rigid (glass flume-bottom), in the second (50 runs) and third (10 runs) series, planar beds were made from well-sorted and poorly sorted sand, respectively. Development of flow surface instability above the rigid bed showed the following stages: smooth surface; small wavelets; well-developed waves; and rough flow. Development of bedform morphology in the second series of tests showed the following sequence: smooth bed; flow-aligned ridge and trough pattern; combined ridge and rhomboid pattern; and rhomboid configuration. In presence of flow instability, ridge patterns form in flows with mean values indicative of laminar-subcritical regime, combined ridge and rhomboid patterns in laminar-supercritical regime, and rhomboid patterns in flows with mean values indicative of transitional turbulent-supercritical regime. The third series of experiments demonstrated transverse segregation of the bed material across the ridges.The results, in line with stability theory, show that laminar and transitional flows already become unstable when $\text{Fr}\text{=}\text{1}\text{2}$ and suggest that pulsations may appear in sheet-floods and overland flow, intensifying erosion and transport of sediment. The precise mechanism of origin of the parent kinematic flow configurations instrumental in generation of the ridge and the rhomboid patterns is not yet clear. It may be related to the mechanism operating in transition and generation of turbulence in parallel flows, or flows with a superimposed fluctuation, but other types of hydrodynamic instability are also possible.