Convergent hydraulics at horseshoe steps in bedrock rivers

Horseshoe waterfalls are a common feature of steep bedrock rivers. As a first step toward understanding their geomorphology, a detailed study of the fluid mechanics at a 0.91-m vertical-drop, horseshoe waterfall was performed in a 2.75-m wide flume. Five non-dimensional upstream energy levels, each with 3-5 non-dimensional downstream tailwater depths (21 runs total), were assessed for water surface topography via digital elevation modeling, flow dynamics via digital videography, and overall energy dissipation via an energy and momentum conservation model. Regardless of tail depth, the horseshoe waterfall was found to have three distinct zones beyond the step brink-1) a nappe whose degree of convergence depends on upstream energy and brink configuration, 2) a convergence zone whose features vary strongly with upstream energy, brink configuration, and tail depth, and 3) a downstream tailwater region whose dynamics primarily depend on tail depth. The centerline nappe profile and brink velocity were reasonably predicted using Rouse's jet trajectory equations when (H + P)/H > 2. Peripheral profiles were not predictable using existing equations. For any arbitrary broad-crested step brink configuration, maximum energy dissipation was found to occur when no jump was present and downstream tail depth was exactly critical. Rather than providing maximal energy dissipation, hydraulic jumps below steps provide efficient conversion of kinetic energy to potential energy.