Circular Hydraulic Jumps Triggered by Boundary Layer Separation

Abstract

When a high-flow-rate circular jet impinges vertically on a horizontal plane, it flows out radially and then undergoes a distinctive hydraulic jump on the plane because of boundary layer separation induced by hydrostatic back pressure. The jump radius is shown to be 0.37 a Re1/3 Λ−1/8, where Λ=(ga3/ν2) Re−7/3 is a modified Froude number, Re=(Q/aν) is the jet Reynolds number, a is the jet radius, and Q the liquid flow rate, which is favorably compared to experimental data in the limit of small Λ. When Λ exceeds 3.0×10−4 at low flow rates, the jump radius decreases below a minimum in the film depth and our experiments detect a different jump mechanism that may be triggered by capillary pressure rather than hydrostatic pressure.