Geometry of polygonal hydraulic jumps and the role of hysteresis

An impinging liquid jet impacts a target plate, forming a hydraulic jump that can exhibit a steady polygonal geometry under a range of conditions. Experiments are conducted to determine the effect of weir geometry and flow history on mode selection and the geometry of these polygonal jumps. Modal transitions occur at different flow rates in upscale and downscale flow sweeps, leading to hysteresis and the coexistence of multiple modes at a given flow rate, illustrating the importance of flow history. The characteristic ratio A/PH or normalized jump geometry, where A is the upstream area of the jump, P is the perimeter, and H is the downstream height, is unaffected by the flow history or experimental protocol but has a slight dependence on the weir height h(w) and weir radius r(w) provided the ratio of the weir radius to nozzle radius r(n) is large, r(w)/r(n) >= 28. The collapse of the geometry suggests surface tension plays a critical role in the formation of polygonal jumps. All of our data, approximately 1800 observations, collapse upon plotting the scaled perimeter P/H with the downstream Weber number We, and we show the critical wavelength is approximately constant lambda/H for any given experiment, suggesting the mode selection mechanism is related to Plateau-Rayleigh breakup.