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, $P$ the perimeter, and $H$ 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 weir radius to nozzle radius $r_n$ is large $r_w/r_n\ge 28$. 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, collapses 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.

中文翻译：

---

多边形水力跃迁的几何形状和滞后作用

撞击的液体射流撞击目标板，形成液压跳跃，在一定条件下可显示稳定的多边形几何形状。进行实验以确定堰的几何形状和流动历史对模式选择和这些多边形跳跃的几何形状的影响。模态转换在高档和低级流量扫描中以不同的流量发生，从而导致磁滞现象和给定流量下多种模式的共存，这说明了流量历史的重要性。特性比$\mathrm{一种}/PH$ 或规范化的跳跃几何，其中 $\mathrm{一种}$ 是跳跃的上游区域， $P$ 周边，以及 $H$ 下游高度不受流动历史或实验方案的影响，但对堰高有轻微的依赖性 $H_w$ 和堰半径 ${\mathrm{[R}}_w$ 提供堰半径与喷嘴半径之比 ${\mathrm{[R}}_{ñ}$ 大 ${\mathrm{[R}}_w/{\mathrm{[R}}_{ñ}\ge 28$。几何形状的崩溃表明表面张力在多边形跳跃的形成中起着至关重要的作用。在绘制比例尺周长时，我们的所有数据（约1800个观测值）都会崩溃$P/H$ 下游的韦伯数 $\mathrm{w\; ^}Ë$ 我们显示出临界波长近似恒定 $\lambda /H$ 对于任何给定的实验，表明模式选择机制与高原-瑞利破裂有关。