论文标题
层流通道流中的连续液压跳跃
Continuous hydraulic jumps in laminar channel flow
论文作者
论文摘要
根据粘性的圣式方程，在层流河道流中的液压跳跃是连续的冲击结构。得益于粘度的包含，跳跃并没有突然，通过Rankine-Hugoniot冲击关系使经典的拼布不必要。跳跃是作为管理方程式的稳定固定解决方案而出现的，并非常适合动态系统分析，表现为相位空间中的近核酸轨迹。基于此，我们得出了跳跃长度作为弗洛德和雷诺数的函数的分析表达式，这反映了重力和粘度都有助于塑造跳跃力的力平衡的事实。该论文以数值实验结束，证实了跳跃的稳定性。
On the basis of the viscous Saint-Venant equations, hydraulic jumps in laminar open channel flow are obtained as continuous shock structures. Thanks to the inclusion of viscosity, the jumps are not abrupt, rendering the classic patchwork via the Rankine-Hugoniot shock relations unnecessary. The jumps arise as stable stationary solutions of the governing equations and lend themselves excellently to a Dynamical Systems analysis, manifesting themselves as near-parabolic trajectories in phase space. Based on this, we derive an analytic expression for the jump length as a function of the Froude and Reynolds numbers, reflecting the fact that both gravity and viscosity contribute to the balance of forces that shape the jump. The paper concludes with a numerical experiment confirming the stability of the jumps.
