The new proposed “energy gradient theory,” which physically explains the phenomena of flow instability and turbulent transition in shear flows and has been shown to be valid for parallel flows, is extended to curved flows in this study. Then, three important theorems for fluid dynamics are deduced. These theorems are (1) Potential flow (inviscid and irrotational) is stable. (2) Inviscid rotational (vorticity is not zero) flow is unstable. (3) Velocity profile with an inflectional point is unstable when there is no work input or output to the system, for both inviscid and viscous flows. These theorems are, for the first time, deduced, and are of great significance for the understanding of generation of turbulence and the explanation of complex flows. From these results, it is concluded that the classical Rayleigh theorem (1880) on inflectional velocity instability of inviscid flows is incorrect which has last for more than a century. It is demonstrated that existence of inflection point on velocity profile is a sufficient condition, but not a necessary condition for flow instability, for both inviscid and viscous flows. The paradox of dual role of viscosity has been resolved: viscosity has only stable role. Why the paradox appeared is due to that the Rayleigh Theorem of inviscid flows by linear analysis is incorrect.
谢谢了
參考答案:新提出的"能源梯度理论"所阐述的身体和不稳定的现象流量流向湍流过渡剪 并已证明是有效的平行流动,延伸至弧形流向这项研究. 然后,三个重要定理流体动力学推演. 这些定理都是潜在流(1)(粘和旋)是稳定的. (2)粘转动(不是零涡)流不稳定. (3)流速剖面的屈折点不稳当没有输入或输出的工作体系, 对于粘和粘性流动. 这些定理,首次推导 而具有重要意义的认识和解释产生动荡复杂流动. 从这些结果, 它的结论是对古典瑞利定理(1880)屈折速度不稳已是不正确的粘流 历时一个多世纪. 它表明存在速度剖面拐点充分条件, 但不是必要条件流不稳定,都粘和粘性流动. 悖论已经解决双重角色粘度:粘度只有稳定的作用. 吊诡的是,为何出现瑞利定理,由于粘流线性分析是错误的.
