关于单向流纳维-斯托克斯方程的精确解
On Exact Solutions of the Navier-Stokes Equations for Uni-directional Flows
摘要：
本文证明了矩形通道和圆管中的单向流动是纳维-斯托克斯方程在短时间内的精确时空解。我们断言，经典的平面Poiquille-Couette流和Hagen-Poiquilille流的精确解的时间无关的近似，如果指定一个适当的初始速度分布在起始位置。从概念上讲，不存在从未指定的初始数据开始的绝对稳定的流量。Poiffille的经典实验测量可以用进化解来解释。特别地，管流不具有与时间无关的特征速度。传统的观点认为抛物线型线存在于任意雷诺数下是没有根据的。
英文摘要：
In the present note, we show that the uni-directional flows in a rectangular channel and in a circular pipe are exact spatio-temporal solutions of the Navier-Stokes equations over a short time interval. We assert that the classical plane Poiseuille-Couette flow and Hagen-Poiseuille flow are time-independent approximations of the exact solutions if an appropriate initial velocity distribution at starting location is specified. Conceptually, there do not exist absolute steady flows starting from unspecified initial data. The classic experimental measurements by Poiseuille can be explained in terms of the evolutional solutions. In particular, the pipe flow does not have a time-independent characteristic velocity. The orthodox notion that the parabolic profile exists for arbitrary Reynolds numbers is unwarranted.
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