旋转流中准圆柱近似与临界分类的关系

本文证明了在准圆柱近似下若已给定剖面上的轴向与切向速度分布,径向速度剖面必满足一个二阶常微分方程,它与临界分类的判别方程仅差一与粘性有关的非齐次项。本文还证明了临界状态对应于奇点,当流动从两侧趋近临界状态时,径向速度剖面分別趋向正负无穷,在临界状态两侧流动性态截然相反。此外还证明无粘性的准圆柱近似只能存在严格圆柱形的平凡解以及在亚临界范围内准圆柱近似计算中考虑非线性效应的迭代过程必然发散。

RELATION BETWEEN THE QUASI-CYLINDRICAL APPROXIMATION AND THE CRITICAL CLASSIFICATION FOR SWIRLING FLOW

It is analytically shown that solutions of the quasi-cylindrical approximation are qualitatively governed by the critical classification, the critical state corresponds to a singularity, as flows approach the critical state from both sides, the radial components of velocity go separately to positive and negative infinity, and that for inviscid quasi-cylindrical flow only the trivial solution, i.e. strictly columnar flow is possible. It is also shown that in subcri-tical range the iterative procedure accounting for non-linear effect diverges necessarily.