Formation and Development of Large-Scale Vortex Structures in Turbulent Flows

作为“湍流剪切流的大尺度涡结构”(Tatsum I)的典型例子，研究了矩形管道流动中的三维旋涡结构。首先，矩形管道中定常层流流动对外部扰动进入勒让德多项式的稳定性。结果表明，层流流动对四种可能的扰动模式中的两种是不稳定的，对其余两种模式是稳定的。对于最不稳定的模式，当纵横比A大于临界值Ac=3.2时，流动是不稳定的，而当A低于Ac时，流动是稳定的。对于A的超临界值，流动的临界雷诺数Re随A的增大而单调减小：A=3.5时，Rc=36600，4时为18400，5时为10400，6时为8200，8时为6800，在无限大A的极限下，Rc趋于平面Poiseuille流的已知值5772。当A小于5时，流动是稳定的。这是关于速度分布具有二维变化的层流稳定性的首次结果。目前正在进行流动对有限量级扰动的非线性稳定性。初步结果给出了与实验观测到的旋涡结构的“二次流”定性相似的流型。为了研究旋涡结构，对自然界中的各种旋涡运动进行了遥感研究。

Three-dimensional vortex structure in a rectangular duct flow has been investigated as a typyeal case of the "Large-scale vortex structures of turbulent shear flows" (Tatsumi).First, the stability of the steady laminar flow in a rectangular duct against external disturbance into the Legendre polynomials. It is found that the laminar flow is unstable against two of the four possible modes of the disturbance and stable against the remaining two modes. Against the most unstable mode, the flow is unstable for the aspect ratio A larger than a critical value Ac = 3.2 and stable for A below Ac. For the super-critical- values of A, the critical Reynolds number Re of the flow decreases monotonically with increasing A: Rc = 36600 for A = 3.5, 18400 for 4, 10400 for 5, 8200 for 6, 6800 for 8, and Rc tends to the known value 5772 for the plane Poiseuille flow in the limit of infinite A.The flow is less unstable against another unstable mode: Rc = 31500 for A = 6, 11000 for 8, and the flow is stable for A below 5. These are the first results concerning the stability characteristics of the laminar flows whose velocity distributions have two- dimensional variation.The nonlinear stability of the flow against disturbances of finite magnitude is now being carried on. Preliminary results give qualitatively similar flow patterns to those of the experimentally observed 'secondary flow' of the vortex structure of the turbulent flow.Remote sensing of various vortex motions in nature is studied in order to investigate the vortex structures.