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

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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.