Optimal dynamical systems of Navier-Stokes equations based on generalized helical-wave bases and the fundamental elements of turbulence  

作　　者：NaiFu Peng Hui Guan ChuiJie Wu 

机构地区：[1]State Key Laboratory of Structural Analysis for Industrial Equipment, School of Aeronautics and Astronautics,Dalian University of Technology [2]State Key Laboratory for Turbulence and Complex Systems, Center for Applied Physics and Technology,College of Engineering, Peking University [3]College of Meteorology and Oceanography, PLA University of Science and Technology

出　　处：《Science China(Physics,Mechanics & Astronomy)》2016年第11期61-69,共9页中国科学：物理学、力学、天文学（英文版）

基　　金：supported by the National Natural Science Foundation of China (Grant Nos. 11372068 and 11572350);the National Basic Research Program of China (Grant No. 2014CB744104)

摘　　要：In this paper, we present the theory of constructing optimal generalized helical-wave coupling dynamical systems. Applying the helical-wave decomposition method to Navier-Stokes equations, we derive a pair of coupling dynamical systems based on optimal generalized helical-wave bases. Then with the method of multi-scale global optimization based on coarse graining analysis, a set of global optimal generalized helical-wave bases is obtained. Optimal generalized helical-wave bases retain the good properties of classical helical-wave bases. Moreover, they are optimal for the dynamical systems of Navier-Stokes equations, and suitable for complex physical and geometric boundary conditions. Then we find that the optimal generalized helical-wave vortexes fitted by a finite number of optimal generalized helical-wave bases can be used as the fundamental elements of turbulence, and have important significance for studying physical properties of complex flows and turbulent vortex structures in a deeper level.In this paper, we present the theory of constructing optimal generalized helical-wave coupling dynamical systems. Applying the helical-wave decomposition method to Navier-Stokes equations, we derive a pair of coupling dynamical systems based on optimal generalized helical-wave bases. Then with the method of multi-scale global optimization based on coarse graining analysis, a set of global optimal generalized helical-wave bases is obtained. Optimal generalized helical-wave bases retain the good properties of classical helical-wave bases. Moreover, they are optimal for the dynamical systems of Navier-Stokes equations, and suitable for complex physical and geometric boundary conditions. Then we find that the optimal generalized helical-wave vortexes fitted by a finite number of optimal generalized helical-wave bases can be used as the fundamental elements of turbulence, and have important significance for studying physical properties of complex flows and turbulent vortex structures in a deeper level.

关 键 词：optimal dynamical systems helical-wave decomposition fundamental elements of turbulence vortex structures 

分 类 号：O357.5[理学—流体力学] O19[理学—力学]