Investigations Of Turbulent Spots And Coherent Structure In The Wall Region Of A Shear Flow

The numerical methods with high accuracy and resolution are proposed to research the generation and evolutional process of the turbulent spots and coherent structures in turbulent flow of the wall region. The fourth-order time splitting methods are developed for the temporal discretization of Navier-Stokes equations and perturbation equations. Three-dimensional coupling difference methods are presented in the spatial discretization for the Poisson equation of the pressure and Helmholtz equations of the velocity, and fourth-order compact central difference schemes are derived. The fourth-order explicit upwind-biased compact difference schemes are used in the spatial discretization of the nonlinear convection terms. These difference schemes can be used in all computational region including the boundary neighborhood, and can overcome the difficulty not adapting simultaneously in the boundary neighborhood for general three-dimensional fourth-order central difference schemes, and improve computational stability and resolution. The compact difference equations with high accuracy and resolution for solving the incompressible N-S equations and perturbation equations are composed of these compact difference schemes, and provides an effective numerical method for the investigations of the turbulent spots and coherent structures.The numerical models with the wall impulse as initial perturbation of turbulent spots were proposed. The above compact difference systems are used in the several typical flows, such as .the channel, open-channel and boundary layer flows The various complicated boundary conditions satisfying N-S equations are carefully conducted. The above spatial and temporal discretization in the boundary, and two-directional average in the intersection, can satisfy completely N-S equations, and have high accuracy in the all computational regions. The direct numerical simulation methods for turbulent spots in the channel, open-channel and boundary layer flows are built respectively. Effective algorithms composed of time-advancing, over-relax iteration and multiple grid methods are planned to raise computational efficiency. The evolutional process of the wall impulses in different Reynolds number, grid schemes, and various flows are studied, and the generative and development mechanisms of the turbulent spots in the wall region of a shear flow are analyzed. The results show generation and development of the turbulent spots are closelyrelative to the Reynolds number, initial disturbance and shear rate of the velocity, and are consistent with experiment results.The resonant three-wave model and laminar-turbulent velocity profile composed are used as a model of coherent structures in .turbulent flow. The forming and variation of turbulent coherent structures in the channel are simulated by the compact differential method with high accuracy and resolution derived in this paper. Results of studying several non-coplanar coherent structures of .turbulent flow show the variable process of each turbulent coherent structures with different initial locations and interactive law, and are relative closely with their locations.The turbulent spots and coherent structures of .turbulent flow researched in the paper are an important discovery for the turbulent flow and transition, and the front problem in this field, and have important theoretic meaning and practical prospect.