Analysis of Universal Structure and Development of Statistical Theory of Inhomogeneous Anisotropic Turbulence

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The aim of this study is to understand the universal structure of turbulence, which is indispensable for developing statistical theory of inhomogeneous anisotropic turbulence. On the basis of the method of statistical theory of turbulence and large scale Direct Numerical Simulation(DNS), the study has clarified the followings :(A)DNS of Turbulence and Data-Analysis :By analyzing the data of the world largest DNS of turbulence with the number of grid points up to 4096^3, more than 10^11 degrees of freedom and 10^22 nonlinear interactions, we clarified some of (i)Reynolds(Re)-dependence of various statistics, and (ii)asymptotic universality in the high Re-limit. We also performed quantitative examination of (iii)Kolmogorov's similarity hypotheses, and (iv)the eddy-viscosity hypothesis in Large Eddy Simulation, at high Re.(B)Universal Structure and Modeling of Anisotropic Turbulence :We derived an expression for the anisotropic spectrum at small scales of homogeneous turbulent shear flow on the basis of the analysis of a Lagrangian spectral closure equation. We also derived a general expression for the anisotropic spectrum in stratified turbulence, confirmed its form by DNS, and showed the validity of an idea similar to that of the linear responses theory for non-equilibrium system.(C)DNS of Wall Bounded Turbulence and Data-Analysis :Plane Poiseuille turbulence is one of the most basic turbulences among boundary layer turbulences or turbulences with solid wall. In order to perform the DNS, we made codes based on the Chebyshev-tau method and a Combined Compact Scheme, respectively, and validated their performance. By the DNS, we clarified the dependence on the wall normal distance and Re of eddy-scale distribution, by analyzing the wall-normal velocity correlation spectrum.