Velocity Gradient Statistics in Fully Developed Turbulence - Statistical Evolution Equations, DNS Investigations and Implications for Reduced Models

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The small scales of fully developed hydrodynamic turbulence can be comprehensively characterized in terms of the derivatives of the velocity field, which define the velocity gradient tensor. In this project, the statistical properties of these small-scale features are studied within the framework of exact statistical equations governing the evolution of the probability density functions of the velocity gradient tensor. Due to the nonlinear and nonlocal character of the equations of fluid motion, the resulting statistical equations appear unclosed when only a finite number of spatial points is considered. Within the project, the information missing due to this closure problem will be contributed by data from direct numerical simulations. In particular, the influence of the local self-amplification, dissipation and nonlocal pressure contributions will be studied. The goal is to gain a deeper understanding of the impact of these dynamical contributions on the observed small-scale statistics. Apart from characterizing the shape and evolution of the studied statistical quantities, the results will help to formulate improved closures for low-dimensional stochastic models. By this, a natural connection between fundamental turbulence research and applied modeling, e.g. in the field of wind energy conversion, is established.