Statistics of Filtered Turbulence: Experiments and Simulations

S. Cerutti
PhD Thesis, The Johns Hopkins University
March 1999, Baltimore MD

ABSTRACT: Experiments and numerical simulations are performed in order to study the statistics of turbulence above and below a cutoff scale. Documentation and study of filtered and sub-grid scale (SGS) turbulence is important for improving turbulence models for Large Eddy Simulation (LES). A novel hot-wire probe array is built, enabling the measurement of very long data sets, which can be filtered in two dimensions. Unlike previous hot-wire measurements, which only allow stream-wise filtering, the array permits cross-stream filtering as well. Turbulence data is collected in the far wake of a circular cylinder and in grid turbulence. A low Reynolds number data base, which can be filtered in three dimensions, is obtained using Direct Numerical Simulation (DNS), and is used in conjunction with the high Reynolds number experimental data. Classical equilibrium considerations are applied to the transport equations of resolved kinetic energy and enstrophy, and motivate a mixed Smagorinsky/hyper-viscosity model. The required parameters are related to the skewness coefficient of the filtered velocity derivative, which is first estimated and then directly measured from the filtered data. Results are used to quantify the relative importance of hyper-viscosity. Fundamental differences between filtered and unfiltered velocity fields are examined through the scaling behavior of structure functions. It is shown that a recent technique for measuring inertial range scaling exponents (Extended Self-Similarity) cannot be applied to resolved structure functions. A comparative study of filtered and unfiltered pdfs of velocity increments shows that the tails of the distributions are affected by the filtering even at scales much larger than the filter scale. Using the DNS data, stare examined through the scaling behavior of structure functions. It is shown that a recent technique for measuring inertial range scaling exponents (Extended Self-Similarity) cannot be applied to resolved structure functions. A comparative study of filtered and unfiltered pdfs of velocity increments shows that the tails of the distributions are affected by the filtering even at scales much larger than the filter scale. Using the DNS data, statistical properties of the SGS dissipation are studied, with emphasis on its analogy with third-order structure functions, on scaling laws, and intermittency. Several LES models are then tested, and their performance rated according to their ability to reproduce the observed features of the SGS dissipation.

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