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L ehrstuhl für Modellierung und Simulation Statistical theory of the isotropic turbulence (K-41 theory) 1. Basic definitions of the statistical theory of turbulence Lecture 3 UNIVERSITY of ROSTOCK | CHAIR OF MODELLING AND SIMULATION

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Basic definitions. Reynolds averaging 2 UNIVERSITY of ROSTOCK | CHAIR OF MODELLING AND SIMULATION

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3 Basic definitions. Correlation function Correlation function Correlation function in homogeneous turbulence Autocorrelation function Integral length Autocorrelation temporal function Integral time UNIVERSITY of ROSTOCK | CHAIR OF MODELLING AND SIMULATION

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Samples 4 50 mm Resolution 300 µ 2D A B C A B C Typical form of the autocorrelation coefficient. Scalar turbulence PLIF Measurements of the LTT Rostock Physical meaning of sign change UNIVERSITY of ROSTOCK | CHAIR OF MODELLING AND SIMULATION

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Samples 5 50 mm Resolution 300 µ 2D Typical distribution of the integral length along the jet mixer. Scalar turbulence PLIF Measurements of the LTT Rostock UNIVERSITY of ROSTOCK | CHAIR OF MODELLING AND SIMULATION

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Typical autocorrelation coefficient along the jet 6 (from Ginevsky et al. (2004) Acoustic control of turbulent jets. Springer) UNIVERSITY of ROSTOCK | CHAIR OF MODELLING AND SIMULATION 1 along upper border of nozzle at x/D=0.5 2 along the jet axis at x/d=3.0 autocorrelation coefficient of the longitudinal velocity

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Isotropic turbulence 7 UNIVERSITY of ROSTOCK | CHAIR OF MODELLING AND SIMULATION

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8 Taylor longitudinal length Taylor transverse length Taylor Reynolds number Isotropic turbulence UNIVERSITY of ROSTOCK | CHAIR OF MODELLING AND SIMULATION

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Correlation function in Fourrier space 9 Usually it is possible to measure only the One dimensional spectral Function UNIVERSITY of ROSTOCK | CHAIR OF MODELLING AND SIMULATION

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Proof 10UNIVERSITÄT ROSTOCK | LEHRSTUHL FÜR Modellierung und SIMULATION

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Spectral density of the kinetic energy 11 E(k) dk is the contribution of oscillations with the wave numbers k

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