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Basic definitions . Reynolds averaging

Statistical theory of the isotropic turbulence (K-41 theory) 1. Basic definitions of the statistical theory of turbulence Lecture 3. Basic definitions . Reynolds averaging. Basic definitions . Correlation function. Correlation function Correlation function in homogeneous turbulence

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Basic definitions . Reynolds averaging

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  1. Statistical theory of the isotropic turbulence (K-41 theory)1. Basic definitions of the statistical theory of turbulenceLecture 3 UNIVERSITY of ROSTOCK | CHAIR OF MODELLING AND SIMULATION

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

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

  4. Samples Resolution 300 µ 50 mm 2D Typical form oftheautocorrelationcoefficient. Scalarturbulence B A C A B C Physicalmeaningofsignchange PLIF Measurementsofthe LTT Rostock UNIVERSITY of ROSTOCK | CHAIR OF MODELLING AND SIMULATION

  5. Samples Resolution 300 µ 50 mm 2D Typicaldistributionofthe integral lengthalongthejetmixer. Scalarturbulence PLIF Measurementsofthe LTT Rostock UNIVERSITY of ROSTOCK | CHAIR OF MODELLING AND SIMULATION

  6. Typicalautocorrelationcoefficientalongthejet autocorrelationcoefficientofthe longitudinal velocity 1 alongupperborderofnozzleat x/D=0.5 2 alongthejetaxisat x/d=3.0 (fromGinevsky et al. (2004) Acoustic control of turbulent jets. Springer) UNIVERSITY of ROSTOCK | CHAIR OF MODELLING AND SIMULATION

  7. Isotropicturbulence UNIVERSITY of ROSTOCK | CHAIR OF MODELLING AND SIMULATION

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

  9. Correlationfunction in Fourrierspace Usuallyitispossibletomeasureonlythe „One dimensional spectralFunction“ UNIVERSITY of ROSTOCK | CHAIR OF MODELLING AND SIMULATION

  10. Proof UNIVERSITÄT ROSTOCK | LEHRSTUHL FÜR Modellierung und SIMULATION

  11. Spectraldensityofthekineticenergy E(k) dkisthecontributionofoscillationswiththewavenumbers k<k<k+dk tothekineticenergyofthe turbulent motion. E(k) isthedensityofthekineticenergydepending on wavenumbers. The dependence E(k) isreferredtoastheenergyspectrum UNIVERSITY of ROSTOCK | CHAIR OF MODELLING AND SIMULATION

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