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Statistical Theory of Isotropic Turbulence (K-41 Theory): Basic Concepts and Correlation Functions

Explore basic definitions and correlation functions in isotropic turbulence, including Reynolds averaging and integral length. Learn about autocorrelation functions, scalar turbulence, and spectral density of kinetic energy.

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Statistical Theory of Isotropic Turbulence (K-41 Theory): Basic Concepts and Correlation Functions

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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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