Introduction to turbulence

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Turbulence

Nature of turbulence

Statistical analysis

Ensemble average Probability Multivariate random variables Estimation from a finite ... Generalization to the esti ...

Reynolds averaging

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Contents 1 Nature of turbulence 2 Elements of statistical analysis 3 Reynolds averaged equations and the turbulence closure problem 4 Turbulence kinetic energy 5 Stationarity and homogeneity 6 Homogeneous turbulence 7 Free turbulent shear flows 8 Wall bounded turbulent flows 9 Credits

Nature of turbulence

• The turbulent world around us
• What is turbulence?
• Why study turbulence?
• The cost of our ignorance
• What do we really know for sure?

Elements of statistical analysis

• Foreword

• The ensemble and ensemble average
  • The mean or ensemble average
  • Fluctuations about the mean
  • Higher moments
• Probability
  • The histogram and probability density function
  • The probability distribution
  • Gaussian (or normal) distributions
  • Skewness and kurtosis
• Multivariate random vaiables
  • Joint pdfs and joint moments
  • The bi-variate normal (or Gaussian) distribution
  • Statistical independence and lack of correlation
• Estimation from a Finite Number of Realizations
  • Estimators for averaged quantities
  • Bias and convergence of estimators
• Generalization to the estimator of any quantity

Reynolds averaged equations and the turbulence closure problem

• The equations governing the instantaneous fluid motions
• Equations for the average velocity
• The turbulence problem
• Origins of turbulence
• The importance of non-linearity
• The Turbulence Closure problem and the Eddy Viscosity
• The Reynolds Stress Equations

Turbulence kinetic energy

• The Fluctuating Kinetic Energy
• The Rate of Dissipation of the Turbulence Kinetic Energy

Stationarity and homogeneity

Homogeneous turbulence

Free turbulent shear flows

Wall bounded turbulent flows

Credits

This text was based on "Lectures in Turbulence for the 21st Century" by Professor William K. George, Professor of Turbulence, Chalmers University of Technology, Gothenburg, Sweden.