Introduction to turbulence

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Contents 1 What is turbulence? 2 The 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 Headline text 9 Credits

What is turbulence?

• Why study turbulence?
• The cost of our ignorance
• What do we really know for sure?

The 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
• The 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

Headline text

Media:Example.oggInsert non-formatted text here--Zemmour,zs 08:41, 4 February 2007 (MST)Italic textBold text'Bold text'Insert non-formatted text here== Wall bounded turbulent flows ==

Credits

This text was based on "Introduction to Turbulence" by Professor William K.George, Chalmers University of Technology, Sweden.

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