Introduction to turbulence

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Introduction to turbulence

Nature of turbulence

Statistical analysis

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

Reynolds averaged equation

Turbulence kinetic energy

Stationarity and homogeneity

Homogeneous turbulence

Free turbulent shear flows

Wall bounded turbulent flows

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This section is currently undergoing heavy reorganization and editing. Please excuse any errors or unfinished parts. --Jola 07:01, 21 June 2007 (MDT)

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?

Statistical analysis

• Ensemble average
  • Mean or ensemble average
  • Fluctuations about the mean
  • Higher moments
• Probability
  • Histogram and probability density function
  • Probability distribution
  • Gaussian (or normal) distributions
  • Skewness and kurtosis
• Multivariate random variables
  • 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

• Equations governing instantaneous fluid motion
• Equations for the average velocity
• The turbulence problem
• Origins of turbulence
• Importance of non-linearity
• Turbulence closure problem and eddy viscosity
• Reynolds stress equations

Turbulence kinetic energy

• Fluctuating kinetic energy
• Rate of dissipation of the turbulence kinetic energy
• Kinetic energy of the mean motion and production of turbulence
• Transport or divergence terms
• Intercomponent transfer of energy

Stationarity and homogeneity

• Processes statistically stationary in time
• Autocorrelation
• Autocorrelation coefficient
• Integral scale
• Temporal Taylor microscale
• Time averages of stationary processes
• Bias and variability of time estimators
• Random fields of space and time
• Multi-point statistics in homogeneous field
• Spatial integral and Taylor microscales

Homogeneous turbulence

• A first look at decaying turbulence
• The dissipation equation and turbulence modelling
• A second look at simple shear flow 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.