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

• Introduction
• The averaged equations
• Two-dimensional Turbulent Jets
• Other free shear flows

Wall bounded turbulent flows

• Introduction
• Review of laminar boundary layers
• The "outer" turbulent boundary layer
• The “inner” turbulent boundary layer
• The viscous sublayer

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.