Introduction to turbulence
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** [[Multivariate random vaiables#The bi-variate normal (or Gaussian) distribution| The bi-variate normal (or Gaussian) distribution]] | ** [[Multivariate random vaiables#The bi-variate normal (or Gaussian) distribution| The bi-variate normal (or Gaussian) distribution]] | ||
** [[Multivariate random vaiables#Statistical independence and lack of correlation| Statistical independence and lack of correlation]] | ** [[Multivariate random vaiables#Statistical independence and lack of correlation| Statistical independence and lack of correlation]] | ||
| - | * [[ | + | * [[Estimation from a finite number of realizations]] |
** [[Estimation from a finite number of realizations#Estimators for averaged quantities| Estimators for averaged quantities]] | ** [[Estimation from a finite number of realizations#Estimators for averaged quantities| Estimators for averaged quantities]] | ||
** [[Estimation from a finite number of realizations#Bias and convergence of estimators| Bias and convergence of estimators]] | ** [[Estimation from a finite number of realizations#Bias and convergence of estimators| Bias and convergence of estimators]] | ||
| - | * [[ | + | * [[Generalization to the estimator of any quantity]] |
== [[Reynolds averaged equations and the turbulence closure problem]] == | == [[Reynolds averaged equations and the turbulence closure problem]] == | ||
Revision as of 12:00, 18 June 2007
| Nature of turbulence |
| Statistical analysis |
| Reynolds averaging |
| Study questions
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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
- The ensemble and ensemble average
- Probability
- Multivariate random vaiables
- Estimation from a finite number of realizations
- 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
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.
