Introduction to turbulence
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+ | '''This section is currently undergoing heavy reorganization and editing. Please excuse any errors or unfinished parts. --[[User:Jola|Jola]] 07:01, 21 June 2007 (MDT)''' | ||
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== [[Introduction to turbulence/Nature of turbulence|Nature of turbulence]] == | == [[Introduction to turbulence/Nature of turbulence|Nature of turbulence]] == | ||
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** [[Introduction to turbulence/Statistical analysis/Probability#Gaussian (or normal) distributions|Gaussian (or normal) distributions]] | ** [[Introduction to turbulence/Statistical analysis/Probability#Gaussian (or normal) distributions|Gaussian (or normal) distributions]] | ||
** [[Introduction to turbulence/Statistical analysis/Probability#Skewness and kurtosis|Skewness and kurtosis]] | ** [[Introduction to turbulence/Statistical analysis/Probability#Skewness and kurtosis|Skewness and kurtosis]] | ||
- | * [[Introduction to turbulence/Multivariate random variables|Multivariate random | + | * [[Introduction to turbulence/Statistical analysis/Multivariate random variables|Multivariate random variables]] |
- | ** [[Introduction to turbulence/Multivariate random | + | ** [[Introduction to turbulence/Statistical analysis/Multivariate random variables#Joint pdfs and joint moments|Joint pdfs and joint moments]] |
- | ** [[Introduction to turbulence/Multivariate random | + | ** [[Introduction to turbulence/Statistical analysis/Multivariate random variables#The bi-variate normal (or Gaussian) distribution|The bi-variate normal (or Gaussian) distribution]] |
- | ** [[Introduction to turbulence/Multivariate random | + | ** [[Introduction to turbulence/Statistical analysis/Multivariate random variables#Statistical independence and lack of correlation|Statistical independence and lack of correlation]] |
- | * [[Introduction to turbulence/Estimation from a finite number of realizations]] | + | * [[Introduction to turbulence/Statistical analysis/Estimation from a finite number of realizations|Estimation from a finite number of realizations]] |
- | ** [[Introduction to turbulence/Estimation from a finite number of realizations#Estimators for averaged quantities|Estimators for averaged quantities]] | + | ** [[Introduction to turbulence/Statistical analysis/Estimation from a finite number of realizations#Estimators for averaged quantities|Estimators for averaged quantities]] |
- | ** [[Introduction to turbulence/Estimation from a finite number of realizations#Bias and convergence of estimators|Bias and convergence of estimators]] | + | ** [[Introduction to turbulence/Statistical analysis/Estimation from a finite number of realizations#Bias and convergence of estimators|Bias and convergence of estimators]] |
- | * [[Introduction to turbulence/Generalization to the estimator of any quantity]] | + | * [[Introduction to turbulence/Statistical analysis/Generalization to the estimator of any quantity|Generalization to the estimator of any quantity]] |
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+ | == [[Introduction to turbulence/Reynolds averaged equations|Reynolds averaged equations and the turbulence closure problem]] == | ||
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+ | * [[Introduction to turbulence/Reynolds averaged equations#Equations governing instantaneous fluid motion|Equations governing instantaneous fluid motion]] | ||
+ | * [[Introduction to turbulence/Reynolds averaged equations#Equations for the average velocity|Equations for the average velocity]] | ||
+ | * [[Introduction to turbulence/Reynolds averaged equations#The turbulence problem|The turbulence problem]] | ||
+ | * [[Introduction to turbulence/Reynolds averaged equations#Origins of turbulence|Origins of turbulence]] | ||
+ | * [[Introduction to turbulence/Reynolds averaged equations#Importance of non-linearity|Importance of non-linearity]] | ||
+ | * [[Introduction to turbulence/Reynolds averaged equations#Turbulence closure problem and eddy viscosity|Turbulence closure problem and eddy viscosity]] | ||
+ | * [[Introduction to turbulence/Reynolds averaged equations#Reynolds stress equations|Reynolds stress equations]] | ||
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+ | == [[Introduction to turbulence/Turbulence kinetic energy|Turbulence kinetic energy]] == | ||
+ | * [[Introduction to turbulence/Turbulence kinetic energy#Fluctuating kinetic energy|Fluctuating kinetic energy]] | ||
+ | * [[Introduction to turbulence/Turbulence kinetic energy#Rate of dissipation of the turbulence kinetic energy|Rate of dissipation of the turbulence kinetic energy]] | ||
+ | * [[Introduction to turbulence/Turbulence kinetic energy#Kinetic energy of the mean motion and production of turbulence|Kinetic energy of the mean motion and production of turbulence]] | ||
+ | * [[Introduction to turbulence/Turbulence kinetic energy#Transport or divergence terms|Transport or divergence terms]] | ||
+ | * [[Introduction to turbulence/Turbulence kinetic energy#Intercomponent transfer of energy|Intercomponent transfer of energy]] | ||
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+ | == [[Introduction to turbulence/Stationarity and homogeneity|Stationarity and homogeneity]] == | ||
+ | * [[Introduction to turbulence/Stationarity and homogeneity#Processes statistically stationary in time|Processes statistically stationary in time]] | ||
+ | * [[Introduction to turbulence/Stationarity and homogeneity#Autocorrelation|Autocorrelation]] | ||
+ | * [[Introduction to turbulence/Stationarity and homogeneity#Autocorrelation coefficient|Autocorrelation coefficient]] | ||
+ | * [[Introduction to turbulence/Stationarity and homogeneity#Integral scale|Integral scale]] | ||
+ | * [[Introduction to turbulence/Stationarity and homogeneity#Temporal Taylor microscale|Temporal Taylor microscale]] | ||
+ | * [[Introduction to turbulence/Stationarity and homogeneity#Time averages of stationary processes|Time averages of stationary processes]] | ||
+ | * [[Introduction to turbulence/Stationarity and homogeneity#Bias and variability of time estimators|Bias and variability of time estimators]] | ||
+ | * [[Introduction to turbulence/Stationarity and homogeneity#Random fields of space and time|Random fields of space and time]] | ||
+ | * [[Introduction to turbulence/Stationarity and homogeneity#Multi-point statistics in homogeneous field|Multi-point statistics in homogeneous field]] | ||
+ | * [[Introduction to turbulence/Stationarity and homogeneity#Spatial integral and Taylor microscales|Spatial integral and Taylor microscales]] | ||
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+ | == [[Introduction to turbulence/Homogeneous turbulence|Homogeneous turbulence]] == | ||
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+ | * [[Introduction to turbulence/Homogeneous turbulence#A first look at decaying turbulence |A first look at decaying turbulence ]] | ||
+ | * [[Introduction to turbulence/Homogeneous turbulence#The dissipation equation and turbulence modelling |The dissipation equation and turbulence modelling ]] | ||
+ | * [[Introduction to turbulence/Homogeneous turbulence#A second look at simple shear flow turbulence |A second look at simple shear flow turbulence ]] | ||
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+ | == [[Introduction to turbulence/Free turbulent shear flows|Free turbulent shear flows]] == | ||
+ | * [[Introduction to turbulence/Free turbulent shear flows#Introduction|Introduction]] | ||
+ | * [[Introduction to turbulence/Free turbulent shear flows#The averaged equations|The averaged equations]] | ||
+ | * [[Introduction to turbulence/Free turbulent shear flows#Two-dimensional Turbulent Jets|Two-dimensional Turbulent Jets]] | ||
+ | * [[Introduction to turbulence/Free turbulent shear flows#Other free shear flows|Other free shear flows]] | ||
- | == [[ | + | == [[Introduction to turbulence/Wall bounded turbulent flows|Wall bounded turbulent flows]] == |
- | * [[ | + | * [[Introduction to turbulence/Wall bounded turbulent flows#Introduction|Introduction]] |
- | * [[ | + | * [[Introduction to turbulence/Wall bounded turbulent flows#Review of laminar boundary layers|Review of laminar boundary layers]] |
- | + | * [[Introduction to turbulence/Wall bounded turbulent flows#The "outer" turbulent boundary layer|The "outer" turbulent boundary layer]] | |
- | + | * [[Introduction to turbulence/Wall bounded turbulent flows#The “inner” turbulent boundary layer|The “inner” turbulent boundary layer]] | |
- | * [[ | + | * [[Introduction to turbulence/Wall bounded turbulent flows#The viscous sublayer|The viscous sublayer]] |
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{{Turbulence credit wkgeorge}} | {{Turbulence credit wkgeorge}} | ||
[[Category: Turbulence]] | [[Category: Turbulence]] |
Latest revision as of 12:34, 15 March 2012
Nature of turbulence |
Statistical analysis |
Reynolds averaged equation |
Turbulence kinetic energy |
Stationarity and homogeneity |
Homogeneous turbulence |
Free turbulent shear flows |
Wall bounded turbulent flows |
Study questions
... template not finished yet! |
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
- Probability
- Multivariate random variables
- Estimation from a finite number of realizations
- 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
- 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.