CFD Online URL
[Sponsors]
Home > Wiki > Introduction to turbulence/Statistical analysis

Introduction to turbulence/Statistical analysis

From CFD-Wiki

(Difference between revisions)
Jump to: navigation, search
Line 23: Line 23:
** [[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/Statistical analysis/Estimation from a finite number of realizations#Bias and convergence of estimators| Bias and convergence of estimators]]
*  [[Introduction to turbulence/Statistical analysis/Generalization to the estimator of any quantity]]
*  [[Introduction to turbulence/Statistical analysis/Generalization to the estimator of any quantity]]
-
 
-
{{Chapter navigation|Nature of turbulence|Statistical analysis/Ensemble average}}
 
{{Turbulence credit wkgeorge}}
{{Turbulence credit wkgeorge}}
 +
 +
{{Chapter navigation|Nature of turbulence|Next link not set yet}}

Revision as of 12:40, 21 June 2007

Introduction to turbulence
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!

Much of the study of turbulence requires statistics and stochastic processes, simply because the instanteous motions are too complicated to understand. This should not be taken to mean that the govering equations (usually the Navier-Stokes equations) are stochastic. Even simple non-linear equations can have deterministic solutions that look random. In other words, even though the solutions for a given set of initial and boundary conditions can be perfectly repeatable and predictable at a given time and point in space, it may be impossible to guess from the information at one point or time how it will behave at another (at least without solving the equations). Moreover, a slight change in the intial or boundary conditions may cause large changes in the solution at a given time and location; in particular, changes that we could not have anticipated.

Most of the statistical analyses of turbulent flows are based on the idea of an ensemble average in one form or another. In some ways this is rather inconvenient, since it will be obvious from the definitions that it is impossible to ever really measure such a quantity. Therefore we will spendlast part of this chapter talking about how the kind of averages we can compute from data correspond to the hypotetical ensemble average we wish we could have measured. In later chapters we shall introduce more statistical concepts as we require them. But the concepts of this chapter will be all we need to begin a discussion of the averaged equations of motion in page ???

Further details about statistical analysis in turbulence can be found in:

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.

Nature of turbulence · Next link not set yet
Nature of turbulence · Introduction to turbulence · Next link not set yet
My wiki