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Orthogonal Decomposition of the Axisymmetric Jet Mixing Layer Including Azimuthal Dependence

  • M. N. Glauser
  • W. K. George

Abstract

In 1967 LUMLEY [4] proposed an approach to the objective determination of coherent structures. The method uses an orthogonal decomposition to extract eigenvectors from two point velocity measurements, the lowest order eigenvector representing the largest structure. If the flow is homogenous, stationary or periodic the orthogonal decomposition reduces to a harmonic decomposition. These directions therefore are fit with the harmonic eigenfunctions before applying Lumley’s orthogonal decomposition to the inhomogeneous directions.

Keywords

Coherent Structure Strouhal Number Azimuthal Mode Azimuthal Dependence Azimuthal Variation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Nomenclature

Aij

Azimuthal Complex Coefficients

B11

A11 summed over frequency

m

Azimuthal Mode Number

Rij

Velocity Correlation Tensor

r

Radial Distance Across Jet Mixing Layer

t

Time

\(\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle\thicksim}$}}{u}\)

Velocity Vector

\(\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle\thicksim}$}}{x}\)

Inhomogeneous Spatial Vector

θ

Azimuthal Angle in Jet

Eigenvalues

Φij

Cross—Spectral Tensor

φ

Eigenvectors

ψ

Eigenvectors in Transformed Domain

ω

Frequency

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References

  1. 1.)
    Crow, S.C., Champagne, F.H. (1971) J. Fluid Mech. 48, 547.CrossRefADSGoogle Scholar
  2. 2.)
    Glauser, M.N., Leib, S.J., George, W.B. (1985) Coherent structures in the axisymmetric jet mixing layer, Proc. of the 5th symposium turbulent shear flow conf. Cornell. (also Springer, selected papers from TSF5).Google Scholar
  3. 3.)
    Leib, S.7., Glauser, M.N., George, W.K. (1984) An Application of Lumley’s orthogonal decomposition to the axisymmetric turbulent jet mixing layer. Proceedings 9th Rolla Symposium.Google Scholar
  4. 4.)
    Lumley, J.L. (1967) The structure of inhomogenous turbulent flows. In Atm. Turb. and Radio Wave. Prop., (Yaglom and Tatarsky, ed.) Nauka, Moscow, 166178.Google Scholar
  5. 5.)
    Sreenivasan, K.R. (1984) The azimuthal correlations of velocity and temperature fluctuations in an axisymmetric jet. Phys. Fluids 27 (4).Google Scholar
  6. 6.)
    Widnall, S.P., Sullivan, I.P. (1973) Proc. R. Soc. London Ser. A 332, 335.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1987

Authors and Affiliations

  • M. N. Glauser
    • 1
  • W. K. George
    • 1
  1. 1.Turbulence Research Laboratory, Department of Mechanical and Aerospace EngineeringUniversity at Buffalo, SUNYBuffaloUSA

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