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.
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Abbreviations
- 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
References
Crow, S.C., Champagne, F.H. (1971) J. Fluid Mech. 48, 547.
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).
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.
Lumley, J.L. (1967) The structure of inhomogenous turbulent flows. In Atm. Turb. and Radio Wave. Prop., (Yaglom and Tatarsky, ed.) Nauka, Moscow, 166178.
Sreenivasan, K.R. (1984) The azimuthal correlations of velocity and temperature fluctuations in an axisymmetric jet. Phys. Fluids 27 (4).
Widnall, S.P., Sullivan, I.P. (1973) Proc. R. Soc. London Ser. A 332, 335.
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© 1987 Springer-Verlag Berlin Heidelberg
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Glauser, M.N., George, W.K. (1987). Orthogonal Decomposition of the Axisymmetric Jet Mixing Layer Including Azimuthal Dependence. In: Comte-Bellot, G., Mathieu, J. (eds) Advances in Turbulence. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-83045-7_40
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DOI: https://doi.org/10.1007/978-3-642-83045-7_40
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-83047-1
Online ISBN: 978-3-642-83045-7
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