Abstract
In 1967 Lumley proposed two different, but complimentary approaches to the objective determination of coherent structures. The first uses an orthogonal decomposition to extract eigenvectors from two point velocity measurements, the lowest order eigenvector representing the largest structure. Where there are partial homogeneities, or when the flow is stationary, the eigenfunctions are the harmonic ones and the coherent features are impossible to identify. To organize these fluctuating Fourier modes into coherent features, a second decomposition is used, the shot-noise decomposition.
The initial experiment (on which this paper is based) has generated cross-spectral data at seven radial positions across the jet mixing layer. The 49 cross-spectra have then been decomposed to obtain the eigenvectors and the time development of the streamwise velocity component of the large eddies in the mixing layer. The results to date show clearly the existence of a large scale structure in the mixing layer containing 40% of the turbulent energy. The second and third order structures contain another 40% of the energy. Thus nearly all the energy is contained in the first three modes.
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Abbreviations
- a(n)):
-
Random coefficients
- f):
-
Characteristic eddy
- g):
-
Random distribution function
- Rij):
-
Velocity correlation tensor
- S):
-
Streamwise velocity spectrum
- t):
-
Time
- u):
-
Velocity vector
- u):
-
Streamwise velocity
- û):
-
Fourier transform of velocity
- W):
-
Weighting function
- x):
-
Special vector
- y):
-
Radial distance across jet mixing layer
- α):
-
Inner product of velocity vector and candidate eddy
- δmn):
-
Kroneker delta function
- λ(n)):
-
Eigenvalues
- Фij):
-
Cross spectral tensor
- ø):
-
Eigenvectors
- ψ):
-
Eigenvectors in transformed domain
- ω):
-
Frequency
References
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© 1987 Springer-Verlag Berlin Heidelberg
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Glauser, M.N., Leib, S.J., George, W.K. (1987). Coherent Structures in the Axisymmetric Turbulent Jet Mixing Layer. In: Durst, F., Launder, B.E., Lumley, J.L., Schmidt, F.W., Whitelaw, J.H. (eds) Turbulent Shear Flows 5. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-71435-1_13
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DOI: https://doi.org/10.1007/978-3-642-71435-1_13
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