Summary
The passage of axi-symmetric turbulence in a suddenly contracting stream has been investigated. A form of axi-symmetric tensor suitable for this study has been derived. Assuming that the form of turbulence is initially axi-symmetric, upstream of the contraction, the spectral forms downstream have been given. The ratio of the turbulence levels, on either side of the contraction, has been evaluated in integral form. Further, the integrals have been solved, assuming that the defining scalars are functions only of the wave number Κ. The method of evaluating one-dimensional spectra has been indicated. The whole investigation is based on the linearised approach.
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Abbreviations
- u :
-
turbulent fluctuation
- x :
-
co-ordinates
- l 1 :
-
mean velocity ratio
- l 2,l 3 :
-
vertical and lateral contraction ratios
- Κ:
-
wave number vector
- σ:
-
compressibility factor (σ = 1, for incompressible flows)
- Г:
-
spectral tensor
- R:
-
correlation tensor
- A, B:
-
sections upstream and downstream, respectively, of the contraction
- 1, 2, 3; α, β,γ:
-
subscripts for denoting directions
- Г1 Г2 :
-
defining scalars
- ∈ =l 2 2/l 1 2 :
-
Other symbols are defined in the text, as and when they appear for the first time.
References
Batchelor, G. K.The Theory of Homogeneous Turbulence, Cambridge, 1953.
Ribner, H. S. and Tucker, M.N.A.C.A. Report, 1113.
Proudman, I. and Reid, W.H.Phil. Trans. Roy. Soc. Series A, 1954,247 (926), 163–89.
Additional references
Batchelor, G. K. and Ian ProudmanQ.J.M.A.M., 1954,3, Pt. I, p. 83.
Townsend, A. A.Ibid, p. 104.
Additional information
Communicated by Dr. P. Nilakantan, F.A.SC.
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Acharya, Y.V.G. Spectrum of axi-symmetric turbulence in a contracting stream. Proc. Indian Acad. Sci. 44, 63–71 (1956). https://doi.org/10.1007/BF03048803
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DOI: https://doi.org/10.1007/BF03048803