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Orderly structure in jet turbulence

Published online by Cambridge University Press:  29 March 2006

S. C. Crow
Affiliation:
The Boeing Company, Seattle, Washington
F. H. Champagne
Affiliation:
The Boeing Company, Seattle, Washington

Abstract

Past evidence suggests that a large-scale orderly pattern may exist in the noiseproducing region of a jet. Using several methods to visualize the flow of round subsonic jets, we watched the evolution of orderly flow with advancing Reynolds number. As the Reynolds number increases from order 102 to 103, the instability of the jet evolves from a sinusoid to a helix, and finally to a train of axisymmetric waves. At a Reynolds number around 104, the boundary layer of the jet is thin, and two kinds of axisymmetric structure can be discerned: surface ripples on the jet column, thoroughly studied by previous workers, and a more tenuous train of large-scale vortex puffs. The surface ripples scale on the boundary-layer thickness and shorten as the Reynolds number increases toward 105. The structure of the puffs, by contrast, remains much the same: they form at an average Strouhal number of about 0·3 based on frequency, exit speed, and diameter.

To isolate the large-scale pattern at Reynolds numbers around 105, we destroyed the surface ripples by tripping the boundary layer inside the nozzle. We imposed a periodic surging of controllable frequency and amplitude at the jet exit, and studied the response downstream by hot-wire anemometry and schlieren photography. The forcing generates a fundamental wave, whose phase velocity accords with the linear theory of temporally growing instabilities. The fundamental grows in amplitude downstream until non-linearity generates a harmonic. The harmonic retards the growth of the fundamental, and the two attain saturation intensities roughly independent of forcing amplitude. The saturation amplitude depends on the Strouhal number of the imposed surging and reaches a maximum at a Strouhal number of 0·30. A root-mean-square sinusoidal surging only 2% of the mean exit speed brings the preferred mode to saturation four diameters downstream from the nozzle, at which point the entrained volume flow has increased 32% over the unforced case. When forced at a Strouhal number of 0·60, the jet seems to act as a compound amplifier, forming a violent 0·30 subharmonic and suffering a large increase of spreading angle. We conclude with the conjecture that the preferred mode having a Strouhal number of 0·30 is in some sense the most dispersive wave on a jet column, the wave least capable of generating a harmonic, and therefore the wave most capable of reaching a large amplitude before saturating.

Type
Research Article
Copyright
© 1971 Cambridge University Press

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References

Batchelor, G. K. & Gill, A. E. 1962 J. Fluid Mech. 14, 529.
Becker, H. A. & Massaro, T. A. 1968 J. Fluid Mech. 31, 435.
Bradshaw, P. 1966 J. Fluid Mech. 26, 225.
Bradshaw, P., Ferriss, D. H. & Johnson, R. F. 1964 J. Fluid Mech. 19, 591.
Browand, F. K. 1966 J. Fluid Mech. 26, 281.
Brown, G. B. 1935 Proc. Phys. Soc. 47, 703.
Crow, S. C. 1970 AIAA J. 8, 2172.
Ffowcs Williams, J. E. 1963 Phil. Trans. Roy. Soc. A, 255, 469.
Freymuth, P. 1966 J. Fluid Mech. 25, 683.
Hussain, A. K. M. F. & Reynolds, W. C. 1970 J. Fluid Mech. 41, 241.
Kline, S. J., Reynolds, W. C., Schraub, F. A. & Runstadler, P. W. 1967 J. Fluid Mech. 30, 741.
Ko, D. R. S., Kubota, T. & Lees, L. 1970 J. Fluid Mech. 40, 315.
Landahl, M. T. 1967 J. Fluid Mech. 29, 441.
Leconte, J. 1858 Phil. Mag. 15, 235.
Lees, L. & Gold, H. 1966 Fundamental phenomena in hypersonic flow. Proceedings of the International Symposium Sponsored by Cornell Aeronautical Laboratory, Buffalo, 1964. Cornell University Press.
Lumley, J. L. 1966 Atmospheric Turbulence and ratio wave propagation. Proceedings of the International Colloquium, Moscow, 1965.
Malkus, W. 1956 J. Fluid Mech. 1, 521.
Michalke, A. 1964 J. Fluid Mech. 19, 543.
Michalke, A. 1965 J. Fluid Mech. 23, 521.
Michalke, A. & Wille, R. 1966 Applied mechanics. Proceedings of the Eleventh International Congress of Applied Mechanics, Munich, 1964. New York: Springer.
Moffatt, H. K. 1969 Computation of turbulent boundary layers. Proceedings of the AFOSRIFP-Stanford Conference, Stanford University, 1968. Distributed by the Thermosciences Division, Department of Mechanical Engineering, Stanford University.
Mollo-Christensen, E., Kolpin, M. A. & Martuccelli, J. R. 1964 J. Fluid Mech. 18, 285.
Mollo-Christensen, E. 1967 J. Appl. Mech. 89, 1.
Orszag, S. A. & Crow, S. C. 1970 Studies in Appl. Math. 49, 167.
Pao, Y.-H., Hansen, S. D. & Macgregor, G. R. 1969 Boeing Scientific Research Laboratories Document D1-82–0863.
Rayleigh, Lord 1896 The Theory of Sound. London: Macmillan. Reproduced by Dover Publications.
Reynolds, A. J. 1962 J. Fluid Mech. 14, 552.
Reynolds, O. 1894 Phil. Trans. Roy. Soc. A, 186, 123.
Roshko, A. 1961 J. Fluid Mech. 10, 345.
Sami, S., Carmody, T. & Rouse, H. 1967 J. Fluid Mech. 27, 231.
Sato, H. 1960 J. Fluid Mech. 7, 53.
Stuart, J. T. 1960 J. Fluid Mech. 9, 353.
Tyndall, J. 1867 Sound. London: Longmans.
Watson, J. 1960 J. Fluid Mech. 9, 371.
Wille, R. 1952 Jb. Schiffbautech. Ges. 46, 174.
Wygnanski, I. 1964 Aero. Quart. 15, 373.
Wygnanski, I. & Fiedler, H. 1969 J. Fluid Mech. 38, 577.