Hostname: page-component-cd9895bd7-p9bg8 Total loading time: 0 Render date: 2024-12-19T00:05:37.007Z Has data issue: false hasContentIssue false
  • English
  • Français

Influence of wave dispersion on vortex pairing in a jet

Published online by Cambridge University Press:  19 April 2006

R. A. Petersen
R. A. Petersen
Affiliation:
Department of Aerospace Engineering, University of Southern California, Los Angeles
Get access Rights & Permissions [Opens in a new window]

Abstract

The geometry of large-scale structures in the turbulent mixing layer of a moderate Reynolds number jet is deduced from measurements of the fluctuating pressure in the hydrodynamic near field. The structures are rings of concentrated vorticity that distort with downstream distance until statistical axisymmetry disappears. The rings are spaced quasi-periodically and coalesce with each other, producing larger spacings. Statistical and flow-visualization techniques are applied to free and forced jets over a range of Reynolds numbers from 5000 to 50000 to demonstrate that rings of a given spacing do not coalesce with each other until they are far enough downstream that the local mixing layer has attained some critical thickness which scales with the wavelength of the vortex pair. Wave dispersion is evaluated as a plausible mechanism for localizing the coalescences. The central feature of the model is the observation that a shear layer is dispersive to wavelengths much longer than its thickness and non-dispersive to shorter waves.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 89 , Issue 3 , 13 December 1978 , pp. 469 - 495
Copyright
© 1978 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Anderson, A. B. C. 1955 Structure and velocity of the periodic vortex-ring flow pattern of a pipe tone jet. J. Acoust. Soc. Am. 27, 1048–1052.Google Scholar
Bradshaw, P., Ferriss, D. H. & Johnson, R. F. 1964 Turbulence in the noise-producing region of a circular jet. J. Fluid Mech. 19, 591–624.Google Scholar
Browand, F. K., Chu, W. T. & Laufer, J. 1975 Exploratory experiments on the entrance effects in subsonic jet flows. Dept. Aero. Engng, Univ. Southern Calif. Rep. no. 130.Google Scholar
Browand, F. K. & Laufer, J. 1975 The role of large scale structures in the initial development of circular jets. Proc. 4th Symp. Turbulence in Liquids, Univ. Missouri–Rolla.
Browand, F. K. & Weidman, P. D. 1976 Large scales in the developing mixing layer. J. Fluid Mech. 76, 127–144.Google Scholar
Brown, G. & Roshko, A. 1971 The effect of density differences on the turbulent mixing layer. Turbulent Shear Flows, AGARD Current Paper, no. 93, pp. 23.1–23.12.Google Scholar
Brown, G. & Roshko, A. 1974 On density effects in turbulent mixing layers. J. Fluid Mech. 64, 775.Google Scholar
Crighton, D. G. & Gaster, M. 1976 Stability of slowly diverging jet flow. J. Fluid Mech. 77, 397–413.Google Scholar
Crow, S. C. & Champagne, F. H. 1971 Orderly structure in jet turbulence. J. Fluid Mech. 48, 547–591.Google Scholar
Davies, P. O. A. L., Fisher, M. J. & Barratt, M. J. 1963 The characteristics of the turbulence in the mixing regions of a round jet. J. Fluid Mech. 15, 337–367.Google Scholar
Domm, U. 1956 Uber eine Hypothese, die den Mechanismus der Turbulenz–Enstehung betrifft. Dsche Versuchsanstalt Luftfahrt (DVL) Rep. no. 23.Google Scholar
Fuchs, H. V. 1972 Measurements of pressure fluctuations within subsonic turbulent jets. J. Sound Vib. 22, 361–378.Google Scholar
Fuchs, H. V. 1974 Resolution of turbulent jet pressures into azimuthal components. AGARD Conf. Proc. no. 131, paper 27.Google Scholar
Ko, N. W. M. & Davies, P. O. A. L. 1971 The near field within the potential core of subsonic cold jets. J. Fluid Mech. 50, 49–78.Google Scholar
Konrad, J., Roshko, A. & Brown, G. L. 1976 The development of three dimensionality and the extent of the molecular mixing in a turbulent shear flow. Bull. Am. Phys. Soc., Div. Fluid Dyn. no. 21, paper CB2.Google Scholar
Lau, J. C., Fisher, M. J. & Fuchs, H. V. 1972 The intrinsic structure of turbulent jets. J. Sound Vib. 22, 379–406.Google Scholar
Laufer, J. 1974 On the mechanism of noise generation by turbulence. Omaggio a Carlo Ferrari (ed. Levrotto & Bella), pp. 449–464.
Laufer, J., Kaplan, R. E. & Chu, W. T. 1974 On the generation of jet noise. AGARD Conf. Proc. no. 131, paper 21.Google Scholar
Mattingly, G. E. & Chang, C. C. 1974 Unstable waves on an axisymmetric jet column. J. Fluid Mech. 65, 541–560.Google Scholar
Michalke, A. 1971 Instabilität eines Kompressiblen runden Freistrahls unter Berücksichtigung des Einflusses der Strahlgrenzschichtdicke. Z. Flugwiss. 19, 319–328.Google Scholar
Michalke, A. & Fuchs, H. V. 1975 On turbulence noise of an axisymmetric shear flow. J. Fluid Mech. 70, 179–205.Google Scholar
Mollo-Christensen, E. 1967 Jet noise and shear flow instability seen from an experimenter's viewpoint. Trans. A.S.M.E., J. Appl. Mech. 34, 1–7.Google Scholar
Moore, C. J. 1977 The role of shear-layer instability waves in jet exhaust noise. J. Fluid Mech. 80, 321–367.Google Scholar
Patnaik, P. C., Sherman, R. S. & Corcos, G. M. 1976 A numerical simulation of Kelvin–Helmholtz waves of finite amplitude. J. Fluid Mech. 73, 215–240.Google Scholar
Siddon, T. E. 1969 On the response of pressure measuring instrumentation in unsteady flow. Univ. Toronto UTIAS Rep. no. 136.Google Scholar
Townsend, A. A. 1956 The Structure of Turbulent Shear Flow. Cambridge University Press.
Winant, C. D. & Browand, F. K. 1974 Vortex pairing: the mechanism of turbulent mixing-layer growth at moderate Reynolds number. J. Fluid Mech. 63, 237–255.Google Scholar