Hostname: page-component-76d6cb85b7-2r2wp Total loading time: 0 Render date: 2026-07-10T12:41:42.819Z Has data issue: false hasContentIssue false
  • English
  • Français

Vortex pairing : the mechanism of turbulent mixing-layer growth at moderate Reynolds number

Published online by Cambridge University Press:  29 March 2006

C. D. Winant  and
F. K. Browand
C. D. Winant
Affiliation:
Division of Engineering and Applied Mechanics, University of Southern California, Los Angeles, California 90007 Present address: Scripps Institution of Oceanography, University of California at San Diego, La Jolla, California 92037.
F. K. Browand
Affiliation:
Division of Engineering and Applied Mechanics, University of Southern California, Los Angeles, California 90007
Get access Rights & Permissions [Opens in a new window]

Abstract

A mixing layer is formed by bringing two streams of water, moving at different velocities, together in a lucite-walled channel. The Reynolds number, based on the velocity difference and the thickness of the shear layer, varies from about 45, where the shear layer originates, to about 850 at a distance of 50 cm. Dye is injected between the two streams just before they are brought together, marking the vorticity-carrying fluid. Unstable waves grow, and fluid is observed to roll up into discrete two-dimensional vortical structures. These turbulent vortices interact by rolling around each other, and a single vortical structure, with approximately twice the spacing of the former vortices, is formed. This pairing process is observed to occur repeatedly, controlling the growth of the mixing layer. A simple model of the mixing layer contains, as the important elements controlling growth, the degree of non-uniformity in the vortex train and the ‘lumpiness’ of the vorticity field.

Information

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 63 , Issue 2 , 3 April 1974 , pp. 237 - 255
Copyright
© 1974 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.)

Article purchase

Temporarily unavailable

References

Becker, H. A. & Massaro, T. A. 1968 Vortex evolution in a round jet. J. Fluid Mech. 31, 435–448.Google Scholar
Browand, F. K. 1966 An experimental investigation of the instability of an incompressible separated shear layer. J. Fluid Mech. 26, 281–307.Google Scholar
Browand, F. K. & Winant, C. D. 1973 Laboratory observations of shear layer in-stability in stratified fluid. Boundary Layer Meteor, 5, 67–77.Google Scholar
Broltu, G. & Roshko, A. 1971 The effect of density differences on the turbulent mixing layer. Turbulent Shear Flows, Agard Current Paper, no. 93, § § 23.1–23.12.
Crow, S.C. & Champagne, F. H. 1971 Orderly structure in jet turbulence. J. Fluid Mech. 48, 547–591.Google Scholar
Freymuth, P. 1966 On transition in a separated laminar boundary layer. J. Fluid Mech. 26, 683–704.Google Scholar
Holinboe, J. 1962 The behaviour of symmetric waves in stratified shear layers. Geophys. Publ. 24, 67–113.Google Scholar
Lamb, H. 1945 Hydrodynamics. Dover.
Laufer, J., Kaplan, R. E. & Chu, W. T. 1973 On the generation of jet noise. AGARD Specialists Meeting ‘Noise Mechanisms’, Brussels.
Liepmann, H. W. & Laufer, J. 1947 Investigation of free turbulent mixing. N.A.C.A. Tech. Note, no. 1257.
Lock, R. C. 1951 The velocity distribution in the laminar boundary layer between parallel streams. Quart. J. Appl. Math. 4, 42–63.Google Scholar
Michalke, A. 1965a Vortex formation in a free boundary layer according to stability theory. J. Fluid Mech. 22, 371–383.Google Scholar
Michalke, A. 1965b On spatially growing disturbances in an inviscid shear layer. J. Fluid Mech. 23, 521–544.Google Scholar
Michalke, A. 1970 The instability of free shear layers: a survey of the state of the art. Dsch. Luft- & Raumfahrt. Mitteilung, no. 70-04.
Miksad, R. W. 1972 Experiments on the nonlinear stages of free-shear-layer transitions. J. Fluid Mech. 56, 695–719.Google Scholar
Rockwell, D. O. & Nicholls, W. O. 1972 Natural breakdown of planar jets. Trans. A.S.M.E., J. Basic. Eng. 94, 720–728.Google Scholar
Spencer, B. W. & Jones, B. G. 1971 Statistical investigation of pressure and velocity fields in the turbulent two-stream mixing layer. A.I.A.A. Paper, no. 71–613.
Stuart, J. T. 1961 On three-dimensional non-linear effects in the stability of parallel flows. Adv. in Aero. Sci. 3, 121–142.Google Scholar
Stuart, J. T. 1967 On finite amplitude oscillations in laminar mixing layers. J. Fluid Mech. 29, 417–440.Google Scholar
Stuart, J. T. 1971 Nonlinear stability theory. Ann. Rev. Fluid Mech. 3, 347–370.Google Scholar
Winant, C. D. 1972 Vortex pairing in a turbulent shear layer at moderate Reynolds numbers. Ph.D. Thesis, Department of Aerospace Engineering, University of Southern California, Los Angeles.
Wygnanski, I. & Fiedler, H. E. 1970 The two-dimensional mixing region. J. Fluid Mech. 41, 327–361.Google Scholar