Hostname: page-component-cd9895bd7-gbm5v Total loading time: 0 Render date: 2024-12-19T10:13:35.589Z Has data issue: false hasContentIssue false
  • English
  • Français

Experiments on nonlinear interactions in the transition of a free shear layer

Published online by Cambridge University Press:  29 March 2006

Richard W. Miksad
Richard W. Miksad
Affiliation:
Department of Mathematics, Imperial College, London
Present address: Division of Atmospheric Science, University of Miami, Miami, Florida.
Get access Rights & Permissions [Opens in a new window]

Abstract

An experimental study is made of nonlinear interactions in a laminar free shear layer. Two disturbances (f1 and f2), excited by sound, amplify and grow independently for small amplitudes. At larger amplitudes the disturbances interact to generate fluctuations of sum and difference frequencies (f2 ± f1). Harmonics and subharmonics of f1 and f2 are also generated and all fluctuations interact to generate additional fluctuations of the form (nf2/m) ± (pf1/q); n, p = 1,2,3,…, m, q = 1,2. Nonlinear mode competition suppresses the growth of f1 or f2, depending on their relative amplitudes, and contributes to finite amplitude equilibration. An upper bound on the modal integral of total u′r.m.s.2 fluctuation energy is found. Fluctuation energy tends to be distributed among all possible frequency components, and its upper bound does not increase as the number of components increases.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 59 , Issue 1 , 5 June 1973 , pp. 1 - 21
Copyright
© 1973 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

Chen, M. & Whitehead, J. 1968 J. Fluid Mech. 31, 1.
Coles, D. 1965 J. Fluid Mech. 21, 315.
Kelly, R. E. 1967 J. Fluid Mech. 27, 657.
Lashinsky, H. 1965 Phys. Rev. Lett. 14, 1064.
Miksad, R. W. 1972 J. Fluid Mech. 56, 695.
Newell, A. C., Lange, C. G. & Aucoin, P. J. 1970 J. Fluid Mech. 40, 513.
Newell, A. C. & Whitehead, J. 1969 J. Fluid Mech. 38, 279.
Ru-Sue Ko, D., Kubuta, T. & Lees, L. 1970 J. Fluid Mech. 40, 315.
Sato, H. 1970 J. Fluid Mech. 44, 741.
Snyder, H. 1969 J. Fluid Mech. 35, 273.
Stuart, J. T. 1958 J. Fluid Mech. 4, 1.
Stuart, J. T. 1962 Proc. Int. Congr. Appl. Mech., Stresa, pp. 63–97. Elsevier.
Taylor, G. I. 1923 Phil. Trans. A 223, 289.