Hostname: page-component-78c5997874-t5tsf Total loading time: 0 Render date: 2024-11-10T06:49:54.922Z Has data issue: false hasContentIssue false
  • English
  • Français

On the resonant interaction of neutral disturbances in two inviscid shear flows

Published online by Cambridge University Press:  28 March 2006

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

Abstract

The second-order resonant interaction of two disturbances which are neutrally stable on a linear basis is investigated for cases when the mean flow is, first, an inviscid, homogeneous jet and, secondly, a stably stratified, antisymmetric shear layer for which the linear eigen-solutions are regular. For the former case, the periodic nature of the neutral disturbances is unaffected by the interaction. For the latter, the interaction can lead to an O(ε½) temporal growth rate of one disturbance, where ε is a characteristic disturbance amplitude.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 31 , Issue 4 , 18 March 1968 , pp. 789 - 799
Copyright
© 1968 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

Benney, D. J. & Niell, A. M. 1962 J. Math. Phys. 41, 254.
Browand, F. K. 1965 An experimental investigation of the instability of an incompressible separated shear layer, Mass. Inst. of Tech. Aeroelastic and Structures Res. Lab. Rept. TR-92-4. Cambridge, Mass.Google Scholar
Browand, F. K. 1966 J. Fluid Mech. 26, 281.
Drazin, P. G. & Howard, L. N. 1966 Adv. Appl. Mech. 9, 1.
Howard, L. N. 1963 J. Fluid Mech. 16, 333.
Ince, E. L. 1956 Ordinary Differential Equations. New York: Dover.
Kelly, R. E. 1967 J. Fluid Mech. 27, 657.
Lin, C. C. 1955 The Theory of Hydrodynamic Stability. Cambridge University Press.
Longuet-Higgins, M. S. 1963 Prepared comment on the papers concerning nonlinear aspects of the spectrum. Ocean Wave Spectra (Nat. Acad. Sci.), p. 197. Englewood Cliffs, New Jersey: Prentice-Hall.
Miles, J. W. 1961 J. Fluid Mech. 10, 496.
Miles, J. W. 1963 J. Fluid Mech. 16, 209.
Phillips, O. M. 1960 J. Fluid Mech. 9, 193.
Phillips, O. M. 1966 The Dynamics of the Upper Ocean. Cambridge University Press.
Raetz, G. S. 1959 A new theory of the cause of transition in fluid flows, Norair, Rept. NOR-59-383. California: Hawthorne.
Schade, H. 1964 Phys. Fluids, 7, 623.
Stoker, J. J. 1950 Nonlinear Vibrations. New York: Interscience.
Stuart, J. T. 1962 Nonlinear effects in hydrodynamic stability. Proc. Xth Int. Congr. Appl. Mech., Stresa, 1960, p. 63. Amsterdam: Elsevier.
Watson, J. 1960 J. Fluid Mech. 9, 371.