Hostname: page-component-cd9895bd7-p9bg8 Total loading time: 0 Render date: 2024-12-18T15:47:38.159Z Has data issue: false hasContentIssue false
  • English
  • Français

Finite-amplitude instability of parallel shear flows

Published online by Cambridge University Press:  28 March 2006

W. C. Reynolds  and
Merle C. Potter
W. C. Reynolds
Affiliation:
Department of Mechanical Engineering, Stanford University
Merle C. Potter
Affiliation:
Mechanical Engineering Department, Michigan State University
Get access Rights & Permissions [Opens in a new window]

Abstract

A formal expansion method for analysis of the non-linear development of an oblique wave in a parallel flow is presented. The present approach constitutes an extension and modification of the method of Stuart and Watson. Results are obtained for plane Poiseuille flow, and for a combination of plane Poiseuille and plane Couette flow. The Poiseuille flow exhibits finite-amplitude subcritical instability, and relatively weak but finite disturbances markedly reduce the critical Reynolds number. The combined flow, which becomes stable to infinitesimal disturbances at all Reynolds numbers when the Couette component is sufficiently great, remains unstable to finite disturbances.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 27 , Issue 3 , 24 February 1967 , pp. 465 - 492
Copyright
© 1967 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

Coles, D. 1965 J. Fluid Mech. 21, 385.
Davey, A. 1902 J. Fluid Mech. 14, 336.
Davies, S. J. & White, C. M. 1928 Proc. Roy. Soc. Lond., A 119, 92.
Diprima, R. C. & Stuart, J. T. 1964 Nonlinear aspects of instability in flow between rotating cylinders. NPL Aero. Report 1111. (Presented at XIth Int. Congr. App. Mech., Munich 1964.)Google Scholar
Kaplan, R. E. 1964 Solution of Orr-Sommerfeld equation for laminar boundary layer flow over compliant boundaries. ASRL-TR-116-1, Cambridge Aeroelastic and Structures Research Lab. Report, Mass. Inst. Tech., June 1964 (STAR N64–29052).Google Scholar
Lin, C. C. 1955 The Theory of Hydrodynamic Stability. Cambridge University Press.
Meksyn, D. & Stuart, J. T. 1951 Proc. Roy. Soc. A, 208, 517.
Nachtsheim, P. R. 1964 An initial value method for the numerical treatment of the Orr-Sommerfeld equation for the case of plane Poiseuille flow. NASA TN D-2414.Google Scholar
Potter, M. C. 1966 J. Fluid Mech. 24, 609.
Stuart, J. T. 1958 J. Fluid Mech. 4, 1.
Stuart, J. T. 1960a J. Fluid Mech. 9, 353.
Stuart, J. T. 1960b Non-linear effects in hydrodynamic stability. Proc. Xth Int. Cong. App. Mech. Stresa, 1960. Elsevier, 1962.
Stuart, J. T. 1961 On three-dimensional non-linear effects in the stability of parallel flows. Adv. Aero. Sci. 3–4, 121. Pergamon Press.
Thomas, L. H. 1953 Phys. Rev. 91, 780.
Watson, J. 1960 J. Fluid Mech. 9, 371.
Watson, J. 1962 J. Fluid Mech. 14, 221.