Hostname: page-component-8448b6f56d-t5pn6 Total loading time: 0 Render date: 2024-04-24T00:59:19.139Z Has data issue: false hasContentIssue false
  • English
  • Français

On the stability of the decelerating laminar boundary layer

Published online by Cambridge University Press:  20 April 2006

Mohamed Gad-El-Hak ,
Stephen H. Davis ,
J. Thomas Mcmurray  and
Steven A. Orszag
Mohamed Gad-El-Hak
Affiliation:
Flow Research Company, 21414 68th Avenue South, Kent, Washington 98032
Permanent address: Department of Engineering Science and Applied Mathematics, North-western University, Evanston, IL 60201.
Stephen H. Davis
Affiliation:
Flow Research Company, 21414 68th Avenue South, Kent, Washington 98032
Permanent address: Department of Engineering Science and Applied Mathematics, North-western University, Evanston, IL 60201.
J. Thomas Mcmurray
Affiliation:
Flow Research Company, 21414 68th Avenue South, Kent, Washington 98032
Permanent address: Department of Engineering Science and Applied Mathematics, North-western University, Evanston, IL 60201.
Steven A. Orszag
Affiliation:
Flow Research Company, 21414 68th Avenue South, Kent, Washington 98032
Permanent address: Department of Engineering Science and Applied Mathematics, North-western University, Evanston, IL 60201.
 Permanent address: Department of Mathematics, Massachusetts Institute of Technology, Cambridge, MA 02139.
Get access Rights & Permissions [Opens in a new window]

Abstract

The stability of a decelerating boundary-layer flow is investigated experimentally and numerically. Experimentally, a flat plate having a Blasius boundary layer is decelerated in an 18 m towing tank. The boundary layer becomes unstable to two-dimensional waves, which break down into three-dimensional patterns, hairpin vortices, and finally turbulent bursts when the vortices lift off the wall. The unsteady boundary-layer equations are solved numerically to generate instantaneous velocity profiles for a range of boundary and initial conditions. A quasi-steady approximation is invoked and the stability of local velocity profiles is determined by solving the Orr–Sommerfeld equation using Chebyshev matrix methods. Comparisons are made between the numerical predictions and the experimentally observed instabilities.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 138 , January 1984 , pp. 297 - 323
Copyright
© 1984 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

Anders, J. B. & Blackwelder, R. F. 1979 Longitudinal vortices in a transitioning boundary layer. In Laminar–Turbulent Transition (ed. R. Eppler & H. Fasel), p. 110. Springer.
Craik, A. D. D. 1971 Non-linear resonant instability in boundary layers J. Fluid Mech. 50, 393.Google Scholar
Craik, A. D. D. 1980 Nonlinear evolution and breakdown in unstable boundary layers J. Fluid Mech. 99, 247.Google Scholar
Davis, S. H. 1976 The stability of time-periodic flows Ann. Rev. Fluid Mech. 8, 57.Google Scholar
Davis, S. H. & GAD-EL-HAK, M. 1981 Transition in decelerating boundary layers Bull. Am. Phys. Soc. 26, 1251.Google Scholar
Drazin, P. & Reid, W. 1981 Hydrodynamic Stability. Cambridge University Press.
Fales, E. N. 1955 A new laboratory technique for investigation of the origin of fluid turbulence J. Franklin Inst. 259, 491.Google Scholar
Fox, L. & Parker, I. B. 1968 Chebyshev Polynomials in Numerical Analysis. Oxford University Press.
Gad-El-Hak, M., Blackwelder, R. F. & Riley, J. J. 1979 A visual study of the growth and entrainment of turbulent spots. In Laminar–Turbulent Transition (ed. R. Eppler & H. Fasel), p. 297. Springer.
Gad-El-Hak, M., Blackwelder, R. F. & Riley, J. J. 1981 On the growth of turbulent regions in laminar boundary layers J. Fluid Mech. 110, 73.Google Scholar
Hegarty, J. C. 1958 Investigation of transition caused by the stopping of a flat plate. AFOSR TN58-627.
Jordinson, R. 1970 The flat plate boundary layer. Part 1. Numerical integration of the Orr–Sommerfeld equation J. Fluid Mech. 43, 801.Google Scholar
Klebanoff, P. S., Tidstrom, K. D. & Sargent, L. M. 1962 The three-dimensional nature of boundary layer instability J. Fluid Mech. 12, 1.Google Scholar
Liepmann, H. W., Brown, G. L. & Nosenchuck, D. M. 1982 Control of laminar-instability waves using a new technique J. Fluid Mech. 118, p. 187.Google Scholar
Lin, C. C. 1955 The Theory of Hydrodynamic Stability. Cambridge University Press.
Nayfeh, A. H. & Bozatli, A. N. 1979 Nonlinear wave interactions in boundary layers. AIAA 12th Fluid & Plasma Dyn. Conf., Williamsburg, Paper 79–1496.Google Scholar
Orszag, S. A. 1971 Accurate solution of the Orr–Sommerfeld stability equation J. Fluid Mech. 50, 689.Google Scholar
Orszag, S. A. & Patera, A. T. 1983 Secondary instability of wall-bounded shear flows J. Fluid Mech. 128, 347.Google Scholar
Perry, A. E., Lim, T. T. & Teh, E. W. 1981 A visual study of turbulent spots J. Fluid Mech. 104, 387.Google Scholar
ROSENHEAD, L. (ed.) 1963 Laminar Boundary Layers. Clarendon.
Saric, W. S. & Nayfeh, A. H. 1975 Non-parallel stability of boundary-layer flows Phys. Fluids 18, 945.Google Scholar
Schlichting, H. 1968 Boundary Layer Theory. McGraw-Hill.
Squire, H. B. 1933 On the stability of three-dimensional disturbances of viscous flow between parallel walls. Proc. R. Soc. Lond. A 142, 621.
Stewartson, K. 1951 On the impulsive motion of a flat plate in a viscous fluid Q. J. Mech. Appl. Maths 4, 182.Google Scholar
Stuart, J. T. 1965 The production of intense shear layers by vortex stretching and convection. AGARD Rep. 514.Google Scholar