Hostname: page-component-7c8c6479df-p566r Total loading time: 0 Render date: 2024-03-27T08:11:55.319Z Has data issue: false hasContentIssue false

The three-dimensional nature of boundary-layer instability

Published online by Cambridge University Press:  28 March 2006

P. S. Klebanoff
Affiliation:
National Bureau of Standards, Washington, D.C.
K. D. Tidstrom
Affiliation:
National Bureau of Standards, Washington, D.C.
L. M. Sargent
Affiliation:
National Bureau of Standards, Washington, D.C.

Abstract

An experimental investigation is described in which principal emphasis is given to revealing the nature of the motions in the non-linear range of boundary-layer instability and the onset of turbulence. It has as its central purpose the evaluation of existing theoretical considerations and the provision of a sound physical model which can be taken as a basis for a theoretical approach. The experimental method consisted of introducing, in a two-dimensional boundary layer on a flat plate at ‘incompressible’ speeds, three-dimensional disturbances under controlled conditions using the vibrating-ribbon technique, and studying their growth and evolution using hot-wire methods. It has been definitely established that longitudinal vortices are associated with the non-linear three-dimensional wave motions. Sufficient data were obtained for an evaluation of existing theoretical approaches. Those which have been considered are the generation of higher harmonics, the interaction of the mean flow and the Reynold stress, the concave streamline curvature associated with the wave motion, the vortex loop and the non-linear effect of a three-dimensional perturbation. It appears that except for the latter they do not adequately describe the observed phenomena. It is not that they are incorrect or may not play a role in some aspect of the local behaviour, but from the over-all point of view the results suggest that it is the non-linear effect of a three-dimensional perturbation which dominates the behaviour. A principal conclusion to be drawn is that a new perspective, one that takes three-dimensionality into account, is required in connexion with boundary-layer instability. It is demonstrated that the actual breakdown of the wave motion into turbulence is a consequence of a new instability which arises in the aforementioned three-dimensional wave motion. This instability involves the generation of ‘hairpin’ eddies and is remarkably similar in behaviour to ‘inflexional’ instability. It is also shown that the results obtained from the study of controlled disturbances are equally applicable to ‘natural’ transition.

Type
Research Article
Copyright
© 1962 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. 1961 A non-linear theory for oscillations in a parallel flow. J. Fluid Mech. 10, 209.Google Scholar
Benney, D. J. & Lin, C. C. 1960 On the secondary motion induced by oscillations in a shear flow. Phys. Fluids, 4, 656.Google Scholar
Betchov, R. 1960 On the mechanism of turbulent transition. Phys. Fluids, 3, 1026.Google Scholar
Emmons, H. W. 1951 The laminar-turbulent transition in a boundary layer. J. Aero. Sci. 18, 490.Google Scholar
Fales, E. N. 1955 A new laboratory technique for investigation of the origin of fluid turbulence. J. Franklin Inst. 259, 491.Google Scholar
Görtler, H. & Witting, H. 1957 Theorie der sekundären instabilität der laminaren grenzschichten. Boundary Layer Research Symposium, Freiburg (Ed. H. Görtler), p. 110. Berlin: Springer-Verlag.
Hama, F. R., Long, J. D. & Hegarty, J. C. 1957 On transition from laminar to turbulent flow. J. Appl. Phys. 28, 388.Google Scholar
Klebanoff, P. S. & Tidstrom, K. D. 1959 Evolution of amplified waves leading to transition in a boundary layer with zero pressure gradient. N.A.S.A. Tech. note, no. D-195.Google Scholar
Kovásznay, L. S. G. 1960 A new look at transition. Aeronautics and Astronautics, p. 161. London: Pergamon.
Lin, C. C. 1957 On the instability of laminar flow and its transition to turbulence. Boundary Layer Research Symposium, Freiburg (Ed. H. Görtler), p. 144. Berlin: Springer-Verlag.
Meksyn, D. & Stuart, J. T. 1951 Stability of viscous motion between parallel planes for finite disturbances. Proc. Roy. Soc. A, 208, 517.Google Scholar
Sato, H. 1956 Experimental investigation on the transition of laminar separated flow. J. Phys. Soc. Japan, 11, 702.Google Scholar
Sato, H. 1960 The stability and transition of a two-dimensional jet. J. Fluid Mech. 7, 53.Google Scholar
Schubauer, G. B. 1957 Mechanism of transition at subsonic speeds. Boundary Layer Research Symposium, Freiburg (Ed. H. Görtler), p. 85. Berlin: Springer-Verlag.
Schubauer, G. B. & Klebanoff, P. S. 1956 Contributions on the mechanics of boundary layer transition. N.A.C.A. Rep. no. 1289.Google Scholar
Schubauer, G. B. & Skramstad, H. K. 1948 Laminar boundary layer oscillations on a flat plate. N.A.C.A. Rep. no. 909.Google Scholar
Spangenberg, W. G. & Rowland, W. R. 1960 Optical study of boundary layer transition processes in a supersonic air stream. Phys. Fluids, 3, 667.Google Scholar
Stuart, J. T. 1958 On the non-linear mechanics of hydrodynamic stability. J. Fluid Mech. 4, 1.Google Scholar
Stuart, J. T. 1960a Non-linear effects in hydrodynamic stability. 10th Internat. Cong. Appl. Mech., Stresa.Google Scholar
Stuart, J. T. 1960 On three-dimensional non-linear effects in the stability of parallel flows. 2nd Internat. Cong. I.C.A.S., Zürich.Google Scholar
Theodorsen, T. 1955 The structure of turbulence. 50 Jahre Grenzschichtforschung (Ed. H. Görtler & W. Tollmien), p. 55. Braunschweig: Veiweg und Sohn.
Weske, J. R. 1957 Experimental study of detail phenomena of transition in boundary layers. Univ. of Maryland Tech. Note, no. BN-91.Google Scholar