Hostname: page-component-cd9895bd7-dk4vv Total loading time: 0 Render date: 2024-12-26T08:22:43.746Z Has data issue: false hasContentIssue false
  • English
  • Français

Formation of longitudinal vortices in the sublayer due to boundary-layer turbulence

Published online by Cambridge University Press:  26 April 2006

Y. Aihara
Y. Aihara
Affiliation:
Department of Aeronautics, Faculty of Engineering, University of Tokyo, Japan
Get access Rights & Permissions [Opens in a new window]

Abstract

A number of experiments have indicated that the behaviour of longitudinal vortices in the sublayer of a turbulent boundary layer has a significant effect on the equilibrium of the whole flow field, but the formation of such longitudinal vortices remains unclarified. In the present paper, paying attention to the random turbulent motions normal to the wall which induce a dynamic instability causing the generation of the regular longitudinal vortices, a turbulence model is introduced to analyse the generation of the longitudinal vortices in the sublayer of a turbulent boundary layer.

By integrating the results of the analysis with previous experimental results for the behaviour of developing longitudinal vortices, a feedback loop linking regular and irregular motions in the turbulent boundary layer is presented.

It has been experimentally confirmed that even at low Reynolds number, regular longitudinal vortices are formed when a disturbance is applied to a boundary layer. As for the stability region described in terms of the intensity of the disturbance and the wavenumber of the longitudinal vortices, no conflict between analysis and experiment is observed. Using the thermodynamic argument of irreversible processes the formation of longitudinal vortices close to the wall by the turbulence in the boundary layer is shown to be physically reasonable.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 214 , May 1990 , pp. 111 - 129
Copyright
© 1990 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

Aihara, Y. & Koyama, H. 1981a Secondary instability of Görtler vortices – formation of periodic three-dimensional coherent structure. Trans. Japan Soc. Aero. Space Sci. 24, 78.Google Scholar
Aihara, Y. & Koyama, H. 1981b Nonlinear development and secondary instability of Görtler vortices. In Stability in the Mechanics of Continua (ed. F. H. Schroeder), p. 345. Springer.
Aihara, Y. & Koyama, H. 1982 Three-dimensional turbulent boundary layer along a concave wall. In Three-Dimensional Turbulent Boundary Layers (ed. H. H. Fernholz & K. Krause), p. 210. Springer.
Aihara, Y., Tomita, Y. & Ito. A. 1985 Generation, development and distortion of longitudinal vortices in boundary layers along concave and flat plates. In Laminar-Turbulent Transition (ed. V. V. Kozlov), p. 447. Springer.
Benny, D. J. & Lin, C. C. 1960 On the secondary motion induced by oscillations in shear flow. Phys. Fluids 3, 656.Google Scholar
Blackwelder, R. F. & Eckelmann, H. 1979 Streamwise vortices associated with the bursting phenomenon. J. Fluid Mech. 94, 577.Google Scholar
Brown, G. L. & Thomas, A. S. W. 1977 Large structure in a turbulent boundary layer. Phys. Fluids 20, (10) S 243.Google Scholar
Cantwell, B. J. 1981 Organized motion in turbulent flow. Ann. Rev. Fluid Mech. 13, 457.Google Scholar
Coles, D. 1978a model for flow in the viscous sublayer. In Workshop on Coherent Structure of Turbulent Boundary Layers, p. 462. Lehigh University.
Corino, E. R. & Brodkey. R. S. 1969 A visual investigation of the wall region in turbulent flow. J. Fluid Mech. 37, 1.Google Scholar
Finlayson, B. A. 1972 The Method of Weighted Residuals and Variational Principles. Academic.
Glansdorff, P. & Prigogine, L. 1971 Thermodynamic Theory of Structure, Stability and Fluctuations. Wiley-Interscience.
Görtler, H. 1940 über eine dreidimensionale Instabilität laminarer Grenzschichten an konkaven Wänden. Nachr. Ges. Wiss. Göttingen, New Ser. 2, no. 1.Google Scholar
Görtler, H. & Witting. H. 1958 Theorie der sekundären Instabilität der laminaren Grenzschichten. In Boundary Layer Research (ed. H. Görtler), p. 110. Springer.
Greenspan, H. P. & Benny, D. J. 1963 On shear-layer instability, breakdown and transition. J. Fluid Mech. 15, 133.Google Scholar
Kim, H. T., Kline, S. J. & Reynolds, W. C. 1971 The production of the wall region in turbulent flow. J. Fluid Mech. 50, 133.Google Scholar
Haken, H. 1978 Synergetics. Springer.
Klebanoff, P. S. 1955 Characteristics of turbulence in a boundary layer with zero pressure gradient. NACA Rep. 1247.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
Kline, S. J., Reynolds, W. C., Schraub, F. A. & Rundtadler, P. W. 1967 The structure of turbulent boundary layers. J. Fluid Mech. 30, 741.Google Scholar
Launder, B. E. & Spalding, D. B. 1972 Mathematical Models of Turbulence. Academic.
Prandtl, L. 1925 über die ausgebildete Turbulenz. Z. angew. Math. Mech. 5, 136.Google Scholar
Praturi, A. K. & Brodkey, R. S. 1978 A stereoscopic visual study of coherent structures in turbulent shear flow. J. Fluid Mech. 89, 251.Google Scholar
Rao, K. N., Narasimha, R. & Narayanan, M. A. B. 1971 Bursting in a turbulent boundary layer. J. Fluid Mech. 48, 339.Google Scholar
Schlichting, H. 1968 Boundary Layer Theory. McGraw-Hill.
Swearingen, J. D. & Blackwelder, R. F. 1987 The growth and breakdown of streamwise vortices in the presence of a wall. J. Fluid Mech. 182, 225.Google Scholar
Taylor, G. I. 1923 Stability of a viscous liquid contained between two rotating cylinders.. Phil. Trans. R. Soc. Lond. A 223, 289.Google Scholar
Terada, T. 1928 Some experiments on periodic columnar formation of vortices caused by convection. Tokyo Imperial Univ. Aero. Res. Inst. Rep. 3 (31).Google Scholar
Willmarth, W. W. & Lu, S. S. 1972 Structure of the Reynolds stress near the wall. J. Fluid Mech. 55, 65.Google Scholar