Hostname: page-component-78c5997874-g7gxr Total loading time: 0 Render date: 2024-11-17T20:17:29.422Z Has data issue: false hasContentIssue false
  • English
  • Français

Similarity solutions of the two-dimensional unsteady boundary-layer equations

Published online by Cambridge University Press:  26 April 2006

Philip K. H. Ma  and
W. H. Hui
Philip K. H. Ma
Affiliation:
University of Waterloo, Waterloo, Ontario, Canada. N2L 3G1
W. H. Hui
Affiliation:
University of Waterloo, Waterloo, Ontario, Canada. N2L 3G1
Get access Rights & Permissions [Opens in a new window]

Abstract

The method of Lie group transformations is used to derive all group-invariant similarity solutions of the unsteady two-dimensional laminar boundary-layer equations. A new method of nonlinear superposition is then used to generate further similarity solutions from a group-invariant solution. Our results are shown to include all the existing solutions as special cases. A detailed analysis is given to several classes of solutions which are also solutions to the full Navier–Stokes equations and which exhibit flow separation.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 216 , July 1990 , pp. 537 - 559
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

Blasius, H. 1908 Z. Angew. Math. Phys. 56, 1–37.
Char, B. W., Geddes, K. O., Gonnet, G. H., Monagan, M. B. & Watt, S. M. 1988 Maple Reference Manual, 5th edn. Symbolic Computation Group, University of Waterloo.
Falkner, V. M. & Skan, S. W. 1931 Some approximate solutions of the boundary-layer equations. Phil. Mag. 12 (7), 865–896.Google Scholar
Glauert, M. B. 1956 The laminar boundary layer on oscillating plates and cylinders. J. Fluid Mech. 1, 97–110.Google Scholar
Hiemenz, K. 1911 Die Grenzschicht an einem in den gleichformigen Flussigkeitsstrom eingetauchten geraden Kreiszylinder. Dinglers Polytech. J. 326, 321.Google Scholar
Hui, W. H. 1971 A solution for hypersonic flow past slender bodies. J. Fluid Mech. 48, 23–31.Google Scholar
Hui, W. H. & Tobak, M. 1989 Topology of steady and unsteady three-dimensional incompressible separated flows. In Continuum Mechanics and Its Applications (ed. G. A. C. Graham & S. K. Malik), pp. 519–542. Hemisphere.
Olver, P. J. 1986 Applications to Lie Groups to Differential Equations. Springer.
Ovsiannikov, L. V. 1982 Group Analysis of Differential Equations. Academic. (Translation edited byW. F. Ames.)
Rayleigh, Lord 1911 On the motion of solid bodies through viscous liquid. Phil. Mag. 21, 697–711.Google Scholar
Rott, N. 1956 Unsteady viscous flow in the vicinity of a stagnation point. Q. Appl. Maths. 13, 444–451.Google Scholar
Tobak, M. 1990 Topology of pressure surfaces in three-dimensional separated flows. NASA TM (to be published).Google Scholar
Williams, J. C. & Johnson, W. D. 1974 Semisimilar solutions to unsteady boundary-layer flows including separation. AIAA J. 12, 1388–1393.Google Scholar