Hostname: page-component-78c5997874-t5tsf Total loading time: 0 Render date: 2024-11-10T07:20:40.127Z Has data issue: false hasContentIssue false
  • English
  • Français

Nonlinear instability and break-up of separated flow

Published online by Cambridge University Press:  21 April 2006

S. N. Brown ,
H. K. Cheng  and
F. T. Smith
S. N. Brown
Affiliation:
Department of Mathematics, University College London. Gower Street, London WC1E 6BT, UK
H. K. Cheng
Affiliation:
Department of Aerospace Engineering, University of Southern California, Los Angeles, California, USA
F. T. Smith
Affiliation:
Department of Mathematics, University College London. Gower Street, London WC1E 6BT, UK
Get access Rights & Permissions [Opens in a new window]

Abstract

Unsteady effects in a separated recirculating eddy beneath a subsonic or supersonic mainstream are considered, with emphasis on nonlinear properties. The eddy is slender and predominantly inviscid, its length being comparable with, or less than, the chord of an airfoil, for instance. It is found, from the study of a family of integro-differential equations, that the planar eddy can break up nonlinearly within a finite time, causing an eruption into the main stream and setting up a subsequent Euler stage in the unsteady motion. Comparisons with recent experiments and further applications of the theory are discussed.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 193 , August 1988 , pp. 191 - 216
Copyright
© 1988 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

Abramowitz, M. & Stegun, I. A. 1965 Handbook of Mathematical Functions. Dover Press.
Brotherton-Ratcliffe, R. V. & Smith, F. T. 1987 Mathematika 34, 86.
Davis, R. T. & Werle, M. J. 1982 In Numerical and Physical Aspects of Aerodynamic Flows (ed. T. Cebeci). Springer.
Dovgal, A. V., Kozlov, V. V. & Simonov, O. A. 1987 In Boundary-Layer Separation (ed. F. T. Smith & S. N. Brown). Springer.
Drazin, P. G. & Reid, W. H. 1981 Hydrodynamic Stability. Cambridge University Press.
Elliott, J. W., Cowley, S. J. & Smith, F. T. 1983 Geophys. Astrophys. Fluid Dyn. 25, 77.
Gaster, M. 1966 AGARD Conf. Proc. 4, 819. (Also Aeronaut. Res. Council Rep. & Mem. no. 3595, 1969.)
Goldstein, M. E. 1984 J. Fluid Mech. 145, 71.
Gruber, K., Bestek, H. & Fasel, H. 1987 AIAA paper 87-1256.
Henkes, R. A. W. M. & Veldman, A. E. P. 1987 In Boundary-Layer Separation (ed. F. T. Smith & S. N. Brown). Springer.
Kozlov, V. V. 1987 In Boundary-Layer Separation (ed. F. T. Smith & S. N. Brown). Springer.
Mezaris, T. B., Telionis, D. P., Barbi, C. & Jones, G. S. 1988 Proc. R. Soc. Lond. A, to appear.
Mueller, T. J. & Batill, S. M. 1980 AIAA paper 80-1440.
Peridier, V. J., Smith, F. T. & Walker, J. D. A. 1988 AIAA paper 88-0604.
Smith, F. T. 1985a Utd Tech. Res. Cent., E. Hartford, ct, USA Rep. UT85-55: also in Stability of Time Dependent and Spatially Varying Flows (ed. D. L. Dwoyer & M. Y. Hussain). Springer 1987.
Smith, F. T. 1985b J. Fluid Mech. 155, 175.
Smith, F. T. & Burggraf, O. R. 1985 Proc. R. Soc. Lond. A 399, 25
Stewart, P. A. & Smith, F. T. 1987 Proc. R. Soc. Lond. A 409, 229
Tani, I. 1964 Prog. Aeronaut. Sci. 5, 70.
Van Dommelen, L. L. 1981 Ph.D. thesis, Cornell University.
Van Dyke, M. 1982 An Album of Fluid Motion. Parabolic Press.
Varley, E. & Blythe, P. 1983 Stud. Appl. Maths 68, 103.