Hostname: page-component-586b7cd67f-vdxz6 Total loading time: 0 Render date: 2024-11-28T07:36:24.738Z Has data issue: false hasContentIssue false
  • English
  • Français

On the non-linear response of a marginally unstable plane parallel flow to a three-dimensional disturbance

Part of: Hydrodynamic stability Incompressible viscous fluids

Published online by Cambridge University Press:  26 February 2010

L. M. Hocking  and
K. Stewartson
L. M. Hocking
Affiliation:
Department of Mathematics, University College London.
K. Stewartson
Affiliation:
Department of Mathematics, University College London.
Get access

Extract

The properties of the solution of the differential equation governing the evolution of localised line-centred disturbances to a marginally unstable plane parallel flow were described by Hocking and Stewartson (1972). A corresponding study of the properties when the initial disturbance is point-centred is presented here. A localised burst at a finite time can be produced, for certain values of the coefficients which can be determined analytically. When the equation permits solutions with circular symmetry, two kinds of bursting solutions, as well as solutions which remain finite, are possible, but the boundary between bursting and finite solutions could not be determined analytically.

MSC classification

Secondary: 76D99: None of the above, but in this section 76E30: Nonlinear effects
Type
Research Article
Information
Mathematika , Volume 18 , Issue 2 , December 1971 , pp. 219 - 239
Copyright
Copyright © University College London 1971

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

Davies, S. J. and White, C. M., 1928, Proc. Roy. Soc., 119, 92–107.Google Scholar
Douglas, J. and Gunn, J. E., 1964, Numerische Mathematik, 4, 428–453.CrossRefGoogle Scholar
Grohne, D., 1969, A V A Gottingen Rep., 69-A-30.Google Scholar
Hocking, L. M. and Stewartson, K., 1972, Proc. Roy. Soc. A., 326, 289–313.Google Scholar
Hocking, L. M. and Stewartson, K., and Stuart, J. T., 1972, 51, 705–795. J. Fluid Mech.CrossRefGoogle Scholar
Kao, T. W. and Park, C., 1970, J. Fluid Mech., 43, 145–164.CrossRefGoogle Scholar
Peaceman, D. W. and Rachford, H. H., 1955, J. Soc. Ind. Appl. Math., 3, 28–41.CrossRefGoogle Scholar
Pekeris, C. L. and Shkoller, B., 1967, J. Fluid Mech., 29, 31–38.CrossRefGoogle Scholar
Reynolds, W. C. and Potter, M. C., 1967, J. Fluid Mech., 27, 465–492.CrossRefGoogle Scholar
Schiller, L., 1923, Z. angew. Math. Mech., 3, 2–13.CrossRefGoogle Scholar
Stewartson, K. and Stuart, J. T., 1971, J. Fluid Mech., 48, 529–545.CrossRefGoogle Scholar
Stuart, J. T., 1960, J. Fluid Mech., 9, 352–370.CrossRefGoogle Scholar
Stuart, J. T., 1971, Annual Review of Fluid Mechanics., 3, 347–370. (Annual Reviews Inc., Palo Alto, Calif.)CrossRefGoogle Scholar