Hostname: page-component-77c89778f8-rkxrd Total loading time: 0 Render date: 2024-07-19T10:37:07.421Z Has data issue: false hasContentIssue false
  • English
  • Français

Evolution of disturbances in stagnation-point flow

Published online by Cambridge University Press:  26 April 2006

W. O. Criminale ,
T. L. Jackson  and
D. G. Lasseigne
W. O. Criminale
Affiliation:
Department of Applied Mathematics, University of Washington, Seattle, WA 98195, USA
T. L. Jackson
Affiliation:
Institute for Computer Applications in Science and Engineering, NASA Langley Research Center, Hampton, VA 23681, USA
D. G. Lasseigne
Affiliation:
Department of Mathematics and Statistics, Old Dominion University, Norfolk, VA 23529, USA
Get access Rights & Permissions [Opens in a new window]

Abstract

The evolution of three-dimensional disturbances in an incompressible three-dimensional stagnation-point flow in an inviscid fluid is investigated. Since it is not possible to apply classical normal-mode analysis to the disturbance equations for the fully three-dimensional stagnation-point flow to obtain solutions, an initial-value problem is solved instead. The evolution of the disturbances provides the necessary information to determine stability and indeed the complete transient as well. It is found that when considering the disturbance energy, the planar stagnation-point flow, which is independent of one of the transverse coordinates, represents a neutrally stable flow whereas the fully three-dimensional flow is either stable or unstable, depending on whether the flow is away from or towards the stagnation point in the transverse direction that is neglected in the planar stagnation point.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 270 , 10 July 1994 , pp. 331 - 348
Copyright
© 1994 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

Brattkus, K. & Davis, S. H. 1991 The linear stability of plane stagnation-point flow against general disturbances. Q. J. Mech. Appl. Maths 44, 135–146.Google Scholar
Criminale, W. O. & Drazin, P. G. 1990 The evolution of linearized perturbations of parallel flows. Stud. Appl. Maths 83, 123–157.Google Scholar
Davey, A. 1961 Boundary-layer flow at a saddle point of attachment. J. Fluid Mech. 38, 593–610.Google Scholar
Eady, E. A. 1949 Long waves and cyclone waves. Tellus 1, 33–52.Google Scholar
Farrell, B. F. 1989 Transient development in confluent and diffluent flow. J. Atmos. Sci. 46, 3279–3288.Google Scholar
Hall, P., Malik, M. R. & Poll, D. I. A. 1984 On the stability of an infinite swept attachment line boundary layer. Proc. R. Soc. Lond. A 395, 229–245.Google Scholar
Kazakov, A. V. 1991 Effect of surface temperature on the stability of the swept attachment line boundary layer. Fluid Dyn. 25, 875–878.Google Scholar
Kelvin, W. 1887 Rectilinear motion of viscous fluid between two parallel plates. Phil. Mag. 24, 188–196.Google Scholar
Lasseigne, D. G. & Jackson, T. L. 1992 Stability of a non-orthogonal stagnation flow to three dimensional disturbances. Theor. Comput. Fluid Dyn. 3, 207–218.Google Scholar
Lasseigne, D. G., Jackson, T. L. & Hu, F. Q. 1992 Temperature and suction effects on the instability of an infinite swept attachment line. Phys. Fluids A 4, 2008–2012.Google Scholar
Lyell, M. J. & Huerre, P. 1985 Linear and nonlinear stability of plane stagnation flow. J. Fluid Mech. 161, 295–312.Google Scholar
Orr, W. M’F. 1907a The stability or instability of the steady motions of a perfect liquid and a viscous liquid. Part I. Proc. R. Irish Acad. 27, 9–68.Google Scholar
Orr, W. M’F. 1907b The stability or instability of the steady motions of a perfect liquid and a viscous liquid. Part II. Proc. R. Irish Acad. 27, 69–138.Google Scholar
Spalart, P. R. 1989 Direct numerical study of leading-edge contamination. AGARD Conf. Proc. 438, 51–5.13.Google Scholar
Wilson, S. D. R. & Gladwell, I. 1978 The stability of a two-dimensional stagnation flow to three-dimensional disturbances. J. Fluid Mech. 84, 517–527.Google Scholar