Laminar-Turbulent Transition pp 625-630 | Cite as
On the connection between cross-flow vortices and attachment-line instabilities
Abstract
The connection between cross-flow vortices and attachment-line instabilities is identified in the swept Hiemenz flow. Starting from an exact description of the perturbation vorticity field in the free-stream based on confluent hypergeometric functions, we derive an eigenvalue problem that yields a more complete set of the attachment-line instabilities than previously possible. For eigenvalues of the form −n/2, n an integer, the hypergeometric functions reduce to Hermite polynomials that fully describe the previously known instabilities, which, however, do not connect to the cross-flow vortices. For eigenvalues with both real and imaginary parts, a new family of attachment-line instabilities appears, having members that connect to the cross-flow modes. (Supported by DFG project Da 183/3-2)
Keywords
Neutral Curve Neutral Stability Curve Confluent Hypergeometric Function Attachment Line Parabolized Stability EquationPreview
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References
- 1.Görtler, H. (1955) Dreidimensionale Instabilität der ebenen Staupunktströmung gegenüber wirbelartigen Störungen (eds. H. Görtler, W. Tollmien), page 304. Vieweg und Sohn.Google Scholar
- 2.Hxmmerlin, G. (1955) Zur Instabilitätstheorie der ebenen Staupunkströmung (eds. H. Görtler, W. Tollmien), page 315. Vieweg und Sohn.Google Scholar
- 3.Hall, P., Malik, M., Poll, D. I. (1984) On the stability of an infinite swept attachment-line boundary layer. Proc. R. Soc. Lond. A, 395: 229–245.MathSciNetADSCrossRefGoogle Scholar
- 4.Spalart, P. R. (1988) Direct numerical study of leading-edge contamination. In Fluid Dyn. of 3D Turb. Shear Flows and Transition, CP-438. AGARD, 1988.Google Scholar
- 5.Lin, R. S., Malik, M. R. (1996) On the stability of attachment-line boundary layers. part 1. the incompressible swept Hiemenz flow. J. Fluid Mech., 311: 239.MathSciNetADSzbMATHCrossRefGoogle Scholar
- 6.Theofilis, V. (1997) On the verification and extension of the GörtlerHämmerlin assumption in three-dimensional incompressible swept attachment-line boundary layer flow. In DLR-IB 223–97 A44.Google Scholar
- 7.Hall, P., Seddougui, S. O. (1990) Wave interactions in a three-dimensional attachment-line boundary layer. J. Fluid Mech., 217: 367–390.ADSzbMATHCrossRefGoogle Scholar
- 8.Bertolotti, F. P. (1994) A partial simulation of receptivity and transition in 3-d boundary layers. In Laminar-Turbulent Transition. Proc. 4th IUTAM Symp., Sendai, Japan, Springer-Verlag, 1995.Google Scholar
- 9.Spalart, P. R. (1989) Direct numerical study of crossflow instability. In Laminar-Turbulent Transition. Proc. 3th IUTAM Symp., Toulouse, France, Springer-Verlag, 1990.Google Scholar
- 10.Bateman, H. (1953) Higher Transcendental Functions,volume 1. MacGraw-Hill.Google Scholar