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)
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Görtler, H. (1955) Dreidimensionale Instabilität der ebenen Staupunktströmung gegenüber wirbelartigen Störungen (eds. H. Görtler, W. Tollmien), page 304. Vieweg und Sohn.
Hxmmerlin, G. (1955) Zur Instabilitätstheorie der ebenen Staupunkströmung (eds. H. Görtler, W. Tollmien), page 315. Vieweg und Sohn.
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.
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.
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.
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.
Hall, P., Seddougui, S. O. (1990) Wave interactions in a three-dimensional attachment-line boundary layer. J. Fluid Mech., 217: 367–390.
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.
Spalart, P. R. (1989) Direct numerical study of crossflow instability. In Laminar-Turbulent Transition. Proc. 3th IUTAM Symp., Toulouse, France, Springer-Verlag, 1990.
Bateman, H. (1953) Higher Transcendental Functions,volume 1. MacGraw-Hill.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2000 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Bertolotti, F.P. (2000). On the connection between cross-flow vortices and attachment-line instabilities. In: Fasel, H.F., Saric, W.S. (eds) Laminar-Turbulent Transition. IUTAM Symposia. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-03997-7_97
Download citation
DOI: https://doi.org/10.1007/978-3-662-03997-7_97
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-08752-3
Online ISBN: 978-3-662-03997-7
eBook Packages: Springer Book Archive