Abstract
The weakly nonlinear evolution of an inviscid marginally unstable wave growing on a boundary layer supporting a streamwise vortex structure is investigated. The nonlinear growth of the wave is found to be controlled by the diffusion layer located at the edge of the critical layer associated with the wave. The evolution equation is found to depend on the upstream history of the wave and the solution of the equation suggests that the wave either restructures the mean state so as to make it stable or develops a singularity at a finite distance downstream of the point of neutral stability.
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References
Blackaby, N. D. & Hall, P. 1995 The nonlinear evolution of the inviscid secondary instability of streamwise vortex structures. To appear in Phil. Trans. Roy. Soc. Lond.
Hall, P. 1988 The nonlinear development of Görtier vortices in growing boundary layers. J. Fluid Mech. 193, 243–266.
Hall, P. & Horseman, N.J. 1991 The linear inviscid secondary instability of longitudinal vortex structures in boundary layers. J. Fluid Mech. 232, 357–375.
Hall, P. & Lakin, W.D. 1988 The fully nonlinear development of Görtier vortices in growing boundary layers. Proc. R. Soc. Lond. A 415, 421–444.
Hall, P. & Seddougui, S. O. 1989 On the onset of three-dimensionality and time-dependence in the Görtier vortex problem. J. Fluid Mech. 204, 405–420.
Hall, P. & Smith, F.T. 1991 On strongly nonlinear vortex/wave interactions in boundary-layer transition. J. Fluid Mech. 227, 641–666.
Hickernell, F.J. 1984 Time-dependent critical layers in shear flows on the beta-plane. J. Fluid Mech. 142, 431–449.
Li, F. & Malik, M. 1995 On the breakdown of Görtier vortices: nonlinear development and secondary instabilities. To appear in J. Fluid Mech.
Smith, F.T., Brown, S.N. & Brown, P.G. 1993 Initiation of three-dimensional nonlinear transition paths from an inflectional profile. Eur. J. Mech. B/Fluids 12, 447–473.
Swearingen, J.D. & Blackwelder, R.F. 1987 The growth and breakdown of streamwise vortices in the presence of a wall. J. Fluid Mech. 182, 255–290.
Wu, X. 1993 On critical-layer and diffusion-layer nonlinearity in the three-dimensional stage of boundary-layer transition. Proc. R. Soc. Lond. A 443, 95–106.
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© 1996 Kluwer Academic Publishers
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Blackaby, N.D. (1996). The Nonlinear Evolution of Inviscid Secondary Instabilities of a Fully Nonlinear Görtler Vortex Flow. In: Duck, P.W., Hall, P. (eds) IUTAM Symposium on Nonlinear Instability and Transition in Three-Dimensional Boundary Layers. Fluid Mechanics and Its Applications, vol 35. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-1700-2_11
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DOI: https://doi.org/10.1007/978-94-009-1700-2_11
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-010-7261-8
Online ISBN: 978-94-009-1700-2
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