Abstract
Vortex breakdown is the abrupt change in the core of a longitudinal vortex leading, depending on the magnitude of the swirl to axial velocity ratio, to either a large recirculating bubble or a spiralling or helical motion of the central filament. Experiments and numerical simulations of such flows show a marked instability in the breakdown location and a parametric sensitivity that suggest a subtle ellipticity in what otherwise appears to be a strongly parabolic problem. That this is in fact the case is shown analytically. The analysis also sheds further light on the etiology of breakdown, particularly the role of viscosity. The relevance of breakdown of longitudinal vortices to boundary-layer transition, particularly in its latter stages, is discussed.
The author would like to acknowledge support from ICASE in the summers of 1990 and 1991 and from NSF/DARPA, Grant DMS-8919074 through the Center for Pure and Applied Mathematics at Berkeley.
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© 1992 Springer-Verlag New York, Inc.
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Berger, S.A. (1992). Ellipticity in the Vortex Breakdown Problem. In: Hussaini, M.Y., Kumar, A., Streett, C.L. (eds) Instability, Transition, and Turbulence. ICASE NASA LaRC Series. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-2956-8_11
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DOI: https://doi.org/10.1007/978-1-4612-2956-8_11
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