Recent Development in the Asymptotic Theory of Vortex Breakdown
Abstract
Slender vortex dynamics is dominated by two very different sources of nonlinearity. There is first the nonlinearity inherent in the motion of a vortex filament due to nonlocal self-induction and local curvature effects. Secondly, there is a nonlinear core flow, which produces local axisymmetric breakdown under suitable boundary and initial conditions. Both these aspects of slender vortex dynamics have been studied in the past using tools of matched asymptotic analysis. The non-axisymmetric spiral mode of vortex breakdown appears to be due to an interaction of the core flow and the vortex centerline motion. Thus, it is a challenge to derive a unified formulation in the slender vortex limit which includes both the filament dynamics and nontrivial core structures.
Keywords
Direct Numerical Simulation Vortex Tube Critical Layer Vortex Breakdown Outer SolutionPreview
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References
- Benjamin T.B. (1967) Some developments in the theory of vortex breakdown, J. Fluid Mech 28, 65–84.MATHCrossRefGoogle Scholar
- Callegari, A. and Ting, L. (1978) Motion of a Curved Vortex Filament with Decaying Vortical Core and Axial Velocity, SIAM J. Appl. Math.35, pp. 148–175.MathSciNetMATHCrossRefGoogle Scholar
- Escudier M.P., Keller J.J. (1983) Vortex Breakdown: A two Stage Transition, AGARD CP, 342 Google Scholar
- Klein R., Ting L. (1992) Vortex filaments with axial core structure variation, Appl. Math. Lett.5, pp. 99–103.MathSciNetMATHCrossRefGoogle Scholar
- Krause E. (1989) Pressure Variation in Axially Symmetric Breakdown, Conf. Proc. Proc. “Col-loquium on Vortex Breakdown”, RWTH Aachen, Febr. 11./12., (1989).Google Scholar
- Reyna L.G., Menne S. (1988) Numerical Prediction of Flow in Slender Vortices, Computers and Fluids 16, pp. 239–256.MATHCrossRefGoogle Scholar
- Schmitz M. (1995) Axiale Entwicklung der Kernstruktur schlanker Wirbelfäden, Dissertation, RWTH-Aachen.Google Scholar
- Ting L., Klein R. (1991) Viscous Vortical Flows,Lecture Notes in Physics, 374 Springer-Verlag.MATHGoogle Scholar
- Weimer M. (1995), Personal communication, Aerodyn. Institut, RWTH Aachen, Germany (See also Althaus’ contribution to this volume).Google Scholar