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Analytic structure of vortex sheet dynamics. Part 1. Kelvin–Helmholtz instability

Published online by Cambridge University Press:  20 April 2006

Daniel I. Meiron
Affiliation:
Massachusetts Institute of Technology, Department of Mathematics, Cambridge, MA 02139
Gregory R. Baker
Affiliation:
Massachusetts Institute of Technology, Department of Mathematics, Cambridge, MA 02139
Steven A. Orszag
Affiliation:
Massachusetts Institute of Technology, Department of Mathematics, Cambridge, MA 02139

Abstract

The instability of an initially flat vortex sheet to a sinusoidal perturbation of the vorticity is studied by means of high-order Taylor series in time t. All finite-amplitude corrections are retained at each order in t. Our analysis indicates that the sheet develops a curvature singularity at t = tc < ∞. The variation of tc with the amplitude a of the perturbation vorticity is in good agreement with the asymptotic results of Moore. When a is O(1), the Fourier coefficient of order n decays slightly faster than predicted by Moore. Extensions of the present prototype of Kelvin-Helmholtz instability to other layered flows, such as Rayleigh-Taylor instability, are indicated.

Type
Research Article
Copyright
© 1972 Cambridge University Press

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References

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