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Superasymptotic Perturbation Analysis of the Kelvin-Helmholtz Instability of Supersonic Shear Layers

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Differential Equations and Nonlinear Mechanics

Part of the book series: Mathematics and Its Applications ((MAIA,volume 528))

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Abstract

A global asymptotic analysis of the traveling wave Kelvin-Helmholtz instability of a supersonic, finite-width velocity shear layer is carried out. The resulting solution, comprising a composite WKBJ and boundary-layer solution, satisfying outgoing, spatially damping radiative wave boundary conditions, has important applications in elucidating the energy transfer between the fluid and the unstable traveling wave solutions. Limitations in the use of this global asymptotic solution arise from the well-known directional character of the “connection formulae” at the turning points of the potential. In order to overcome these limitations, a superasymptotic analysis is developed based on recent work of Dingle, Berry and others. The structure of the resulting traveling wave solutions agrees closely with previously computed numerical solutions. In addition, the condition for the occurrence of the traveling wave instability is derived, and the absence of this mode in compressible tangential velocity discontinuities is explained.

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Authors and Affiliations

  1. Department of Mathematics, University of Central Florida, Orlando, Florida, 32816-1364, USA

    S. Roy Choudhury

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  1. S. Roy Choudhury
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Editors and Affiliations

  1. University of Central Florida, USA

    K. Vajravelu

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© 2001 Kluwer Academic Publishers

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Choudhury, S.R. (2001). Superasymptotic Perturbation Analysis of the Kelvin-Helmholtz Instability of Supersonic Shear Layers. In: Vajravelu, K. (eds) Differential Equations and Nonlinear Mechanics. Mathematics and Its Applications, vol 528. Springer, Boston, MA. https://doi.org/10.1007/978-1-4613-0277-3_4

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  • DOI: https://doi.org/10.1007/978-1-4613-0277-3_4

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-0-7923-6867-0

  • Online ISBN: 978-1-4613-0277-3

  • eBook Packages: Springer Book Archive

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