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Nonlinear critical layers in the boundary layer on a rotating disk

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Abstract

The work of Gregory, Stuart and Walker (1955, Proc R Soc Ser A 406:93–106) and Hall (1986, Phil Trans R Soc London Ser A 248:155–199) is extended to include nonlinear effects for the stationary cross-flow vortex. It is shown that amplitude-dependent neutral modes are described by a forced Haberman equation. The corrections to the neutral wavenumbers and waveangles are derived and it is suggested that the nonlinear neutral modes can have wavenumbers decreased by an O(1) amount as compared to linear theory.

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Authors and Affiliations

  1. School of Mathematics, University of Manchester, Manchester, M13 9PL, UK

    J. S. B. Gajjar

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  1. J. S. B. Gajjar
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Correspondence to J. S. B. Gajjar.

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Gajjar, J.S.B. Nonlinear critical layers in the boundary layer on a rotating disk. J Eng Math 57, 205–217 (2007). https://doi.org/10.1007/s10665-006-9096-4

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  • DOI: https://doi.org/10.1007/s10665-006-9096-4

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