Uniformly-valid asymptotic solutions to the Orr-Sommerfeld equation using multiple scales

Lyle N. Long

doi:10.1007/BF00127462

Uniformly-valid asymptotic solutions to the Orr-Sommerfeld equation using multiple scales

Lyle N. Long

Aerospace Engineering

Research output: Contribution to journal › Article › peer-review

2 Scopus citations

Abstract

The Orr-Sommerfeld equation is studied using the method of multiple scales. The leading-order uniformly-valid asymptotic solutions are obtained without recourse to heuristic methods for two different types of velocity profiles. Solutions were obtained for arbitrary velocity profiles without inflection or critical points and for profiles with simultaneous inflection and critical points. These are shown to reproduce previously obtained solutions in the inner and outer regions.

Original language	English (US)
Pages (from-to)	167-178
Number of pages	12
Journal	Journal of Engineering Mathematics
Volume	21
Issue number	3
DOIs	https://doi.org/10.1007/BF00127462
State	Published - Sep 1 1987

All Science Journal Classification (ASJC) codes

Mathematics(all)
Engineering(all)

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10.1007/BF00127462

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title = "Uniformly-valid asymptotic solutions to the Orr-Sommerfeld equation using multiple scales",

abstract = "The Orr-Sommerfeld equation is studied using the method of multiple scales. The leading-order uniformly-valid asymptotic solutions are obtained without recourse to heuristic methods for two different types of velocity profiles. Solutions were obtained for arbitrary velocity profiles without inflection or critical points and for profiles with simultaneous inflection and critical points. These are shown to reproduce previously obtained solutions in the inner and outer regions.",

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N2 - The Orr-Sommerfeld equation is studied using the method of multiple scales. The leading-order uniformly-valid asymptotic solutions are obtained without recourse to heuristic methods for two different types of velocity profiles. Solutions were obtained for arbitrary velocity profiles without inflection or critical points and for profiles with simultaneous inflection and critical points. These are shown to reproduce previously obtained solutions in the inner and outer regions.

AB - The Orr-Sommerfeld equation is studied using the method of multiple scales. The leading-order uniformly-valid asymptotic solutions are obtained without recourse to heuristic methods for two different types of velocity profiles. Solutions were obtained for arbitrary velocity profiles without inflection or critical points and for profiles with simultaneous inflection and critical points. These are shown to reproduce previously obtained solutions in the inner and outer regions.

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Uniformly-valid asymptotic solutions to the Orr-Sommerfeld equation using multiple scales

Abstract

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