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

Lyle N. Long

Research output: Contribution to journalArticle

2 Citations (Scopus)

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 languageEnglish (US)
Pages (from-to)167-178
Number of pages12
JournalJournal of Engineering Mathematics
Volume21
Issue number3
DOIs
StatePublished - Sep 1 1987

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Orr-Sommerfeld Equation
Point of inflection
Multiple Scales
Asymptotic Solution
Velocity Profile
Critical point
Valid
Method of multiple Scales
Heuristic methods
Heuristic Method
Arbitrary
Profile

All Science Journal Classification (ASJC) codes

  • Mathematics(all)
  • Engineering(all)

Cite this

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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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Uniformly-valid asymptotic solutions to the Orr-Sommerfeld equation using multiple scales. / Long, Lyle N.

In: Journal of Engineering Mathematics, Vol. 21, No. 3, 01.09.1987, p. 167-178.

Research output: Contribution to journalArticle

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