The linear stability of a Stokes layer subjected to high-frequency perturbations

Christian Thomas, P. J. Blennerhassett, Andrew P. Bassom*, Christopher Davies

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

17 Citations (Scopus)

Abstract

Quantitative results for the linear stability of planar Stokes layers subject to small, high-frequency perturbations are obtained for both a narrow channel and a flow approximating the classical semi-infinite Stokes layer. Previous theoretical and experimental predictions of the critical Reynolds number for the classical flat Stokes layer have differed widely with the former exceeding the latter by a factor of two or three. Here it is demonstrated that only a 1 % perturbation, at an appropriate frequency, to the nominal sinusoidal wall motion is enough to result in a reduction of the theoretical critical Reynolds number of as much as 60 %, bringing the theoretical conditions much more in line with the experimentally reported values. Furthermore, within the various experimental observations there is a wide variation in reported critical conditions and the results presented here may provide a new explanation for this behaviour.

Original languageEnglish
Pages (from-to)193-218
Number of pages26
JournalJournal of Fluid Mechanics
Volume764
DOIs
Publication statusPublished - 10 Feb 2015
Externally publishedYes

Keywords

  • boundary layers
  • boundary layer stability

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