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

C. Thomas, P.J. Blennerhassett, Andrew Bassom, C.J. Davies

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    Abstract

    © 2014 Cambridge University Press. 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
    JournalJournal of Fluid Mechanics
    Volume764
    DOIs
    Publication statusPublished - Feb 2015

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    Reynolds number
    perturbation
    channel flow
    predictions

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    Thomas, C. ; Blennerhassett, P.J. ; Bassom, Andrew ; Davies, C.J. / The linear stability of a Stokes layer subjected to high-frequency perturbations. In: Journal of Fluid Mechanics. 2015 ; Vol. 764. pp. 193-218.
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    abstract = "{\circledC} 2014 Cambridge University Press. 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.",
    author = "C. Thomas and P.J. Blennerhassett and Andrew Bassom and C.J. Davies",
    year = "2015",
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    doi = "10.1017/jfm.2014.710",
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    The linear stability of a Stokes layer subjected to high-frequency perturbations. / Thomas, C.; Blennerhassett, P.J.; Bassom, Andrew; Davies, C.J.

    In: Journal of Fluid Mechanics, Vol. 764, 02.2015, p. 193-218.

    Research output: Contribution to journalArticle

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    T1 - The linear stability of a Stokes layer subjected to high-frequency perturbations

    AU - Thomas, C.

    AU - Blennerhassett, P.J.

    AU - Bassom, Andrew

    AU - Davies, C.J.

    PY - 2015/2

    Y1 - 2015/2

    N2 - © 2014 Cambridge University Press. 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.

    AB - © 2014 Cambridge University Press. 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.

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    JO - Journal of Fluid Mechanics.

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