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Direct numerical simulations of small disturbances in the classical Stokes layer

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Abstract

Direct numerical simulations are used to investigate the stability characteristics of the classical semi-infinite Stokes layer that is generated by an oscillating flat plate. The calculations are based upon a velocity–vorticity formulation of the governing equations which allows efficient tracking of the time evolution of disturbances. The neutral-stability curve for two-dimensional disturbances was computed and found to agree well with the predictions of earlier semi-analytical studies. Further previously determined properties of two-dimensional disturbances in a Stokes layer were also compared to the results obtained by direct numerical simulation. The two-dimensional neutral stability results were then used to validate the extension of the direct numerical solution code to three-dimensional disturbances in the form of oblique waves.

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Authors and Affiliations

  1. School of Mathematics and Statistics, University of Western Australia, Crawley, 6009, Australia

    Christian Thomas & Andrew P. Bassom

  2. School of Mathematics and Statistics, University of New South Wales, Sydney, 2052, Australia

    P. J. Blennerhassett

  3. School of Mathematics, Cardiff University, Cardiff, CF24 4AG, UK

    Christopher Davies

Authors
  1. Christian Thomas
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  2. Andrew P. Bassom
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  3. P. J. Blennerhassett
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  4. Christopher Davies
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Correspondence to Andrew P. Bassom.

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Thomas, C., Bassom, A.P., Blennerhassett, P.J. et al. Direct numerical simulations of small disturbances in the classical Stokes layer. J Eng Math 68, 327–338 (2010). https://doi.org/10.1007/s10665-010-9381-0

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  • DOI: https://doi.org/10.1007/s10665-010-9381-0

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