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    Cassel, K. W. and Conlisk, A. T. 2014. Unsteady separation in vortex-induced boundary layers. Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, Vol. 372, Issue. 2020, p. 20130348.

    Lang, Amy W Bradshaw, Michael T Smith, Jonathon A Wheelus, Jennifer N Motta, Philip J Habegger, Maria L and Hueter, Robert E 2014. Movable shark scales act as a passive dynamic micro-roughness to control flow separation. Bioinspiration & Biomimetics, Vol. 9, Issue. 3, p. 036017.

    Gargano, F. Sammartino, M. and Sciacca, V. 2011. High Reynolds number Navier–Stokes solutions and boundary layer separation induced by a rectilinear vortex. Computers & Fluids, Vol. 52, p. 73.

    Cassel, K W and Obabko, A V 2010. A Rayleigh instability in a vortex-induced unsteady boundary layer. Physica Scripta, Vol. T142, p. 014006.

    Eggers, Jens and Fontelos, Marco A 2009. The role of self-similarity in singularities of partial differential equations. Nonlinearity, Vol. 22, Issue. 1, p. R1.

    Bowles, Robert 2007. Lighthill and the triple-deck, separation and transition. Journal of Engineering Mathematics, Vol. 56, Issue. 4, p. 445.

    Bowles, Robert Davies, Christopher Marshall, James and Smith, Frank 2005. 4th AIAA Theoretical Fluid Mechanics Meeting.

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    Conlisk, A. Terrance Cassel, Kevin and Smith, Chuck 2005. 4th AIAA Theoretical Fluid Mechanics Meeting.

    Allen, T. 2004. The evolution of free-disturbances in a two-dimensional nonlinear critical layer. European Journal of Mechanics - B/Fluids, Vol. 23, Issue. 6, p. 797.

    Cassel, Kevin and Obabko, Aleksandr 2004. 42nd AIAA Aerospace Sciences Meeting and Exhibit.

    Lagrée, Pierre-Yves 2001. Removing the marching breakdown of the boundary-layer equations for mixed convection above a horizontal plate. International Journal of Heat and Mass Transfer, Vol. 44, Issue. 17, p. 3359.

    Cassel, Kevin and Obabko, Aleksandr 1999. 37th Aerospace Sciences Meeting and Exhibit.

    Wu, J. Zhu, F. Tramel, R. and Yin, X. 1999. 30th Fluid Dynamics Conference.

    Cassel, K. and Cassel, K. 1997. 28th Fluid Dynamics Conference.

    Dodia, B. Doorly, D. Smith, F. Dodia, B. Doorly, D. and Smith, F. 1997. 28th Fluid Dynamics Conference.

  • Journal of Fluid Mechanics, Volume 315
  • May 1996, pp. 223-256

The onset of instability in unsteady boundary-layer separation

  • K. W. Cassel (a1), F. T. Smith (a2) and J. D. A. Walker (a1)
  • DOI:
  • Published online: 01 April 2006

The process of unsteady two-dimensional boundary-layer separation at high Reynolds number is considered. Solutions of the unsteady non-interactive boundary-layer equations are known to develop a generic separation singularity in regions where the pressure gradient is prescribed and adverse. As the boundary layer starts to separate from the surface, however, the external pressure distribution is altered through viscous—inviscid interaction just prior to the formation of the separation singularity; hitherto this has been referred to as the first interactive stage. A numerical solution of this stage is obtained here in Lagrangian coordinates. The solution is shown to exhibit a high-frequency inviscid instability resulting in an immediate finite-time breakdown of this stage. The presence of the instability is confirmed through a linear stability analysis. The implications for the theoretical description of unsteady boundary-layer separation are discussed, and it is suggested that the onset of interaction may occur much sooner than previously thought.

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Journal of Fluid Mechanics
  • ISSN: 0022-1120
  • EISSN: 1469-7645
  • URL: /core/journals/journal-of-fluid-mechanics
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