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  • Journal of Fluid Mechanics, Volume 607
  • July 2008, pp. 267-277

Convective instability and transient growth in steady and pulsatile stenotic flows

  • H. M. BLACKBURN (a1), S. J. SHERWIN (a2) and D. BARKLEY (a3)
  • DOI:
  • Published online: 25 July 2008

We show that suitable initial disturbances to steady or long-period pulsatile flows in a straight tube with an axisymmetric 75%-occlusion stenosis can produce very large transient energy growths. The global optimal disturbances to an initially axisymmetric state found by linear analyses are three-dimensional wave packets that produce localized sinuous convective instability in extended shear layers. In pulsatile flow, initial conditions that trigger the largest disturbances are either initiated at, or advect to, the separating shear layer at the stenosis in phase with peak systolic flow. Movies are available with the online version of the paper.

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H. M. Blackburn & S. J. Sherwin 2004 Formulation of a Galerkin spectral element–Fourier method for three-dimensional incompressible flows in cylindrical geometries. J. Comput. Phys. 197 (2), 759778.

J.-M. Chomaz 2005 Global instabilities in spatially developing flows: non-normality and nonlinearity. Annu. Rev. Fluid Mech. 37, 357392.

C. Cossu & J. M. Chomaz 1997 Global measures of local convective instabilities. Phys. Rev. Lett. 78, 43874390.

A. M. A. Khalifa & D. P. Giddens 1981 Characterization and evolution of poststenotic disturbances. J. Biomech. 14 (5), 279296.

F. Mallinger & D. Drikakis 2002 Instability in three-dimensional, unsteady, stenotic flows. Intl J. Heat Fluid Flow 23, 657663.

P. J. Schmid & D. S. Henningson 2001 Stability and Transition in Shear Flows. Springer.

T. Sexl 1930 Über den von E. G. Richardson entdeckten ‘annulareffekt’. Z. Phys. 61, 349362.

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