Transient growth and bypass transition in stenotic flow with a physiological waveform

  • X. Mao
  • S. J. Sherwin
  • H. M. Blackburn
Original Article


A direct analysis method is applied to compute optimal transient growth initial conditions for physiologically relevant pulsatile flows in a smooth axisymmetric stenosis with 75% occlusion. The flow waveform employed represents phase-average measurements obtained in the human common carotid artery. Floquet analysis shows that the periodic flow is stable to infinitesimal eigenmodal-type perturbations that would grow from one cycle to the next at the Reynolds numbers considered. However, the same flows display explosive transient growth of optimal disturbances, with our analysis predicting disturbance energy growths of order 1025 within half a pulse period at a mean bulk flow Reynolds number Re = 300, which is significantly lower than the physiological value of Re = 450 at this location. Direct numerical simulation at Re = 300 shows that when the base flow is perturbed a small amount with the optimal growth initial condition, the disturbance grows rapidly in time in agreement with the linear analysis, and saturates to provide a locally turbulent state within half a pulse period. This transition resulting from non-normal growth mechanisms shows the flow exhibits bypass transition to turbulence. Our analysis suggests that this route to localized turbulent states could be relatively common in human arterial flows.


Physiological flow Transient growth Stability Global modes Bypass transition 


47.63.Cb 47.15.Fe 47.20.Ib 47.27.Nf 


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Copyright information

© Springer-Verlag 2009

Authors and Affiliations

  1. 1.Department of AeronauticsImperial CollegeLondonUK
  2. 2.Department of Mechanical and Aerospace EngineeringMonash UniversityClaytonAustralia

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