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Hugh M Blackburn |
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Animation of bypass transition in pulsatile stenotic pipe flow in which the pulse waveform represents typical flow in the human common carotid artery (Mao, Sherwin & Blackburn 2010). Linear transient energy growth is extremely large, of order 1×1025 within half a pulse period for suitable intial disturbances at Reynolds number Re=300. For even a tiny seeding with the optimal initial disturbance, a puff of turbulence is generated downstream of the stenosis. This washes slowly downstream and decays during subsequent pulse cycles. Mean flow is from left to right and the stenosis is to the left of the field of view.
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Animation of transient two-dimensional convective instability in flow over a backward-facing step at Re=500 (Blackburn, Barkley & Sherwin 2008, Barkley, Blackburn & Sherwin 2008), visualised as contours of perturbation vorticity. The optimal disturbance initial condition is a wave packet that is very tightly clustered around the step edge, and grows into an array of counter-rotating rollers that fill the downstream channel, at a location past both (upper and lower) separation zones, before eventually decaying. The maximum two-dimensional energy growth at this Reynolds number is 63.1×103.

| Mode A, Re=195 | Mode B, Re=265 | Mode TW, Re=400 |
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| t=t0 | t=t0+T/2 |
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| Periodic axisymmetric state, Re=3000 | Rotating wave with 6-fold symmetry, Re=4000 |
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Instabilities of the flow produced by steady rotation of the lower lid of a cylindrical cavity with height/radius ratio H/R=2.5. At low Reynolds numbers the flow is axisymetric, steady, and has an axial vortex breakdown. The flow first becomes unstable to a periodic axisymmetric instability through a Hopf bifurcation at Re=2707, but at higher Reynolds numbers rotating waves also become unstable, and are modulated by the axisymmetric pulsation. Blackburn & Lopez (2000), Blackburn (2002), Blackburn & Lopez (2002).


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