Transient growth in Taylor–Couette flow

Transient growth due to non-normality is investigated for the Taylor–Couette problem with counter-rotating cylinders as a function of aspect ratio η and Reynolds number Re. For all Re⩽500, transient growth is enhanced by curvature, i.e., is greater for η 130 the greatest transient growth is achieved for η on the linear stability boundary. Transient growth is shown to be approximately 20% higher near the linear stability boundary at Re=310, η=0.986 than at Re=310, η=1, near the threshold observed for transition in plane Couette flow. The energy in the optimal inputs is primarily meridional; that in the optimal outputs is primarily azimuthal. Pseudospectra are calculated for two contrasting cases. For large curvature, η=0.5, the pseudospectra adhere more closely to the spectrum than in a narrow gap...

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