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 For all transient growth is enhanced by curvature, i.e., is greater for than for the plane Couette limit. For fixed it is found that the greatest transient growth is achieved for η between the Taylor–Couette linear stability boundary, if it exists, and one, while for 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 than at 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, the pseudospectra adhere more closely to the spectrum than in a narrow gap case,
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