Abstract
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<1
than for
η=1,
the plane Couette limit. For fixed
Re
<130
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
Re
>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 case,
η=0.99.