Transient growth in Taylor–Couette flow

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.