Transient Growth in Exactly Counter-Rotating Couette–Taylor Flow

Transient growth due to non-normality is investigated for the Couette-Taylor 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 on the linear stability boundary. Transient growth is approximately 20% higher near the Couette-Taylor 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. For 106<Re<130, the greatest transient growth occurs for a value of η between the linear stability boundary and one. For Re<106, the flow is linearly stable and the greatest transient growth occurs for a value of η less than one. The energy in the optimal inputs is primarily meridional; that in the optimal outputs is primarily azimuthal. Pseudospectra are calculated for two contrasting cases. Received 5 November 2001 and accepted 29 March 2002 Published online: 2 October 2002 Communicated by H.J.S. Fernando