Energy transient growth in the Taylor–Couette problem

Abstract

This work is devoted to the study of transient growth of perturbations in the Taylor–Couette problem due to linear mechanisms. The study is carried out for a particular small gap case and is mostly focused on the linearly stable regime of counter-rotation. The exploration covers a wide range of inner and outer angular speeds as well as axial and azimuthal modes. Significant transient growth is found in the regime of stable counter-rotation. The numerical results are in agreement with former analyses based on energy methods. Similarities with transient growth mechanisms in plane Couette flow and in Hagen–Poiseuille flow are discussed. This is reflected in the modulation of the basic circular Couette flow by the presence of azimuthal streaks as a result of the nonmodal growth of initial axisymmetric perturbations. This study might shed some light on the subcritical transition to turbulence which is found experimentally in Taylor–Couette flow when the cylinders rotate in opposite directions.