Nonnormal 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 nonnormal 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. Clear evidence of transient growth is found as long as the counter-rotation is increased. 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 found. 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.\ud \ud This work was supported by UK Engineering and Physical Sciences Research Council Grant GR/M30890