Transient Growth of Perturbations in a Columnar Vortex

Prof. Fazle Hussain, Department of Mechanical Engineering, University of Houston

Transient growth is studied in a normal-mode-stable vortex column via linear analysis and direct numerical simulation (DNS). Energetically “optimal” perturbations – attaining over thousand-fold amplification at moderate Reynolds numbers, Re  ~ 10⁴ – grow via two inviscid mechanisms: (a) 2-D perturbations with “positive-tilt” streamlines (contributing positive Reynolds stress, hence production) grow until the mean swirl transforms the streamlines to “negative tilt” (producing negative Reynolds stress); (b) 3-D perturbations grow via the tilting and stretching of perturbation radial vorticity. Competition between the amplifying effect of mean strain and growth-arresting effect of mean vorticity, in addition to viscous damping, fixes the optimal radius of initial perturbation. With increasing growth, axisymmetric modes originate at increasingly larger radii outside the core, whereas bending wave modes are localized close to the vortex axis, where they resonantly excite vortex core waves. Resulting strong growth of bending waves appears likely to cause core transition, hence enhanced vortex decay – a phenomenon of interest in high Re practical flows, e.g. aircraft wake.