RESONANCE OF NONMODAL PERTURBATIONS IN THE BATCHELOR VORTEX

The resonance phenomenon for nonmodal perturbation of Batchelor vortex is studied. For azimuthal wavenumber n = - 1, two resonant peaks appear and the left one is always dominant. For n = 1, the resonant character becomes very complicated. There is a resonant mode switch from right peak to left peak as swirl parameter q increases from 2 to infinity. The resonant wavenumber k is the largest when q approaches to infinity for n = - 1 while it is the smallest for n = 1. The maximum value of the optimal energy growth for n = 1 is at q approaches to infinity, whereas it decreases monotonically as q increases for n = - 1. The resonance for n = - 1 is the more important one.