On the linear receptivity of trailing vortices

Abstract

The present work investigates the excitation process by which free-stream disturbances are transformed into vortex-core perturbations. This problem of receptivity is modelled in terms of the resolvent in frequency space as the linear response to forcing. This formulation of receptivity suggests that non-normality of the resolvent is necessary to allow free-stream disturbances to excite the vortex core. Considering a local (in frequency) measure of non-normality, we show that vortices are frequency-selectively non-normal in a narrow frequency band of retrograde perturbations while the rest of the range is governed by an effectively normal operator, thus not contributing to receptivity. Canonical decomposition of the resolvent reveals that vortices are most susceptible to coiled filaments localised about the critical layer that induce bending waves on the core. Considering Lamb–Oseen, Batchelor and Moore–Saffman vortices as reference-flow models, we find free-stream receptivity to be essentially generic and independent of the axial wavelength on the considered range. A stochastic interpretation of the results could be a model for trailing-vortex meandering.