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On the linear receptivity of trailing vortices

Published online by Cambridge University Press:  03 December 2020

Tobias Bölle Open the ORCID record for Tobias Bölle [Opens in a new window] ,
Vincent Brion Open the ORCID record for Vincent Brion [Opens in a new window] ,
Jean-Christophe Robinet Open the ORCID record for Jean-Christophe Robinet [Opens in a new window] ,
Denis Sipp Open the ORCID record for Denis Sipp [Opens in a new window]  and
Laurent Jacquin
Tobias Bölle*
Affiliation:
DAAA, ONERA-The French Aerospace Lab, Université Paris Saclay, 92190 Meudon, France
Vincent Brion
Affiliation:
DAAA, ONERA-The French Aerospace Lab, Université Paris Saclay, 92190 Meudon, France
Jean-Christophe Robinet
Affiliation:
DynFLuid, Arts et Métiers Institute of Technology, CNAM, HESAM University, 75013 Paris, France
Denis Sipp
Affiliation:
DAAA, ONERA-The French Aerospace Lab, Université Paris Saclay, 92190 Meudon, France
Laurent Jacquin
Affiliation:
DAAA, ONERA-The French Aerospace Lab, Université Paris Saclay, 92190 Meudon, France
*
†Email address for correspondence: tobias.bolle@onera.fr
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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.

JFM classification

Vortex Flows: Vortex dynamics Mathematical Foundations: General fluid mechanics

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JFM Papers
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Journal of Fluid Mechanics , Volume 908 , 10 February 2021 , A8
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© The Author(s), 2020. Published by Cambridge University Press

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