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On effectiveness of optimal perturbation in hastening instability of counter-rotating vortex pair behind a wing

Published online by Cambridge University Press:  24 November 2025

Mohd. Suhail Naim Open the ORCID record for Mohd. Suhail Naim [Opens in a new window] ,
Navrose Open the ORCID record for Navrose [Opens in a new window]  and
Vincent Brion
Mohd. Suhail Naim
Affiliation:
Department of Aerospace Engineering, Indian Institute of Technology Kanpur , UP 208016, India
Navrose*
Affiliation:
Department of Aerospace Engineering, Indian Institute of Technology Kanpur , UP 208016, India
Vincent Brion
Affiliation:
DAAA, ONERA, Institut Polytechnique de Paris, 92190 Meudon, France
*
Corresponding author: Navrose, navrose@iitk.ac.in
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Abstract

We investigate the effectiveness of linear optimal perturbation (LOP) for the flow past a finite span wing in reducing the lifespan of its trailing vortex system. Two approaches, referred to as local and model analysis, are introduced and used for our investigation. Both analyses assume that the baseflow is parallel. Local analysis is suited for intermediate distance from the wing where both tip vortices (TVs) and trailing edge wake (TEW) are present. Its results suggest that the unperturbed baseflow is stable. The separation between TVs and TEW increases downstream and their dynamics appear to be uncoupled at large distance from the wing. When perturbation corresponding to LOP is added to the baseflow, the vortices are displaced forming a helical twist. With time, the maximum displacement initially increases and then saturates. The perturbation retains its compact wavepacket-like structure, and perturbation energy within the tip vortex remains nearly constant. In the model analysis, the far wake is modelled as a pair of counter-rotating $q$-vortices. For low Reynolds number, the flow is stable. However, for higher Reynolds number, the trailing vortices develop Crow instability. Its growth rate is found to be in good agreement with earlier studies. Instability leads to contact of vortices, resulting in the formation of vortex rings. The time for vortex contact decreases with increase in the strength of the initial perturbation. The results suggest that LOP is effective in reducing the lifespan of trailing vortices.

JFM classification

Vortex Flows: Vortex instability Vortex Flows: Vortex dynamics Flow Control: Instability control

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Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 1023 , 25 November 2025 , A33
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© The Author(s), 2025. Published by Cambridge University Press

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