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Crow instability: nonlinear response to the linear optimal perturbation

Published online by Cambridge University Press:  19 April 2016

Holly G. Johnson ,
Vincent Brion  and
Laurent Jacquin
Holly G. Johnson*
Affiliation:
Fundamental and Experimental Aerodynamics Department, ONERA, 8 rue des Vertugadins, 92190 Meudon, France
Vincent Brion
Affiliation:
Fundamental and Experimental Aerodynamics Department, ONERA, 8 rue des Vertugadins, 92190 Meudon, France
Laurent Jacquin
Affiliation:
Fundamental and Experimental Aerodynamics Department, ONERA, 8 rue des Vertugadins, 92190 Meudon, France
*
†Email address for correspondence: [email protected]
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Abstract

The potential for anticipated destruction of a counter-rotating vortex pair using the linear optimal perturbation of the Crow instability is assessed. Direct numerical simulation is used to study the development of the Crow instability and the subsequent evolution of the flow up to 30 characteristic times at a circulation-based Reynolds number of 1000. The conventional development of the instability leads to multiple contortions of the vortices including the linear growth of sinusoidal deformation, vortex linking and the formation of vortex rings. A new evolution stage is identified, succeeding this well-established sequence: the vortex rings undergo periodic oscillation. Two complete periods are simulated during which the vortical system is hardly altered, thereby demonstrating the extraordinary resilience of the vortices. The possibility of preventing these dynamics using the linear optimal perturbation of the Crow instability, the adjoint mode, is analysed. By appropriately setting the forcing amplitude, the lifetime of the vortices until their loss of coherence is reduced to approximately 13 characteristic times, which is less than half that of the natural Crow behaviour observed with infinitesimal forcing. The dynamics of the flow induced by the linear optimal perturbation that enable this result are connected to processes already known to efficiently alter vortical flows, in particular transient growth and four-vortex dynamics.

JFM classification

Vortex Flows: Vortex dynamics Vortex Flows: Vortex Flows Vortex Flows: Vortex instability
Type
Papers
Information
Journal of Fluid Mechanics , Volume 795 , 25 May 2016 , pp. 652 - 670
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Copyright
© 2016 Cambridge University Press 

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