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Influence of a wall on the three-dimensional dynamics of a vortex pair

Published online by Cambridge University Press:  20 March 2017

Daniel J. Asselin Open the ORCID record for Daniel J. Asselin [Opens in a new window]  and
C. H. K. Williamson
Daniel J. Asselin*
Affiliation:
Sibley School of Mechanical and Aerospace Engineering, Cornell University, Ithaca, NY 14853-7501, USA
C. H. K. Williamson
Affiliation:
Sibley School of Mechanical and Aerospace Engineering, Cornell University, Ithaca, NY 14853-7501, USA
*
†Email address for correspondence: [email protected]
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Abstract

In this paper, we are interested in perturbed vortices under the influence of a wall or ground plane. Such flows have relevance to aircraft wakes in ground effect, to ship hull junction flows, to fundamental studies of turbulent structures close to a ground plane and to vortex generator flows, among others. In particular, we study the vortex dynamics of a descending vortex pair, which is unstable to a long-wave instability (Crow, AIAA J., vol. 8 (12), 1970, pp. 2172–2179), as it interacts with a horizontal ground plane. Flow separation on the wall generates opposite-sign secondary vortices which in turn induce the ‘rebound’ effect, whereby the primary vortices rise up away from the wall. Even small perturbations in the vortices can cause significant topological changes in the flow, ultimately generating an array of vortex rings which rise up from the wall in a three-dimensional ‘rebound’ effect. The resulting vortex dynamics is almost unrecognizable when compared with the classical Crow instability. If the vortices are generated below a critical height over a horizontal ground plane, the long-wave instability is inhibited by the wall. We then observe two modes of vortex–wall interaction. For small initial heights, the primary vortices are close together, enabling the secondary vortices to interact with each other, forming vertically oriented vortex rings in what we call a ‘vertical rings mode’. In the ‘horizontal rings mode’, for larger initial heights, the Crow instability develops further before wall interaction; the peak locations are farther apart and the troughs closer together upon reaching the wall. The proximity of the troughs to each other and the wall increases vorticity cancellation, leading to a strong axial pressure gradient and axial flow. Ultimately, we find a series of small horizontal vortex rings which ‘rebound’ from the wall. Both modes comprise two small vortex rings in each instability wavelength, distinct from Crow instability vortex rings, only one of which is formed per wavelength. The phenomena observed here are not limited to the above perturbed vortex pairs. For example, remarkably similar phenomena are found where vortex rings impinge obliquely with a wall.

JFM classification

Vortex Flows: Vortex dynamics Vortex Flows: Vortex instability Vortex Flows: Vortex interactions
Type
Papers
Information
Journal of Fluid Mechanics , Volume 817 , 25 April 2017 , pp. 339 - 373
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© 2017 Cambridge University Press 

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