Author:
LEWEKE T.,WILLIAMSON C. H. K.
Abstract
In this paper, we investigate the three-dimensional instability
of a counter-rotating
vortex pair to short waves, which are of the order of the vortex core size,
and less
than the inter-vortex spacing. Our experiments involve detailed visualizations
and
velocimetry to reveal the spatial structure of the instability for a vortex
pair, which is
generated underwater by two rotating plates. We discover, in this work,
a
symmetry-breaking phase relationship between the two vortices, which we
show to be consistent
with a kinematic matching condition for the disturbances evolving on each
vortex.
In this sense, the instabilities in each vortex evolve in
a coupled, or ‘cooperative’,
manner. Further results demonstrate that this instability is a manifestation
of an
elliptic instability of the vortex cores, which is here identified clearly
for the first time
in a real open flow. We establish a relationship between elliptic instability
and other
theoretical instability studies involving Kelvin modes. In particular,
we note that the
perturbation shape near the vortex centres is unaffected by the finite
size of the cores.
We find that the long-term evolution of the flow involves the inception
of secondary
transverse vortex pairs, which develop near the leading stagnation point
of the pair.
The interaction of these short-wavelength structures with the long-wavelength
Crow
instability is studied, and we observe significant modifications in the
longevity of large
vortical structures.
Publisher
Cambridge University Press (CUP)
Subject
Mechanical Engineering,Mechanics of Materials,Condensed Matter Physics
Cited by
281 articles.
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