Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Instability and disintegration of vortex rings during head-on collisions
  and wall interactions   The head-on collision of two vortex rings can produce diverse phenomena: a
tiara of secondary rings, vortex sheets which flatten and interact iteratively,
or the violent disintegration of the rings into a turbulent cloud. The outcome
of the interaction is determined by the nature of the instability affecting two
impinging vortex rings. Here, we carry out a systematic study to determine the
dominant instability as a function of the parameters of the problem. To this
end, we numerically simulate the head on collision of vortex rings with
circulation Reynolds numbers between $1000$ and $3500$ and varying slenderness
ratios $\Lambda=a/R$ ranging from $\Lambda=0.1$ to $0.35$, with $a$ the core
radius and $R$ the ring radius. By studying the temporal evolution of the
energy and viscous dissipation, we elucidate the role azimuthal instabilities
play in determining what the outcomes of the collision are. We then compare
these collisions to the head-on impact of a vortex ring on a free-slip and a
no-slip wall. The free-slip wall imposes a mirror symmetry, which impedes
certain instabilities and at sufficiently large Reynolds numbers leads to the
formation of a half-tiara of vortices. Impact against a no-slip wall results in
the process where a secondary vortex ring is formed after the ejection of the
resulting boundary layer. When the Reynolds number is above a certain
threshold, which increases with $\Lambda$, the vortices disintegrate through
azimuthal instabilities, resulting in a turbulent cloud.

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The categories of this paper are: bayes-an
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The categories of this paper are: atom-ph
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The categories of this paper are: stat
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The categories of this paper are: funct-an
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The categories of this paper are: cond-mat
2
The categories of this paper are: math
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The categories of this paper are: econ
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The categories of this paper are: nucl-th
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The categories of this paper are: supr-con
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The categories of this paper are: chao-dyn
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The categories of this paper are: plasm-ph
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The categories of this paper are: hep-th
0
The categories of this paper are: hep-ph
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The categories of this paper are: math-ph
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The categories of this paper are: q-bio
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The categories of this paper are: nlin