Collapse interactions of finite-sized two-dimensional vortices
P.W.C. Vosbeek, J.H.G.M. van Geffen, V.V. Meleshko and G.J.F. van Heijst
Physics of Fluids 9, 3315--3322 (1997)
V. Conclusions
In this paper we have presented numerical simulations that demonstrate the
influence of finite vortex sizes and viscosity effects on vortex
interactions in a situation which leads to a vortex collapse in the point
vortex case. Both in an infinite and in a finite domain, the results show a
good agreement in the behaviour of finite size vortices with point vortices
if their mutual distance is "sufficiently large". When these distances
become of the order of the vortex sizes, their trajectories are seen to
differ from those of the corresponding point vortices and the vortices start
to deform. In the three-vortex configuration considered here, one vortex in
particular deforms very dramatically, due to the growing internal and
external strain. It is believed that this deformation into a long filament,
which is gradually wrapped around the remaining vortices, prevents a
collapse into one single final vortex.
The bigger the vortices initially are, the earlier they start to deform. In
fact, only the time scale of the deformations is influenced by the size of
the vortices; the deformations themselves are very similar for different
initial sizes of the vortices. Viscosity causes the vortex sizes to grow as
time evolves, thus resulting in earlier deformations than in the inviscid
case.
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