Viscous interactions of two co-rotating vortices before merging
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Published:2002-09-24
Issue:
Volume:467
Page:389-410
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ISSN:0022-1120
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Container-title:Journal of Fluid Mechanics
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language:en
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Short-container-title:J. Fluid Mech.
Author:
LE DIZÈS STÉPHANE,VERGA ALBERTO
Abstract
The viscous evolution of two co-rotating vortices is analysed using direct two-dimensional
numerical simulations of the Navier–Stokes equations. The article focuses
on vortex interaction regimes before merging. Two parameters are varied: a steepness
parameter n which measures the steepness of the initial vorticity profiles in a given
family of profiles, and the Reynolds number Re (between 500 and 16 000). Two distinct
relaxation processes are identified. The first one is non-viscous and corresponds
to a rapid adaptation of each vortex to the external (strain) field generated by the
other vortex. This adaptation process, which is profile dependent, is described and explained
using the damped Kelvin modes of each vortex. The second relaxation process
is a slow diffusion phenomenon. It is similar to the relaxation of any non-Gaussian
axisymmetrical vortex towards the Gaussian. The quasi-stationary solution evolves
on a viscous-time scale toward a single attractive solution which corresponds to the
evolution from two initially Gaussian vortices. The attractive solution is analysed in
detail up to the merging threshold a/b ≈ 0.22 where a and b are the vortex radius
and the separation distance respectively. The vortex core deformations are quantified
and compared to those induced by a single vortex in a rotating strain field. A good
agreement with the asymptotic predictions is demonstrated for the eccentricity of
vortex core streamlines. A weak anomalous Reynolds number dependence of the
solution is also identified. This dependence is attributed to the advection–diffusion
of vorticity towards the hyperbolic points of the system and across the separatrix
connecting these points. A Re1/3 scaling for the vorticity at the central hyperbolic
point is obtained. These findings are discussed in the context of a vortex merging
criterion.
Publisher
Cambridge University Press (CUP)
Subject
Mechanical Engineering,Mechanics of Materials,Condensed Matter Physics
Cited by
88 articles.
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