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Spreading of two-dimensional axisymmetric vortices exposed to a rotating strain field

By M.R. Turner and A.D. Gilbert

Abstract

Starting with a point vortex localised at the origin, the applied strain field generates a cat's eye topology in the co--rotating stream function, localised around a radius r_ext. Now the vortex is allowed to spread viscously: initially r_ext lies outside the vortex but as it spreads, vorticity is advected into the cat's eyes, leading to a local flattening of the mean profile of the vortex and so to enhanced mixing and spreading of the vortex. Together with this is a feedback: the response of the vortex to the external strain depends on the modified profile. The feedback is particularly strong when r_ext coincides with the radius r_cat at which the vortex can support cat's eyes of infinitesimal width. There is a particular time at which this occurs, as these radii change with the viscous spread of the vortex: r_ext moves inwards and r_cat outwards. This resonance behaviour leads to increased mixing of vorticity, along with a rapid stretching of vorticity contours and a sharp increase in the amplitude of the non--axisymmetric components. \ud \ud The dynamical feedback and enhanced diffusion are studied for viscously spreading vortices by means of numerical simulations of their time evolution, parameterised only by the Reynolds number R and the dimensionless strength A of the external strain field

Topics: G100 Mathematics, H000 Engineering
Publisher: Cambridge University Press
Year: 2009
DOI identifier: 10.1017/S0022112009006855
OAI identifier: oai:eprints.brighton.ac.uk:6466

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