Spreading of two-dimensional axisymmetric vortices exposed to a rotating strain field
Turner, M.R. and Gilbert, A.D. (2009) Spreading of two-dimensional axisymmetric vortices exposed to a rotating strain field Journal of Fluid Mechanics, 630. pp. 155-177. ISSN 0022-1120
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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. 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.
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