Abstract
Techniques based on the conformal mapping and the numerical method of contour dynamics are presented for computing the motion of a finite area patch of constant vorticity on a sphere in the presence of a thin barrier with two gaps. Finite area patch motion is compared with exact point vortex trajectories and good agreement is found between the point vortex trajectories and the centroid motion of finite area patches when the patch remains close to circular. Patch centroids are, in general, closely constrained to follow point vortex trajectories. However, Kelvin’s theorem constrains the circulation about the barrier to be a constant of the motion, thus, forcing a time-dependent volume flux through the gaps. More exotic motion is observed when the through-gap flow forces the vortex patch close to an edge of a barrier, resulting in the vortex splitting with only part of the patch passing through the gap. As the gap width is decreased this effect becomes more dramatic.
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Nelson, R.B., McDonald, N.R. Vortex motion on a sphere: barrier with two gaps. Theor. Comput. Fluid Dyn. 24, 157–162 (2010). https://doi.org/10.1007/s00162-009-0097-6
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DOI: https://doi.org/10.1007/s00162-009-0097-6