Single Vortex Streets on the Sphere

We study arrangements of point vortices on a sphere in the form of a single von Ka´rma´n vortex street, with and without the addition of pole vortices using the configuration matrix approach recently introduced by (1) and (2) on the sphere. We derive the general form of the von Ka´rma´n matrix thereby obtaining all possible vortex strengths for which the configuration rotates rigidly, perpendicular to the axis of rotation of the sphere. The distribution of normalized singular values of the von Ka´rma´n matrices allows us to calculate their Shannon entropy (as a function of the vortex street parameters), which we interpret as a scalar measure of ‘disorder’ and robustness of the vortex street. We also study the streamline topologies associated with the vortex street and identify a number of distinct topologies which support a jet-stream passing through the street capable of transporting particles globally.