Quantized point vortex equilibria in a one-way interaction model with a Liouville-type background vorticity on a curved torus

We construct point vortex equilibria with strengths quantized by multiples of 2π in a fixed background vorticity field on the surface curved torus. The consists two terms: first, term exponentially related to stream function and second arising from curvature torus, which leads Liouville-type equation for function. By using stereographic projection torus onto an annulus complex plane, admits class exact solutions, given terms loxodromic annulus. show that appropriate choices solution lead stationary patterns 4n̂ vortices identical strengths, n̂∈N. are sense they “one-way interaction” model where evolution is subject continuous vorticity, while distribution not affected velocity induced vortices. choosing functions continuously dependent parameter taking limits respect this parameter, we there solutions inhomogeneous exponential part disappears. always located at innermost outermost rings owing effects. topological features streamlines found change as modulus changes.