Steady buoyant droplets with circulation

Numerical solutions are presented for the steady flow corresponding to a two-dimensional moving droplet with circulation. Differences in the density of the droplet and surrounding fluid result in a buoyancy force which is balanced by a lift force due to the Magnus effect. The droplet is assumed to have constant vorticity in its interior, and its boundary may be a vortex sheet, as in a Prandtl-Batchelor flow. Only symmetric solutions are calculated. For Atwood number A=0 (no density difference) the droplet is a circle. As the Atwood number is increased, the droplet shape begins to resemble a circular cap with a dimpled base. There is a critical Atwood number A_lim at which the droplet develops two corners. For 0≤A≤A_lim, the solution is smooth; while for A_lim<A, we do not find a solution.