text: Hill's spherical vortex is an exact solution of the Euler equations that is commonly used to model a vortex ring. The solution is also used to model the velocity distribution inside a spherical drop of one fluid moving at a constant velocity through another fluid at small Reynolds number. The vortex is named after Micaiah John Muller Hill who discovered the exact solution in 1894. The two-dimensional analogue of this vortex is the Lamb–Chaplygin dipole.
  The solution is described in the spherical polar coordinates system  with corresponding velocity components . The velocity components are identified from Stokes stream function  as follows
  The Hill's spherical vortex is described by
  where  is a constant freestream velocity far away from the origin and  is the radius of the sphere within which the vorticity is non-zero. For , the vorticity is zero and the solution described above in that range is nothing but the potential flow past a sphere of radius . The only non-zero vorticity component for  is the azimuthal component that is given by
  Note that here the parameters  and  can be scaled out by non-dimensionalization.