Two variations on the theme of Lamb–Chaplygin: supersmooth dipole and rotating multipoles

Departing from the classical circular dipole and combining analytical and numerical methods, two kinds of distributed vortical solutions with noncircular boundaries are constructed. These are the translating elliptical dipole with a continuously differentiable vorticity field, and the rotating multipoles (tripole, quadrupole, pentapole etc) with one azimuthal mode in the far field. The features of the new solutions and their correspondence to observations are discussed.