On coadjoint orbits of rotational perfect fluids

In this paper the structure of vortex coadjoint orbits pertaining to perfect fluids having smooth vorticities in R^3, within the framework set up by J. Marsden and A. Weinstein [Physica D 7, 305-323 (1983)], in terms of an associated Hamiltonian Kaehler manifold (the Clebsch manifold, described in terms of the so-called Clebsch variables) is investigated. The topological quantization of Mikhailov and Kuznetsov is related to geometric quantization. Natural candidates for the coherent states on the Clebsch manifold are also exhibited.