We describe a classification of generic coadjoint orbits for the groups of symplectomorphisms and Hamiltonian diffeomorphisms of a closed symplectic surface. We also describe invariants of simple Morse functions on symplectic surfaces with respect to actions of those groups. This gives an answer to V.Arnold's problem on invariants of generic isovortex fields for the 2D ideal fluids. This is a joint work with Anton Izosimov and Mehdi Mousavi.