We formulate the covariant hydrodynamics equations describing the relativistic fluid dynamics as the problem of intersection theory on some infinite dimensional symplectic manifold associated with spacetime. This point of view separates the structures related to the equation of state, the geometry of spacetime, and the structures related to the (differential) topology of spacetime. We point out a five dimensional origin of the formalism of Lichnerowicz and Carter (and of Euler's equations for compressible ideal fluid). Our formalism makes it easy to incorporate the chiral anomaly and Onsager quantization. We clarify the relation between the canonical and Landau-Lifschitz flows, the meaning of Kelvin's theorem. Finally, we discuss some connections to topological strings and to canonical approaches to quasiclassical quantization of gravity. Joint work with Paul Wiegmann.