Phenomenological Lagrangian for nondissipative hydrodynamics of rotating superfluids

An amazing feature of rotating superfluids is that they are threaded by a periodic array of vortex lines with quantized circulation. We construct a phenomenological Lagrangian for obtaining nondissipative hydrodynamic equations of superfluids taking into account the elasticity effects of three-dimensional lattice. This Lagrangian is constructed using a hybrid Lagrangian–Eulerian fluid description and it gives the correct hydrodynamic theory in the Eulerian representation. Hydrodynamic equations corresponding to the two-dimensional vortex lattice are obtained by tending the relevant period (or the lattice vector) to infinity.