Hydrodynamics of Non-Circular Vortices in Beams of Light and Other Two-Dimensional Fluids

The motion of non-circular, two-dimensional vortices is shown to depend on a new form of coupling between vortex ellipticity and the gradient of fluid density. The approach is based on the perspective that an elliptic vortex can be described as the projection of a virtual construct, a circular vortex with a symmetry axis that is tilted with respect to the direction of propagation. The resulting kinetic equation offers new insights as to how tilt and vortex velocity co-evolve in few-body, non-equilibrium settings such as vortex pair nucleation and annihilation. The model is developed and applied in association with optical vortices, and optical experiments are used to verify its predictive power. It is valid for quantum fluids and classical hydrodynamics settings as well.