Self-similar Expansion of a Turbulent Bose-Einstein Condensate: A Generalized Hydrodynamic Model

We generalize the superfluid hydrodynamic equations to describe the expansion of a turbulent condensate cloud. Our Lagrangian formalism includes the kinetic energy associated with an entangled vortex configuration. The expressions developed here clarify the physics behind the self-similar free expansion as seen in experiments. This feature is a crucial and characteristic signature of turbulence. Our present study improves on our previous model (Caracanhas et al. in J. Low Temp. Phys. 166: 49, 2012).