The Reynolds number provides a characterization of the transition to turbulent flow, with wide application in classical fluid dynamics. Identifying such a parameter in superfluid systems is challenging due to their fundamentally inviscid nature. Perf
orming a systematic study of superfluid cylinder wakes in two dimensions, we observe dynamical similarity of the frequency of vortex shedding by a cylindrical obstacle. The universality of the turbulent wake dynamics is revealed by expressing shedding frequencies in terms of an appropriately defined superfluid Reynolds number, ${rm Re}_s$, that accounts for the breakdown of superfluid flow through quantum vortex shedding. For large obstacles, the dimensionless shedding frequency exhibits a universal form that is well-fitted by a classical empirical relation. In this regime the transition to turbulence occurs at ${rm Re}_sapprox 0.7$, irrespective of obstacle width.
We investigate two-dimensional turbulence in finite-temperature trapped Bose-Einstein condensates within damped Gross-Pitaevskii theory. Turbulence is produced via circular motion of a Gaussian potential barrier stirring the condensate. We systematic
ally explore a range of stirring parameters and identify three regimes, characterized by the injection of distinct quantum vortex structures into the condensate: (A) periodic vortex dipole injection, (B) irregular injection of a mixture of vortex dipoles and co-rotating vortex clusters, and (C) continuous injection of oblique solitons that decay into vortex dipoles. Spectral analysis of the kinetic energy associated with vortices reveals that regime (B) can intermittently exhibit a Kolmogorov $k^{-5/3}$ power law over almost a decade of length or wavenumber ($k$) scales. The kinetic energy spectrum of regime (C) exhibits a clear $k^{-3/2}$ power law associated with an inertial range for weak-wave turbulence, and a $k^{-7/2}$ power law for high wavenumbers. We thus identify distinct regimes of forcing for generating either two-dimensional quantum turbulence or classical weak-wave turbulence that may be realizable experimentally.
We study the Kelvin mode excitations on a vortex line in a three-dimensional trapped Bose-Einstein condensate at finite temperature. Our stochastic Gross-Pitaevskii simulations show that the activation of these modes can be suppressed by tightening t
he confinement along the direction of the vortex line, leading to a strong suppression in the vortex decay rate as the system enters a regime of two-dimensional vortex dynamics. As the system approaches the condensation transition temperature we find that the vortex decay rate is strongly sensitive to dimensionality and temperature, observing a large enhancement for quasi-two-dimensional traps. Three-dimensional simulations of the recent vortex dipole decay experiment of Neely et al. [Phys. Rev. Lett. 104, 160401 (2010)] confirm two-dimensional vortex dynamics, and predict a dipole lifetime consistent with experimental observations and suppression of Kelvon-induced vortex decay in highly oblate condensates.
