In a recent experiment Paoletti [Phys. Rev. Lett. 101, 154501 (2008)]10.1103/PhysRevLett.101.154501 monitored the motion of tracer particles in turbulent superfluid helium and inferred that the velocity components do not obey the Gaussian statistics observed in ordinary turbulence. Motivated by their experiment, we create a small 3D turbulent state in an atomic Bose-Einstein condensate, compute directly the velocity field, and find similar nonclassical power-law tails. We obtain similar results in 2D trapped and 3D homogeneous condensates, and in classical 2D vortex points systems. This suggests that non-Gaussian turbulent velocity statistics describe a fundamental property of quantum turbulence. We also track the decay of the vortex tangle in the presence of the thermal cloud.

We consider the evolution and dissipation of vortex rings in a condensate at non-zero temperature, in the context of the classical field approximation, based on the defocusing nonlinear Schrödinger equation. The temperature in such a system is fully determined by the total number density and the number density of the condensate. A vortex ring is introduced into a condensate in a state of thermal equilibrium, and interacts with non-condensed particles. These interactions lead to a gradual decrease in the vortex line density, until the vortex ring completely disappears. We show that the square of the vortex line length changes linearly with time, and obtain the corresponding universal decay law. We relate this to mutual friction coefficients in the fundamental equation of vortex motion in superfluids.PACS numbers: 03.65. Sq, 03.75.Kk, 05.65.+b, 67.40.Vs, 67.57.De The processes of self-organization, formation of largescale coherent localized structures and interactions of these structures with small-scale fluctuations are at the heart of nonlinear sciences, ranging from classical turbulence, superfluids, ultracold gases and Bose-Einstein Condensates (BECs), to the formation of the early Universe. Turbulence is characterised by the co-existence of motions with many length and time scales described by many degrees of freedom. The key to our understanding of turbulence is to elucidate physics of interactions between large scales (eg. large eddies) and small scales (eg. turbulent fluctuations), and to develop mathematical models that account for the effects of small scales without actually solving for them. According to the Landau description, superfluid 4 He consists of the ground state and the excitations -quasiparticles drifting on top of the ground state. In the language of relativistic quantum fields this corresponds to vacuum and matter (eg. gravity waves interacting with a vacuum). Indeed, there is a close relationship between superfluid hydrodynamics and quantum gravity, so that at some level of hierarchy of parameters the interactions of the quantum vacuum and matter can be described by the defocusing nonlinear Schrödinger (NLS) equation [1]. The dynamics of Bose condensates depends on the energy exchange between the condensed and non-condensed parts of the gas. Again, the NLS equation (reformulated as the Gross-Pitaevskii (GP) equation [2]) describes equilibrium and dynamical properties of BEC as well as the formation of BEC from a strongly degenerate gas of weakly interacting bosons [3,4]. The formation of the large-scale coherent localized ground state (condensate) from a non-equilibrium initial state has been studied in a number of papers addressing different stages of the formation. Weak turbulence theory has been used to predict the self-similar evolution of the field in the regime of random phases of Fourier amplitudes [5,6], the transition from the regime of weak turbulence to superfluid turbulence via states of strong turbulence in the long-wavelength region of energy space [7], and the final stage...

Using the vortex filament model and the Gross Pitaevskii nonlinear Schroedinger equation, we show that bundles of quantised vortex lines in helium II are structurally robust and can reconnect with each other maintaining their identity. We discuss vortex stretching in superfluid turbulence and show that, during the bundle reconnection process, Kelvin waves of large amplitude are generated, in agreement with the finding that helicity is produced by nearly singular vortex interactions in classical Euler flows.

We present numerical solutions of the Gross-Pitaevskii equation corresponding to reconnecting vortex lines. We determine the separation of vortices as a function of time during the approach to reconnection, and study the formation of pyramidal vortex structures. Results are compared with analytical work and numerical studies based on the vortex filament method.

The work of Benjamin, Mullin, Pfister and others on the non-uniqueness of solutions of the Navier–Stokes equation in Couette flow at small aspect ratio has revealed the existence of ‘anomalous’ 1-cell modes. A natural question to ask is whether these ‘anomalous’ modes are robust enough to survive the application of a body force, such as an externally applied magnetic field. We find that the answer is positive, although, with increasing magnetic field, steady 2-cell flows are generally more stable than 1-cell states. We also show that new time-dependent flows are easy to excite at relatively low Reynolds numbers compared to the case without a magnetic field, and we present two such flows.