The reciprocal energy and enstrophy transfers between normal fluid and superfluid components dictate the overall dynamics of superfluid 4He including the generation, evolution and coupling of coherent structures, the distribution of energy among lengthscales, and the decay of turbulence. To better understand the essential ingredients of this interaction, we employ a numerical two-way model which self-consistently accounts for the back-reaction of the superfluid vortex lines onto the normal fluid. Here we focus on a prototypical laminar (non-turbulent) vortex configuration which is simple enough to clearly relate the geometry of the vortex line to energy injection and dissipation to/from the normal fluid: a Kelvin wave excitation on two vortex anti-vortex pairs evolving in (a) an initially quiescent normal fluid, and (b) an imposed counterflow. In (a), the superfluid injects energy and vorticity in the normal fluid. In (b), the superfluid gains energy from the normal fluid via the Donnelly-Glaberson instability.

In this paper, we study the influence of the boundary conditions of the velocity fields in superfluid helium counterflow experiments. To make progress, we perform numerical simulations where we allow a slip velocity of the viscous component at the walls, and observe how this impacts on velocity fields and density profiles of distribution of quantized vortices. We conclude that the presence of a slip velocity at the walls generates a more homogeneous vortex distribution throughout the channel.

By combining experiments and numerical simulations which model the dynamics of shaken atomic Bose-Einstein condensates, we reveal the surprising nature of quantum turbulence in these systems. Unlike the tangles of vortex lines described in the superfluid helium literature, we find that our turbulent atomic condensate contains a mixture of strong fragmented density fluctuations and small random vortex loops which are not homogeneously distributed. This unusual form of turbulence, with its own properties and scaling behavior, which we call strong quantum turbulence, is significantly different from the turbulence which is observed in either classical or other quantum systems, thus posing a new challenge in turbulence research.

Drain vortices are among the most common vortices observed in everyday life, yet their physics is complex due to the competition of vorticity's transport and diffusion, and the presence of viscous layers and a free surface. Recently, it has become possible to study experimentally drain vortices in liquid helium II, a quantum fluid whose physics is characterised by the absence of viscosity and the quantisation of the circulation in the superfluid component. Using the Gross-Pitaevskii equation, we make a simple model of the problem which captures the essential physics ingredients, showing that the drain vortex of a pure superfluid consists of a bundle of vortex lines which, in the presence of a radial drain, twist, thus strengthening the axial flow into the drain.

We collect and describe the observed geometrical and dynamical properties of turbulence in quantum fluids, particularly superfluid helium and atomic condensates for which more information about turbulence is available. Considering the spectral features, the temporal decay, and the comparison with relevant turbulent classical flows, we identify three main limiting types of quantum turbulence: Kolmogorov quantum turbulence, Vinen quantum turbulence, and strong quantum turbulence. This classification will be useful to analyze and interpret new results in these and other quantum fluids.

When the intensity of turbulence is increased (by increasing the Reynolds number, e.g., by reducing the viscosity of the fluid), the rate of the dissipation of kinetic energy decreases but does not tend asymptotically to zero: it levels off to a nonzero constant as smaller and smaller vortical flow structures are generated. This fundamental property, called the dissipation anomaly, is sometimes referred to as the zeroth law of turbulence. The question of what happens in the limit of vanishing viscosity (purely hypothetical in classical fluids) acquires a particular physical significance in the context of liquid helium, a quantum fluid which becomes effectively inviscid at low temperatures achievable in the laboratory. By performing numerical simulations and identifying the superfluid Reynolds number, here we show evidence for a superfluid analog to the classical dissipation anomaly. Our numerics indeed show that as the superfluid Reynolds number increases, smaller and smaller structures are generated on the quantized vortex lines on which the superfluid vorticity is confined, balancing the effect of weaker and weaker dissipation.

We show that a toroidal bundle of quantized vortex rings in superfluid helium generates a large-scale wake in the normal fluid which reduces the overall friction experienced by the bundle, thus greatly enhancing its lifetime, as observed in experiments. This collective effect is similar to the drag reduction observed in systems of active, hydrodynamically cooperative agents such as bacteria in aqueous suspensions, fungal spores in the atmosphere, and cyclists in pelotons.