Specific heat of the Kelvin modes in low temperature superfluid turbulence

Quantum turbulence can be generated in superfluid helium either thermally (by applying a heat flux, as in thermal counterflow) or mechanically (by stirring the liquid). By modelling the superfluid vortex lines as reconnecting space curves with fixed circulation, and the driving normal fluid as a uniform flow (for thermal counterflow) and a synthetic turbulent flow (for mechanically-driven turbulence), we determine the difference between thermally-driven and mechanically-drive...

We revise the theory of superfluid turbulence near the absolute zero of temperature and suggest a model with differential approximation for the energy fluxes in the k-space carried by the collective hydrodynamic motions of quantized vortex lines and by their individual uncorrelated motions known as Kelvin waves. The model predicts energy spectra of the hydrodynamic and the Kelvin waves components of the system, which experience a smooth crossover between different regimes of ...

The dynamics of quantized vortices in rotating $^3$He-B is investigated in the low density (single-vortex) regime as a function of temperature. An abrupt transition is observed at $0.5 T_{\rm c}$. Above this temperature the number of vortex lines remains constant, as they evolve to their equilibrium positions. Below this temperature the number of vortices increases linearly in time until the vortex density has grown sufficiently for turbulence to switch on. On the basis of nu...

In superfluid helium, vorticity is quantized and constrained on line-like phase singularities, called quantum or quantized vortices. By visualizing the motion of sub-micron frozen particles in superfluid $^{4}$He, we directly observe for the first time the helical Kelvin waves excited after quantized vortex reconnections. We compare the data with self-similar solutions of vortex filament models. We report the results in a fluid dynamic video.

The energy dissipation of quasiclassical homogeneous turbulence in superfluid $^4$He (He II) is controlled by an effective kinematic viscosity $\nu'$, which relates the energy decay rate $dE/dt$ to the density of quantized vortex lines $L$ as $dE/dt=-{\nu'}({\kappa}L)^2$. The precise value of $\nu'$ is of fundamental importance in developing our understanding of the dissipation mechanism in He II, and it is also needed in many high Reynolds number turbulence experiments and m...

Experiments and numerical simulations of turbulent $^4$He and $^3$He-B have established that, at hydrodynamic length scales larger than the average distance between quantum vortices, the energy spectrum obeys the same 5/3 Kolmogorov law which is observed in the homogeneous isotropic turbulence of ordinary fluids. The importance of the 5/3 law is that it points to the existence of a Richardson energy cascade from large eddies to small eddies. However, there is also evidence of...

Filamentary regions of high vorticity irregularly form and disappear in the turbulent flows of classical fluids. We report an experimental comparative study of these so-called " coherent structures " in a classical versus quantum fluid, using liquid helium with a superfluid fraction varied from 0% up to 83%. The low pressure core of the vorticity filaments is detected by pressure probes located on the sidewall of a 78-cm-diameter Von K\'arm\'an cell driven up to record turbul...

This article reviews recent developments in quantum fluid dynamics and quantum turbulence (QT) for superfluid helium and atomic Bose-Einstein condensates. Quantum turbulence was discovered in superfluid $^4$He in the 1950s, but the field moved in a new direction starting around the mid 1990s. Quantum turbulence is comprised of quantized vortices that are definite topological defects arising from the order parameter appearing in Bose-Einstein condensation. Hence QT is expected...

We show that the vortex dynamics in Fermi superfluids at ultra-low temperatures is governed by the local heating of the vortex cores creating the heat flux carried by non-equilibrium quasiparticles emitted by moving vortices. This mechanism provides a universal zero temperature limit of dissipation in Fermi superfluids. For the typical experimental conditions realized by the turbulent motion of $^3$He-B the temperature of vortex cores is estimated to be of the order $0.2 T_c$...

The fluctuations of the vortex density in a turbulent quantum fluid are deduced from local second-sound attenuation measurements. These measurements are performed with a micromachined open-cavity resonator inserted across a flow of turbulent He-II near 1.6 K. The power spectrum of the measured vortex line density is compatible with a (-5/3) power law. The physical interpretation, still open, is discussed.