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arXiv:2607.00821

Visualization of Inertial and Kelvin Waves on the Quantum Vortex Lattice in Superfluid Helium

Florian Lorin, Charles Peretti, Corentin Bourjaillat, P. Švančara, Pierre-Philippe Cortet, Mathieu Gibert

Published Jul 1, 2026• 0 citations
arXivHTMLPDF

Abstract

Superfluid $^4$He subjected to steady rotation develops a regular lattice of quantum vortices aligned with the rotation axis. We prepare this lattice in a rotating cryostat, perturb it with a constant heat flux, and visualize vortex deformation waves that propagate in the lattice and grow in energy with the forcing. Below twice the rotation rate, we show that these waves feature a continuous frequency spectrum whose structure corresponds to inertial waves. At larger frequencies, we report several observations suggesting the presence of Kelvin waves over a continuous range of frequency. These results, obtained through space- and time-resolved velocity measurements of quantum vortex lines, appear as quantitative constraints for modern two-way coupled vortex filament models. They further offer new insights into perturbed quantum vortex systems in three-dimensional quantum fluids.

DOI
10.48550/arxiv.2607.00821

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Superfluid 4^44He subjected to steady rotation develops a regular lattice of quantum vortices aligned with the rotation axis. We prepare this lattice in a rotating cryostat, perturb it with a constant heat flux, and visualize vortex deformation waves that propagate in the lattice and grow in energy with the forcing. Below twice the rotation rate, we show that these waves feature a continuous frequency spectrum whose structure corresponds to inertial waves. At larger frequencies, we report several observations suggesting the presence of Kelvin waves over a continuous range of frequency. These results, obtained through space- and time-resolved velocity measurements of quantum vortex lines, appear as quantitative constraints for modern two-way coupled vortex filament models. They further offer new insights into perturbed quantum vortex systems in three-dimensional quantum fluids.
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In a recent experiment, Finne et al. discovered an intrinsic condition for the onset of quantum turbulence in 3 He-B, that q = α/(1 − α') < 1.3, where α and α' are mutual friction parameters. The authors put forward a qualitative argument that q is the ratio of dissipative and inertial forces on the superfluid, so for q < 1 inertial forces should overcome the dissipative forces and cause turbulence. Thus 1/ q would play, for a quantum fluid, the same role played in classical fluid dynamics by the Reynolds number (the ratio of inertial forces and dissipative forces in the Navier-Stokes equation). The aim of this work is to supplement this qualitative condition q = 1 with a quantitative calculation. By analysing both axisymmetric and non-axisymmetric modes of a continuum of vortices in a rotating superfluid, we find that in the long axial wavelength limit the condition q = 1 is the crossover between damped and propagating Kelvin waves; thus, for q > 1, perturbations on the vortices are unlikely to cause vortex reconnections and turbulence. Besides the relevance to the experiment of Finne et al. , the spectrum of oscillations which we find is relevant to the study of torsional oscillations of a rotating superfluid and generalises to three dimensions the spectrum of Kelvin waves on an isolated vortex line.
One of the main features of superfluids is the presence of topological defects with quantised circulation. These objects are known as quantum vortices and exhibit a hydrodynamic behaviour. Nowadays, particles are the main experimental tool used to visualise quantum vortices and to study their dynamics. We use a self-consistent model based on the three-dimensional Gross-Pitaevskii (GP) equation to explore theoretically and numerically the attractive interaction between particles and quantized vortices at very low temperature. Particles are described as localised potentials depleting the superfluid and following Newtonian dynamics. We are able to derive analytically a reduced central-force model that only depends on the classical degrees of freedom of the particle. Such model is found to be consistent with the GP simulations. We then generalised the model to include deformations of the vortex filament. The resulting long-range mutual interaction qualitatively reproduces the observed generation of a cusp on the vortex filament during the particle approach. Moreover, we show that particles can excite Kelvin waves on the vortex filament through a resonance mechanism even if they are still far from it.
Quantized vortices are key features of quantum fluids such as superfluid helium and Bose-Einstein condensates. The reconnection of quantized vortices and subsequent emission of Kelvin waves along the vortices are thought to be central to dissipation in such systems. By visualizing the motion of submicron particles dispersed in superfluid (4)He, we have directly observed the emission of Kelvin waves from quantized vortex reconnection. We characterize one event in detail, using dimensionless similarity coordinates, and compare it with several theories. Finally, we give evidence for other examples of wavelike behavior in our system.
Abstract Turbulence under strong influence of rotation is described as an ensemble of interacting inertial waves across a wide range of length scales. In macroscopic quantum condensates, the quasiclassical turbulent dynamics at large scales is altered at small scales, where the quantization of vorticity is essential. The nature of this transition remains an unanswered question. Here we expand the concept of wave-driven turbulence to rotating quantum fluids where the spectrum of waves extends to microscopic scales as Kelvin waves on quantized vortices. We excite inertial waves at the largest scale by periodic modulation of the angular velocity and observe dissipation-independent transfer of energy to smaller scales and the eventual onset of the elusive Kelvin wave cascade at the lowest temperatures. We further find that energy is pumped to the system through a boundary layer distinct from the classical Ekman layer and support our observations with numerical simulations. Our experiments demonstrate a regime of turbulent motion in quantum fluids where the role of vortex reconnections can be neglected, thus stripping the transition between the classical and the quantum regimes of turbulence down to its constituent components.