Quantum-vortex-driven Kelvin wave in the thermal background of superfluid helium

TL;DR

Kelvin waves on quantized vortices in helium II interact with the finite-temperature normal-fluid component through mutual friction. Using the fully coupled FOUCAULT framework and comparing it to Schwarz back-reaction, the study shows that at finite temperatures the normal fluid exhibits a KW-like dispersion whose frequency and damping track the vortex KW, with strong temperature dependence arising from mutual friction and viscous dissipation, while Schwarz predicts weak temperature sensitivity. The normal-fluid response to KW perturbations is directly forced by vortex dynamics, yielding a dispersion relation that matches the vortex KW, enabling potential experimental observation via tracer visualization even in the normal phase. These results illuminate energy transfer between superfluid vortices and the normal fluid and offer concrete pathways for experimentally probing KW dynamics through normal-fluid diagnostics such as particle-tracking velocimetry.

Abstract

We present numerical evidence that Kelvin waves (KWs) on quantized vortices in superfluid helium can be directly observed in the normal fluid component at finite temperatures. Using the Fully cOUpled loCAl model of sUperfLuid Turbulence (FOUCAULT) model, we analyze the propagation and temperature dependence of KWs by simultaneously measuring the dispersion of waves on the vortex displacement and the normal fluid velocity. The results demonstrate that the normal fluid supports a coherent KW-like response, with a dispersion relation matching that of the vortex filament (VF). Unlike the Schwarz model where there is almost no temperature dependence, in FOUCAULT KWs frequency and damping both depend on temperature, highlighting the role of mutual friction in mediating the coupling between the two fluids. These findings open a pathway for experimental observation of KWs in the normal phase using tracer based visualization.

Figures (6)

• Figure 1: Visualization of a VF (in green) perturbed by an ensemble of KWs with independent random phases. The vorticity in the z direction of the normal fluid $\omega_z$ is plotted highlighting the dipolar structure that forms around the vortex core due to the mutual friction. In this simulation, the amplitude of the waves is exaggerated to make the disturbance visible.
• Figure 2: Blue heatmaps: dispersion relation of KWs on vortex lines simulated with the Schwarz model using the full Biot-Savart integral for $T=0, \, 1.7, \, 1.95, \, 2.1 \, {\rm K}$ using Eq. (\ref{['eq:S_k_w']}). The dispersion relation at temperature $T=0$ K calculated via Eq. (\ref{['eq:omega2']}) is indicated (blue dashed line ) and superimposed on all cases.
• Figure 3: Dispersion relation for temperatures $T=1.7 \, {\rm K}$ (a,d), $T=1.95 \, {\rm K}$ ((b,e) and $T=2.1 \, {\rm K}$ (c,f) determined on the basis of FOUCAULT numerical simulations for: KWs on quantum vortices, $|\hat{S}(k_z,\omega)|^2$ (a,b,c, orange colored heatmaps); KWs in the normal fluid $|\hat{V}_x(k_z,\omega)|^2$ (d,e,f, green colored heatmaps). We also show the dispersion relation of KWs on vortices computed with the Schwarz model at $T=0$$\tilde{\omega}^{Sc}_{T=0}(k_z)$ (blue dashed line , as in FIG.\ref{['fig:Fig2']}). and the dispersion relation $\tilde{\omega}^F_T(k_z)$ computed with Foucault at corresponding temperatures (red dashed line ).
• Figure 4: Dispersion relation of KWs on vortices $\tilde{\omega}^{Sc}_T(k_z)$ computed on the basis of the Schwarz model at the three working temperatures (dashed lines). Dispersion relation of KWs in the normal fluid $\tilde{\omega}^{F}_T(k_z)$ computed on the basis of the FOUCAULT model at the three working temperatures (solid lines with markers). Blue, yellow and red curves correspond to $T=1.7, \, 1.95, \, 2.1 \, {\rm K}$, respectively.
• Figure 5: Measurement of the dimensionless damping rate $\alpha (k_z)$ at $T=1.7 \, {\rm K}$ for the FOUCAULT model (blue circles ), Schwarz model (cyan diamond $\mathbf{\Diamond}$) and LIA model (magenta star $\bigstar$). The dashed black line represent the theoretical value $\alpha=0.126$.