Kelvin wave propagation along vortex cores

Nature Physics (2026)Cite this article Kelvin waves are the most fundamental excitations that propagate along vortex lines, and they play a central role in the redistribution of energy and the stability of rotating flows. They are believed to underpin key processes in both classical and quantum turbulence, from the decay of vortex tangles in superfluid helium to dissipation mechanisms in atmospheric vortices. Despite their importance, quantitative observations of Kelvin wave dynamics that resolve their dispersion relation remain a challenging problem. Here we experimentally characterize the propagation of Kelvin waves along a stable, controlled and macroscopic vortex core and access their dispersion relation. Our spatiotemporal measurements, spanning nearly two decades in scale, reveal both helical bending modes and double-helix waves, which validates theoretical predictions for turbulent rotating flows. We also observe the statistics of temporal fluctuations of Kelvin waves and show how their dynamics are shaped by local vortex properties, such as vertical flow and excitation location. Our results provide quantitative insight into the mechanisms driving energy cascades in Kelvin wave turbulence, thus offering a classical analogue to quantum systems in which direct measurements remain inaccessible. 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Particle Image Velocimetry: A Practical Guide 3rd edn (Springer, 2018).Whitham, G. B. Linear and Nonlinear Waves (Wiley-Interscience, 1974).Barckicke, J., Falcon, E. & Gissinger, C. Data for: Kelvin wave propagation along vortex core. figshare https://doi.org/10.6084/m9.figshare.30903347 (2025).Download referencesWe thank A. Di Palma and Y. Le Goas for technical support. We thank B. Semin for providing polystyrene particles and J.-B. Gorce for discussions on PIV. E.F. acknowledges support from the Simons Foundation MPS (Grant No. 651463, Wave Turbulence, USA) and the French National Research Agency (Sogood Project No. ANR-21-CE30-0061-04, Lascaturb Project No. ANR-23-CE30-0043-02 and Provebact Project No. ANR-24-CE09-1394-02). C.G. acknowledges financial support from the French programme ‘JCJC’ managed by the French National Research Agency (MagnetDrive Project No. ANR-19-CE30-0025-01) and the Institut Universitaire de France.Université Paris Cité, CNRS, MSC, UMR 7057, Paris, FranceJason Barckicke & Eric FalconLaboratoire de Physique de l’Ecole Normale Supérieure, ENS, Université PSL, CNRS, Paris, FranceJason Barckicke & Christophe GissingerInstitut Universitaire de France, Paris, FranceChristophe GissingerSearch author on:PubMed Google ScholarSearch author on:PubMed Google ScholarSearch author on:PubMed Google ScholarC.G. conceived of the experiment and designed the set-up with feedback from E.F. and J.B. E.F. led the implementation of the experimental measurements. J.B. and E.F. built the apparatus. J.B. conducted the experiments and performed the data analysis. E.F. received the funding. All authors contributed to the theoretical framework and interpretation of the experimental results. C.G. wrote the first draft of the paper, with substantial input, figures and revisions from J.B. and E.F. All authors outlined the content of the paper and reviewed and edited the paper.Correspondence to Eric Falcon or Christophe Gissinger.The authors declare no competing interests.Nature Physics thanks Daniel Lathrop and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.For azimuthal wavenumbers m = 0, 1, 2, 3, and 7: (A) Top view, (B) Lateral view. Only the m = 1 mode displaces the vortex axis and has no radius variation.(red curve, triangles): Γ measured by PIV in a horizontal plane located at a depth of z = 25 cm and near r ~ 1 cm. Dotted lines show uncertainty of measurements and variability in z: δΓ ≃ 5.10−3m2/s. (blue curve, circles): Γ inferred by fitting data with the solid rotation Rankine model with a0 and vz measured as in Fig. 2b and Extended Data Fig. VerticalVelocity, respectively. Dotted lines correspond to the same fit, but with a0 taking the values of a(z) at the bottom and at the top of the measured range (below and above, respectively). U = 11 V.Measured from the flat free surface (z = 0) for different drain hole diameters d. vz is measured by PTV at r = a(z). U = 11 V. Inset: Same for different pump flow rates U for d = 7 mm. Measurement uncertainty is δvz ≃ 0.05m/s. It is not shown on the graph for the sake of clarity - note that it is smaller than the variations in z.Dotted lines indicate the values of a(z) at the bottom and top of the measured range. The mean radius a0 = 〈a〉z is obtained by contour detection and averaged over the vertical camera field z ∈ [15.5, 28] cm. U = 11 V. Measurement uncertainty is negligible.for m = 1 and m = 2 Kelvin modes, with parameters Vz = 0.3m/s, γ = 70mN/m, a0 = 1.9 mm, and Γ = 0.022. In our range, capillary corrections remain negligible compared to our experimental uncertainties. The black square marks the typical range of our experimental measurements.with experimental parameters a0 = 1.9 mm, Γ = 0.022 and c = 0.05. Different curves correspond to different zeros of the Bessel functions. No agreement is found with the experimental dispersion relations reported here, as m = 1 solutions are always far from (ω, k) ≈ (0, 0) and m = 2 modes never cross f = 0 in the experimental range.\({\sigma }_{\eta }=\sqrt{{\langle {\eta }^{2}\rangle }_{t}}=1.2\) mm is the rms value, corresponding to m = 1 bending Kelvin waves. \({\sigma }_{\eta }=\sqrt{{\langle {\eta }^{2}\rangle }_{t}}=1.2\) mm is the rms value. Sweep-sine forcing. d = 7 mm, U = 6.8 V. Dashed line: Normal distribution of zero mean and unit standard deviation. Inset: corresponding temporal fluctuations of the vortex-core. Measurement uncertainty on η is negligible.Supplementary Discussion.Side view of the vortex generated in the experiment, showing counterrotating bending waves (azimuthal wavenumber m = 1) propagating downwards along the vortex axis. These Kelvin waves are induced by a sweep-sine horizontal forcing (f = 2–2.5 Hz) applied at the top of the fluid column via a vibrating annulus. The deformation manifests as a helical displacement of the vortex axis with no variation in core radius. Experimental parameters: pump flow rate U = 11 V and drain-hole diameter d = 12 mm.Side view of the vortex in the absence of external forcing, showing double-helix flattening modes (m = 2). These Kelvin waves elliptically deform the vortex core without displacing the vortex axis to form a right-handed helical structure. The perturbations come from drain-hole flow fluctuations. Experimental parameters: pump flow rate U = 13 V and drain-hole diameter d = 7 mm.Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.Reprints and permissionsBarckicke, J., Falcon, E. & Gissinger, C. Kelvin wave propagation along vortex cores. Nat. Phys. (2026). https://doi.org/10.1038/s41567-026-03175-wDownload citationReceived: 02 June 2025Accepted: 08 January 2026Published: 10 February 2026Version of record: 10 February 2026DOI: https://doi.org/10.1038/s41567-026-03175-wAnyone you share the following link with will be able to read this content:Sorry, a shareable link is not currently available for this article. Provided by the Springer Nature SharedIt content-sharing initiative