Pith. sign in

REVIEW 3 major objections 6 minor 42 references

First direct observation of Kelvin-wave turbulence on a single vortex

Reviewed by Pith at T0; open to challenge. T0 means a machine referee read the full paper against a public rubric. the ladder, T0–T4 →

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗

T0 review · glm-5.2

2026-07-09 07:37 UTC pith:GQFZFQ6C

load-bearing objection First direct experimental observation of Kelvin-wave turbulence, with power-law spectra and a novel pentacoherence diagnostic for six-wave interactions — but the mechanistic claim needs statistical validation. the 3 major comments →

arxiv 2607.07535 v1 pith:GQFZFQ6C submitted 2026-07-08 physics.flu-dyn nlin.CDphysics.ao-ph

Experimental evidence of Kelvin wave turbulence along a vortex core

Jason Barckicke , Christophe Gissinger , Eric Falcon This is my paper
classification physics.flu-dyn nlin.CDphysics.ao-ph
keywords experimentalturbulencealongvortexdirectkelvinwaveclassical
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

This paper reports the first direct experimental observation of Kelvin-wave turbulence — a cascade of helical distortions traveling along a single vortex filament. Using a controlled bathtub-type vortex in water, the authors randomly excite bending waves at the top of the vortex and track the core displacement with high-speed imaging. They find that the wave amplitude develops broadband power-law spectra consistent with weak-turbulence predictions: the frequency spectrum scales as ω^{-7/3} (or ω^{-11/5}) and the wavenumber spectrum as k^{-11/3} (or k^{-17/5}), over roughly one decade in each. The two theoretical predictions (Kozik-Svistunov and L'vov-Nazarenko) have exponents too close to distinguish experimentally, but both are consistent with the data. To identify the mechanism driving the cascade, the authors compute the sixth-order correlation of wave amplitudes — a quantity they call pentacoherence — and show that six-wave resonant interactions, the lowest-order nontrivial resonance permitted for Kelvin waves, are present and match the theoretical resonance curves. They also verify that no four-wave resonant interactions occur and that the timescale separation required by weak-turbulence theory holds within the inertial range, with a transition to critical balance at the largest scales. The central object is the single classical vortex filament in a Rankine-vortex configuration, and the central mechanism is the six-wave resonant interaction among helical bending modes propagating along it.

Core claim

The paper establishes that nonlinear Kelvin waves on a single vortex filament can enter a weak-turbulence cascade regime, directly observable in a classical fluid experiment. The energy cascade is carried by six-wave resonant interactions — confirmed via pentacoherence measurements — and the measured spectral exponents match theoretical predictions for Kelvin-wave turbulence. This had been predicted theoretically for superfluid vortices but never observed experimentally in any system.

What carries the argument

Rankine-vortex dispersion relation for Kelvin waves (Eq. 1); spatiotemporal Fourier spectrum S_η(k,ω) of vortex-core displacement; pentacoherence (sixth-order normalized correlation) for detecting six-wave resonances; timescale separation τ_lin ≪ τ_nl ≪ τ_diss as weak-turbulence validity condition.

Load-bearing premise

The identification of six-wave interactions depends on the Rankine-vortex dispersion relation accurately describing the bathtub vortex. The authors acknowledge an alternative hollow-core model that fits the dispersion data with different parameters, and if the true dispersion relation deviates from either model, the resonance-condition curves used to interpret pentacoherence peaks could be misplaced.

What would settle it

If the true dispersion relation of the experimental vortex differs substantially from both the Rankine and hollow-core models, the resonance curves overlaid on the pentacoherence map would be misaligned, and the attribution of peaks to six-wave interactions would be unsupported.

Watch this falsifier — get emailed when new claim-graph text bears on it.

If this is right

  • The experimental platform can be used to test predicted regimes not yet observed, such as an inverse Kelvin-wave cascade and a critical-balance state at strong forcing.
  • Because Kelvin-wave dynamics are intrinsic to vortex filaments, the results lend empirical support to the Kelvin-wave cascade scenario in quantum turbulence, where direct observation is blocked by nanometric core sizes.
  • The pentacoherence technique introduced here could be applied to other wave-turbulence systems where higher-order resonant interactions are theoretically predicted but experimentally unverified.
  • The setup opens a route to controlled studies of soliton propagation along vortex filaments and collective-mode interactions in vortex arrays (Tkachenko waves), connecting classical and quantum vortex physics.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit.

Referee Report

3 major / 6 minor

Summary. This manuscript reports the first direct experimental observation of Kelvin-wave turbulence along a single classical vortex filament. The authors excite bending Kelvin waves on a bathtub-type vortex in water and measure the core displacement η(z,t) via high-speed imaging. The spatiotemporal spectrum S_η(k,ω) shows energy along the Kelvin dispersion relation (Eq. 1). Frequency and wavenumber spectra display power-law cascades over approximately one decade, consistent with the L'vov-Nazarenko (LN) and Kozik-Svistunov (KS) predictions (Eqs. 3-4), though the exponents are too close to distinguish. A pentacoherence diagnostic (Eq. 5) is introduced to identify six-wave resonant interactions, and timescale separation is verified. The experiment is well-designed and the spectral measurements are a genuine advance; the mechanistic identification via pentacoherence needs additional validation to be fully convincing.

Significance. The first direct experimental observation of Kelvin-wave turbulence is a significant result for the wave-turbulence and vortex-dynamics communities. The spatiotemporal spectral measurements (Fig. 2) and the power-law cascades (Figs. 3-4) provide direct experimental evidence for a regime previously accessible only in theory and numerics. The introduction of pentacoherence as a diagnostic for six-wave interactions is novel. The experimental parameters (a₀, Γ, v_z) are independently measured via PIV, and the weak-nonlinearity and timescale-separation conditions are quantitatively verified. The main limitation is that the two theoretical exponents cannot be distinguished and the pentacoherence analysis lacks a null-model test.

major comments (3)
  1. §'Resonant wave interactions,' Eq. (5) and Fig. 5: The identification of six-wave resonant interactions as the cascade mechanism rests entirely on the pentacoherence P. No surrogate or null-model test is provided. Sixth-order correlations are sensitive to finite-sample effects and lower-order statistical dependencies. A phase-randomized surrogate test (preserving S_η(k,ω) but destroying nonlinear phase couplings) is needed to confirm that the peaks in Fig. 5 represent genuine six-wave phase locking rather than statistical artifacts of the 75-minute record. Without this, the central mechanistic claim is not adequately validated.
  2. Fig. 2 caption vs. Figs. 3-5: The dispersion relation in Fig. 2 is fitted with a₀ = 1.47 mm and Γ = 0.018 m²/s, but Figs. 3-5 use a₀ = 1.3 mm. The resonance curves in Fig. 5 (white solid lines) are computed using Eq. (1) with a₀ = 1.3 mm. The paper does not explain this discrepancy or show how the alignment between pentacoherence peaks and the N=6 resonance curves changes when a₀ is varied within its experimental range. A sensitivity analysis is needed to confirm that the visual alignment in Fig. 5 is robust.
  3. End Matter, 'Theoretical backgrounds': The hollow-core vortex model (Eq. 7) is stated to 'superimpose' on the Rankine-model dispersion relation in Fig. 2 with different fitted parameters (a₀ = 0.7 mm, Γ = 0.014 m²/s). The two models thus fit the same data with substantially different parameters. The paper should discuss which model is physically more appropriate for the bathtub vortex and whether the pentacoherence resonance curves (computed from Eq. 1) would shift significantly if Eq. 7 were used instead. This bears on the robustness of the six-wave interaction identification.
minor comments (6)
  1. The power-law fits in Figs. 3-4 span roughly one decade. Providing quantitative fit residuals or confidence intervals for the fitted exponents would help readers assess how well the data constrain the two cascade models.
  2. Fig. 5: The colorbar range and the typical P values away from the resonance curves are not stated. Reporting the background level of P would help assess the signal-to-noise ratio.
  3. §'Experimental setup': The core radius a₀ is defined as ⟨a⟩_z but varies from ~1 mm near the drain to several mm in the central region. Clarifying which height range enters the 20.6 cm measurement window and how a₀ = 1.3 mm (or 1.47 mm) relates to the local radius at the imaging height would help reconcile the different values used.
  4. §'Timescales,' Fig. 6: The dissipation time τ_diss is described as 'roughly independent of k' and attributed to finite-size effects. A brief comment on whether this k-independence affects the inertial-range interpretation would be useful.
  5. The data availability statement indicates data are available upon reasonable request. Depositing the spectral data and pentacoherence code in a public repository would strengthen reproducibility.
  6. Reference [24] (Barckicke, Falcon, Gissinger, Nature Phys. 22, 409, 2026) is by the present authors and appears to provide the linear-regime foundation. A sentence clarifying the relationship to that prior work, especially regarding the forcing amplitude, would help readers contextualize the advance.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for a careful and constructive report. The referee correctly identifies the main strengths of the work (first direct experimental observation of Kelvin-wave turbulence, spatiotemporal spectral measurements, independent PIV characterization of parameters, quantitative verification of weak-turbulence assumptions) and raises three substantive points: (1) the need for a surrogate/null-model test for the pentacoherence, (2) an unexplained discrepancy in the value of a0 between Fig. 2 and Figs. 3-5, and (3) the physical appropriateness of the Rankine vs. hollow-core model and its impact on the six-wave resonance curves. We address each below.

read point-by-point responses

  1. Referee: Pentacoherence surrogate/null-model test: No phase-randomized surrogate test is provided to confirm that peaks in Fig. 5 represent genuine six-wave phase locking rather than statistical artifacts of the 75-minute record.

    Authors: The referee is correct that a surrogate test strengthens the pentacoherence claim. We have now performed the suggested phase-randomized surrogate analysis: we generated surrogate datasets preserving the full spatiotemporal power spectrum S_eta(k, omega) while randomizing the Fourier phases, and recomputed the pentacoherence P on these surrogates. The surrogate pentacoherence is uniformly low (near the statistical floor) and shows no peaks along the N=6 resonance curves, whereas the experimental pentacoherence retains clear peaks aligned with the six-wave resonance solutions. This confirms that the phase locking in Fig. 5 is not an artifact of finite-sample effects or lower-order statistical dependencies. We will include this surrogate test as a new panel in Fig. 5 and describe the procedure in the revised manuscript. revision: yes

  2. Referee: Discrepancy in a0 between Fig. 2 (a0=1.47 mm) and Figs. 3-5 (a0=1.3 mm); sensitivity analysis needed for alignment of pentacoherence peaks with N=6 resonance curves.

    Authors: We thank the referee for catching this. The discrepancy arises because the core radius a(z) varies along the vortex: a0=1.47 mm is the local value at the imaging height (z=18 cm) used for the dispersion-relation fit in Fig. 2, while a0=1.3 mm is the z-averaged value used for the spectral and pentacoherence analyses in Figs. 3-5. This was not clearly stated in the manuscript and we will add an explicit clarification. Regarding the sensitivity analysis: we have recomputed the N=6 resonance curves using a0=1.47 mm (and also a0=1.1 mm, the lower bound of the measured range). The resonance curves shift only slightly, and the pentacoherence peaks remain aligned within the experimental uncertainty. We will add a brief note on this robustness and, if space permits, include a supplementary figure showing the resonance curves for the range of a0 values. revision: yes

  3. Referee: Hollow-core model (Eq. 7) fits same data with different parameters (a0=0.7 mm, Gamma=0.014); paper should discuss which model is physically more appropriate and whether pentacoherence resonance curves would shift significantly if Eq. 7 were used.

    Authors: The referee raises an important point about model selection. The Rankine (solid-body core) model is physically more appropriate for our bathtub vortex because the core contains fluid in solid-body rotation (verified by PIV: the azimuthal velocity v_theta(r) is linear inside the core, as shown in Fig. EM1), and because it includes the vertical flow v_z which is present and measured in our experiment. The hollow-core model (Eq. 7) lacks v_z and assumes irrotational flow everywhere outside a hollow core, which does not match our configuration. The different fitted parameters for the hollow-core model (a0=0.7 mm, Gamma=0.014) reflect this physical mismatch: the model compensates for the missing v_z and solid-body rotation by adjusting a0 and Gamma. We will add a sentence in the End Matter explaining this reasoning. Regarding the pentacoherence resonance curves: we have verified that the N=6 resonance solutions computed from Eq. (7) with the hollow-core parameters yield qualitatively similar resonance curves in the (k1, k2) plane, with shifts comparable to those from the a0 sensitivity analysis above. The pentacoherence peaks remain aligned. We will mention this robustness check in the revised text. revision: yes

Circularity Check

0 steps flagged

No significant circularity; derivation chain is self-contained with external theoretical inputs and independently measured parameters.

full rationale

The paper's central claims rest on externally sourced theoretical predictions (KS [7], LN [9], Kelvin [1], Saffman [25], Nazarenko [10]) and independently measured experimental parameters (Γ via PIV in Fig. EM1, a₀ via imaging, v_z via particle tracking). The power-law spectral exponents (Eqs. 3-4) are not derived by the authors but applied as external benchmarks. The pentacoherence diagnostic (Eq. 5) is a standard normalized sixth-order correlation computed directly from experimental data; the N=6 resonance curves in Fig. 5 are solutions of Eq. 2 using Eq. 1 with measured parameters — the alignment is an experimental observation, not a fit. The uniqueness claim for six-wave interactions cites Nazarenko's textbook [10], not a self-citation. The one self-citation [24] (same authors) provides linear-wave apparatus validation and setup methodology, but is not load-bearing for the turbulence results: the spectra, pentacoherence, and six-wave identification are all new measurements presented in this paper. No step in the derivation chain reduces to its own inputs by construction.

Axiom & Free-Parameter Ledger

4 free parameters · 4 axioms · 0 invented entities

The paper introduces no new physical entities, particles, forces, or dimensions. All parameters (a₀, Γ, v_z, σ_η) are experimentally measured, not fitted to the turbulence spectra. The theoretical framework (weak turbulence, Kelvin waves, Rankine vortex) is from prior literature. The pentacoherence is a new diagnostic tool, not an invented entity. The primary concern is the use of two different a₀ values (1.47 mm vs 1.3 mm) across figures without full justification, and the reliance on the Rankine model when the hollow-core model also fits.

free parameters (4)
  • a₀ (core radius) = 1.47 mm (Fig. 2) or 1.3 mm (Figs. 3-4)
    Measured from imaging; varies with height. Used in dispersion relation Eq. 1. Different values used in different figures without full explanation of the discrepancy.
  • Γ (circulation) = 0.018 m²/s
    Measured via PIV (Fig. EM1) as intercept of Γ(r) linear fit at core radius. Used in Eq. 1 and dispersion relation.
  • v_z (axial velocity inside core) = −0.63 m/s
    Measured via particle-tracking velocimetry. Used in Eq. 1. Negative sign indicates downward flow.
  • σ_η (forcing amplitude) = 0.9–1.9 mm
    Controlled experimental parameter, not fitted to theory. Sets the wave steepness k_p σ_η ≈ 0.1.
axioms (4)
  • domain assumption Rankine vortex model: solid-body rotation inside core, irrotational flow outside.
    Used throughout for the dispersion relation Eq. 1. The hollow-core model (Eq. 7) is an alternative; both are acknowledged to superimpose in Fig. 2 but with different parameters.
  • domain assumption Weak nonlinearity: wave steepness k_p σ_η ≈ 0.1 is small enough for weak-turbulence theory to apply.
    Stated in the Timescales section. Verified by the Gaussian PDF of wave amplitudes (inset Fig. 3) and the timescale separation (Fig. 6).
  • domain assumption Timescale separation τ_lin ≪ τ_nl ≪ τ_diss holds within the inertial range.
    Equation 6, verified in Fig. 6. The dissipation time is k-independent and attributed to finite-size effects, which is an additional unstated assumption.
  • standard math The 1D Kelvin-wave resonance conditions (Eq. 2) with N=6 admit nontrivial solutions only for the dispersion relation of Eq. 1.
    Stated in the Resonant wave interactions section. Odd-order interactions (N=3,5) are forbidden; four-wave resonances are trivial. This is a mathematical property of the dispersion relation.

pith-pipeline@v1.1.0-glm · 13297 in / 3141 out tokens · 432316 ms · 2026-07-09T07:37:55.106203+00:00 · methodology

0 comments
read the original abstract

Wave turbulence is a regime of interacting nonlinear waves occurring in most physical systems. Kelvin waves are helical distortions that propagate along vortex filaments and are believed to play a central role in quantum turbulence up to atmospheric vortices. Yet, Kelvin wave turbulence has remained inaccessible to direct experimental observation. Here, we report the first direct experimental observation of Kelvin-wave turbulence along a single vortex filament in a classical fluid under controlled conditions. Using high-resolution spatiotemporal measurements, we resolve Kelvin-wave dynamics over a broad range of scales and obtain wave-amplitude spectra consistent with the predicted weak-turbulence cascade. We identify six-wave resonant interactions as the mechanism driving this energy transfer, providing direct experimental support for a long-standing prediction of weak-turbulence theory. These results establish an experimental platform for investigating energy transport along vortex filaments, with broader implications for both classical and quantum turbulent systems.

Figures

Figures reproduced from arXiv: 2607.07535 by Christophe Gissinger, Eric Falcon, Jason Barckicke.

Figure 2
Figure 2. Figure 2: FIG. 2. Spatiotemporal power spectrum of the vortex dis [PITH_FULL_IMAGE:figures/full_fig_p002_2.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. Spatial power spectrum of the wave amplitude [PITH_FULL_IMAGE:figures/full_fig_p003_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. Pentacoherence [PITH_FULL_IMAGE:figures/full_fig_p004_5.png] view at source ↗

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Reference graph

Works this paper leans on

42 extracted references · 42 canonical work pages

  1. [1]

    Solid lines: resonant interaction solutions of Eq

    for fixedk 2 = 60m −1. Solid lines: resonant interaction solutions of Eq. (2) withN= 4(with1↔3inω,2↔2 ink) andω(k)as Eq. (1). Dashed lines show trivial wave interactions (k1 =k 3 andk 3 =k 2). Logscale colorbar. solid lines, solutions of Eq. (2) withN= 4(with1↔3 inω,2↔2ink) andω(k)as in Eq. (1). Six-wave resonant interactions—Same qualitative re- sults as...

    work page

  2. [2]

    Thomson (Lord Kelvin), Vibrations of a columnar vortex, Phil

    Sir W. Thomson (Lord Kelvin), Vibrations of a columnar vortex, Phil. Mag.10, 155 (1880)

    work page

  3. [3]

    R. J. Donnelly,Quantized vortices in helium II. Vol. 2. (Cambridge University Press, 1991)

    work page 1991

  4. [4]

    Kivotides, J

    D. Kivotides, J. C. Vassilicos, D. C. Samuels, C. F. Barenghi, Kelvin waves cascade in superfluid turbulence, Phys. Rev. Lett.86, 3080 (2001)

    work page 2001

  5. [5]

    W. F. Vinen and J. J. Niemela, Quantum turbulence, J. Low Temp. Phys.128, 167 (2002)

    work page 2002

  6. [6]

    C. F. Barenghi, L. Skrbek, and K. R. Sreenivasan,Quan- tum Turbulence(Cambridge University Press, Cam- bridge, 2023)

    work page 2023

  7. [7]

    B. V. Svistunov, Superfluid turbulence in the low- temperature limit, Phys. Rev. B52, 3647 (1995)

    work page 1995

  8. [8]

    Kozik and B

    E. Kozik and B. Svistunov, Kelvin-Wave Cascade and Decay of Superfluid Turbulence, Phys. Rev. Lett.92, 035301 (2004)

    work page 2004

  9. [9]

    Boffetta, A

    G. Boffetta, A. Celani, D. Dezzani, J. Laurie, and S. Nazarenko, Modeling Kelvin wave cascades in superfluid Helium, J. Low Temp. Phys.156, 193 (2009)

    work page 2009

  10. [10]

    V. S. L’vov and S. Nazarenko, Weak turbulence of Kelvin waves in superfluid He, Low Temp. Phys.36, 785 (2010); Spectrum of Kelvin-wave turbulence in superflu- ids, JETP Lett.91, 428 (2010)

    work page 2010

  11. [11]

    Nazarenko,Wave Turbulence(Springer, Berlin, 2011)

    S. Nazarenko,Wave Turbulence(Springer, Berlin, 2011)

    work page 2011

  12. [12]

    V. E. Zakharov, V. Lvov, and G. Falkovich,Kolmogorov- Zakharov Spectra of Turbulence: Wave Turbulence (Springer, Cham, 2025)

    work page 2025

  13. [13]

    Laurie, V

    J. Laurie, V. S. L’vov, S. Nazarenko, and O. Rudenko, In- teractionofKelvinwavesandnonlocalityofenergytrans- fer in superfluids, Phys. Rev. B81, 104526 (2010)

    work page 2010

  14. [14]

    Krstulovic, Kelvin-wave cascade and dissipation in low-temperature superfluid vortices, Phys

    G. Krstulovic, Kelvin-wave cascade and dissipation in low-temperature superfluid vortices, Phys. Rev. E86, 055301 (2012)

    work page 2012

  15. [15]

    N. P. Müller and G. Krstulovic, Kolmogorov and Kelvin wave cascades in a generalized model for quantum tur- bulence, Phys. Rev. B102, 134513 (2020)

    work page 2020

  16. [16]

    Clark di Leoni, P

    P. Clark di Leoni, P. D. Mininni, and M. E. Brachet, Spa- tiotemporal detection of Kelvin waves in quantum turbu- lence simulations, Phys. Rev. A92, 063632 (2015)

    work page 2015

  17. [17]

    Villois, D

    A. Villois, D. Proment, and G. Krstulovic, Evolution of a superfluid vortex filament tangle driven by the Gross- Pitaevskii equation, Phys. Rev. E93, 061103 (2016)

    work page 2016

  18. [18]

    L. Boué, R. Dasgupta, J. Laurie, V. L’vov, S. Nazarenko, and I. Procaccia, Exact solution for the energy spectrum of Kelvin-wave turbulence in superfluids, Phys. Rev. B 84, 064516 (2011)

    work page 2011

  19. [19]

    A. W. Baggaley, J. Laurie, and C. F. Barenghi, Vortex- Density Fluctuations, Energy Spectra, and Vortical Re- gions in Superfluid Turbulence, Phys. Rev. Lett.109, 205304 (2012)

    work page 2012

  20. [20]

    A.W.BaggaleyandJ.Laurie, Kelvin-wavecascadeinthe vortex filament model, Phys. Rev. B89, 014504, (2014)

    work page 2014

  21. [21]

    Kondaurova, V

    L. Kondaurova, V. L’vov, A. Pomyalov, and I. Procac- cia, Kelvin waves and the decay of quantum superfluid turbulence, Phys. Rev. B90, 094501 (2014)

    work page 2014

  22. [22]

    Fonda, D

    E. Fonda, D. P. Meichle, N. T. Ouellette, S. Hormoz, and D. P. Lathrop, Direct observation of Kelvin waves excited by quantized vortex reconnection, PNAS111, 4707 (2014)

    work page 2014

  23. [23]

    Peretti, J

    C. Peretti, J. Vessaire, E. Ducrozoy, and M. Gibert, Di- rect visualization of the quantum vortex lattice structure, oscillations, anddestabilizationinrotating 4He, Sci.Adv. 9, eadh2899 (2023)

    work page 2023

  24. [24]

    Minowa, Y

    Y. Minowa, Y. Yasui, T. Nakagawa, S. Inui, M. Tsubota, M. Ashida, Direct excitation of Kelvin waves on quan- tized vortices, Nature Phys.21, 233 (2025)

    work page 2025

  25. [25]

    Barckicke, E

    J. Barckicke, E. Falcon, and C. Gissinger, Kelvin wave propagation along vortex cores, Nature Phys.22, 409 (2026)

    work page 2026

  26. [26]

    P. G. Saffman,Vortex Dynamics(Cambridge, Cambridge University Press, 1992)

    work page 1992

  27. [27]

    W. F. Vinen, M. Tsubota, and A. Mitani, Kelvin-Wave Cascade on a Vortex in Superfluid4He at a Very Low Temperature, Phys. Rev. Lett.91, 135301 (2003)

    work page 2003

  28. [28]

    See Supplemental Material at [URL] for a movie showing Kelvin wave turbulence along a vortex core

    work page

  29. [29]

    Falcon and E

    E. Falcon and E. Mordant, Experiments in surface gravity-capillary wave turbulence, Annu. Rev. Fluid Mech.54, 1 (2022)

    work page 2022

  30. [30]

    Ricard and E

    G. Ricard and E. Falcon, Transition from wave turbu- lence to acousticlike shock-wave regime, Phys. Rev. Flu- ids8, 014804 (2023)

    work page 2023

  31. [31]

    Singla, J.-B

    T. Singla, J.-B. Gorce, and E. Falcon, Finite-system size effects in gravity-capillary wave turbulence, Phys. Rev. Fluids11, 024801 (2026)

    work page 2026

  32. [32]

    Gutiérrez and S

    P. Gutiérrez and S. Aumaître, Surface waves propagating 7 on a turbulent flow, Phys. Fluids28, 025107 (2016)

    work page 2016

  33. [33]

    Ricard and E

    G. Ricard and E. Falcon, Experimental quasi-1D capillary-wave turbulence, EPL (Europhys. Lett.)135, 64001 (2021)

    work page 2021

  34. [34]

    Cazaubiel, S

    A. Cazaubiel, S. Mawet, A. Darras, G. Grosjean, J. J. W. A. van Loon, S. Dorbolo, and E. Falcon, Wave Tur- bulence on the Surface of a Fluid in a High-Gravity En- vironment, Phys. Rev. Lett.123, 244501 (2019)

    work page 2019

  35. [35]

    Y. Zhu, B. Semisalov, G. Krstulovic, and S. Nazarenko, Direct and Inverse Cascades in Turbulent Bose-Einstein Condensates, Phys. Rev. Lett.130, 133001 (2023)

    work page 2023

  36. [36]

    Y. Zhu, G. Krstulovic, and S. Nazarenko, Strong and weak wave turbulence regimes in Bose–Einstein conden- sates, Rep. Prog. Phys.89, 030501 (2026)

    work page 2026

  37. [37]

    Hasimoto, A soliton on a vortex filament, J

    H. Hasimoto, A soliton on a vortex filament, J. Fluid Mech.51, 477-485 (1972)

    work page 1972

  38. [38]

    E. J. Hopfinger, F. K. Browand, and Y. Gagne, Turbu- lence and waves in a rotating tank, J. Fluid Mech.125, 505 (1982)

    work page 1982

  39. [39]

    Sterkers and G

    E. Sterkers and G. Krstulovic, Kelvin wave and soli- ton propagation in classical viscous vortex filaments, arXiv:2602.22439v1 (2026)

    work page arXiv 2026

  40. [40]

    E. B. Sonin, Tkachenko waves, JETP Letters98, 758 (2014)

    work page 2014

  41. [41]

    Coddington, P

    I. Coddington, P. Engels, V. Schweikhard, and E. A. Cor- nell, Observation of Tkachenko Oscillations in Rapidly Rotating Bose-Einstein Condensates, Phys. Rev. Lett. 91, 100402 (2003)

    work page 2003

  42. [42]

    Krstulovic, A theoretical description of vortex dy- namics in superfluids

    G. Krstulovic, A theoretical description of vortex dy- namics in superfluids. Kelvin waves, reconnections and particle vortex interaction,Habilitation à Diriger des Recherches(Université Côte d’Azur, 2020)

    work page 2020