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arxiv: 2604.08323 · v1 · submitted 2026-04-09 · ⚛️ physics.flu-dyn

Preferential orientation of slender elastic floaters in gravity waves

Wietze Herreman , Basile Dhote , Frederic Moisy This is my paper

Pith reviewed 2026-05-10 17:35 UTC · model grok-4.3

classification ⚛️ physics.flu-dyn
keywords gravity waveselastic floaterspreferential orientationhydro-elastic theoryyaw momentfloating structureswave-induced drift
0
0 comments X

The pith

Slender elastic floaters in gravity waves rotate to align either along or across the wave direction depending on their stiffness, length and mass.

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

Slender elastic floaters drifting in gravity waves slowly turn toward a preferred orientation because of a wave-induced second-order mean yaw moment. The authors build a diffractionless hydro-elastic theory that calculates this moment for thin flexible structures whose width and thickness are small compared with the wavelength. When the floater length is less than half the wavelength, the theory yields a simple rule: soft, short and heavy floaters settle into the longitudinal state while stiff, long and light floaters settle into the transverse state. For floaters longer than the wavelength the orientational motion can become more complex and admit several stable positions. The result bears directly on the behavior of flexible floating objects such as pontoons and inflatable structures in real wave fields.

Core claim

Slender floaters drifting in propagating gravity waves slowly rotate towards a preferential state of orientation with respect to the angle of incidence. This angular drift arises from a wave-induced, second order mean yaw moment. Using a diffractionless hydro-elastic theory for a thin flexible structure whose width and thickness are small compared with the wavelength, the authors derive that for floater lengths smaller than half the wavelength, soft short heavy floaters prefer the longitudinal state while stiff long light floaters prefer the transverse state. For floaters longer than the wavelength the orientational dynamics become more intricate and may exhibit multiple equilibrium states.

What carries the argument

The diffractionless hydro-elastic theory that computes the second-order mean yaw moment on a thin flexible floater driven by gravity waves.

If this is right

  • For floaters shorter than half the wavelength the preferred orientation is fixed by the relative strength of elastic bending, inertia and weight.
  • Floaters longer than the wavelength can possess multiple stable equilibrium orientations.
  • The mean yaw moment is generated at second order by the wave-floater interaction.
  • The model directly informs the design of flexible floating platforms such as pontoons and inflatable structures.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The same mechanism may govern the long-term alignment of floating debris or ice floes in ocean wave fields.
  • Wave-tank experiments that systematically vary bending stiffness and mass distribution could map the transition at half-wavelength.
  • The theory could be extended to irregular wave spectra to predict average orientations in realistic sea states.

Load-bearing premise

The diffractionless hydro-elastic theory assumes the floater width and thickness are small compared with the wavelength and that the structure remains thin and flexible.

What would settle it

A controlled wave-tank test in which a short, heavy and soft floater consistently rotates to the transverse state rather than the longitudinal state would falsify the derived orientation criterion.

Figures

Figures reproduced from arXiv: 2604.08323 by Basile Dhote, Frederic Moisy, Wietze Herreman.

Figure 1
Figure 1. Figure 1: FIG. 1. Typical deformation of a thin elastic floating structure in waves as a function of the ratios [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Elongated, freely drifting structures placed in propagating gravity waves slowly rotate towards a [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. (a) A flexible strip with center [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. Deformation [PITH_FULL_IMAGE:figures/full_fig_p011_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. Non-dimensional mean yaw moment [PITH_FULL_IMAGE:figures/full_fig_p013_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6. The non-dimensional mean yaw moment [PITH_FULL_IMAGE:figures/full_fig_p014_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7. Theoretical phase diagram for preferential orientation according to the short floater theory. The [PITH_FULL_IMAGE:figures/full_fig_p016_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: FIG. 8. WietzeWH@FM: change 90/795 into 5/42 in (a) Phase diagrams in the [PITH_FULL_IMAGE:figures/full_fig_p017_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: FIG. 9. Mean yaw moments on flexible floating pontoons. (a) Sketch of a typical modular pontoon. (b) [PITH_FULL_IMAGE:figures/full_fig_p018_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: FIG. 10. (a) Sketch of paddle board in waves. We vary wavelength and flexural length. (b) Phase diagram [PITH_FULL_IMAGE:figures/full_fig_p019_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: FIG. 11. Phase diagram for foam mats with varying flexural lengths, lenghts [PITH_FULL_IMAGE:figures/full_fig_p020_11.png] view at source ↗
read the original abstract

Slender floaters drifting in propagating gravity waves slowly rotate towards a preferential state of orientation with respect to the angle of incidence. This angular drift arises from a wave-induced, second order mean yaw moment. We develop a diffractionless, hydro-elastic theory to compute this mean yaw moment for a thin, flexible structure whose width and thickness are small compared with the wavelength. For floater lengths smaller than half the wavelength, we derive a simple, predictive criterion for the preferred orientation: Soft, short and heavy floaters prefer the longitudinal state, while stiff, long and light floaters prefer the transverse state. For floaters longer than the wavelength, the orientational dynamics become more intricate and may exhibit multiple equilibrium states. We discuss the implications of the model for flexible floating structures such as pontoons and inflatable structures.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

1 major / 1 minor

Summary. The manuscript develops a diffractionless hydro-elastic theory to calculate the second-order mean yaw moment on thin, flexible floaters in gravity waves. For floater lengths smaller than half the wavelength, it derives a simple predictive criterion: soft, short and heavy floaters prefer the longitudinal orientation while stiff, long and light floaters prefer the transverse state. For longer floaters the orientational dynamics become more intricate and may exhibit multiple equilibria. The theory assumes the floater width and thickness are small compared to the wavelength and discusses implications for structures such as pontoons and inflatable platforms.

Significance. If the results hold, the work supplies an analytical, parameter-free criterion for the preferred orientation of elastic floaters that could be directly tested and applied to the design of flexible floating structures in wave fields. The derivation of a clear dependence on stiffness, length and mass from standard hydro-elastic principles is a strength.

major comments (1)
  1. [Model assumptions and applicability for L < λ/2] The diffractionless approximation is applied for lengths up to L = λ/2 (see the statement of the criterion for L < λ/2). At this scale the length is no longer ≪ λ, so the neglect of wave scattering and the underlying incident-wave assumption in the second-order mean yaw moment may cease to be uniformly valid. Because the sign of this moment determines the longitudinal versus transverse preference, an error estimate or comparison with a diffraction-inclusive calculation near L = λ/2 is needed to confirm that the reported criterion remains reliable throughout the claimed regime.
minor comments (1)
  1. [Abstract] The abstract presents the orientation criterion at a high level without the explicit functional form; adding a brief statement of the dependence on bending stiffness, mass and length would improve immediate accessibility of the main result.

Simulated Author's Rebuttal

1 responses · 1 unresolved

We thank the referee for their careful reading and constructive feedback. We address the major comment below, acknowledging the limitation of the diffractionless approximation while clarifying its regime of applicability. Revisions have been made to the manuscript to strengthen the discussion of model assumptions.

read point-by-point responses

  1. Referee: [Model assumptions and applicability for L < λ/2] The diffractionless approximation is applied for lengths up to L = λ/2 (see the statement of the criterion for L < λ/2). At this scale the length is no longer ≪ λ, so the neglect of wave scattering and the underlying incident-wave assumption in the second-order mean yaw moment may cease to be uniformly valid. Because the sign of this moment determines the longitudinal versus transverse preference, an error estimate or comparison with a diffraction-inclusive calculation near L = λ/2 is needed to confirm that the reported criterion remains reliable throughout the claimed regime.

    Authors: We agree that the diffractionless theory, which neglects scattering by assuming the incident-wave potential, is formally justified when all dimensions satisfy ≪ λ. The manuscript explicitly restricts the simple predictive criterion to L < λ/2 while noting that width and thickness remain small compared with λ. The second-order yaw moment is obtained from the leading-order hydro-elastic interaction under this assumption. A quantitative error bound or direct comparison with a diffraction-inclusive formulation would indeed be desirable to assess deviations near the upper end of the interval; however, performing such a calculation requires an entirely separate analysis outside the present diffractionless framework. In the revised manuscript we have added a dedicated paragraph in the discussion section that (i) restates the underlying assumptions, (ii) notes that the sign of the moment—and hence the predicted preference—remains robust provided the transverse dimensions stay small, and (iii) cautions that the criterion should be regarded as approximate as L approaches λ/2. This revision makes the domain of validity explicit without altering the derived expressions. revision: partial

standing simulated objections not resolved
  • A quantitative error estimate or direct comparison against a diffraction-inclusive calculation near L = λ/2, which would require extending the theory beyond the diffractionless assumption employed throughout the manuscript.

Circularity Check

0 steps flagged

No circularity: derivation from standard hydro-elastic principles is self-contained

full rationale

The paper develops a diffractionless hydro-elastic theory from first principles to compute the second-order mean yaw moment acting on a thin flexible floater. The predictive criterion for L < λ/2 (soft/short/heavy floaters prefer longitudinal orientation; stiff/long/light prefer transverse) follows directly from the sign of this computed moment under the stated thin-structure assumptions. No load-bearing steps reduce by construction to fitted parameters, self-citations, or definitional equivalences; the abstract and derivation chain contain no evidence of the enumerated circular patterns. The result is independent of its inputs and externally falsifiable via the underlying hydro-elastic equations.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on a diffractionless hydro-elastic theory for computing the mean yaw moment, with the key assumption that floater dimensions are small relative to wavelength; no free parameters or invented entities are mentioned.

axioms (1)
  • domain assumption Width and thickness of the floater are small compared with the wavelength
    Explicitly stated as the condition for the diffractionless hydro-elastic theory to apply.

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Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

  1. Capillary effects on preferential orientation of floaters in gravity waves

    physics.flu-dyn 2026-04 unverdicted novelty 4.0

    Capillary forces alter the effective immersion of floaters, making their preferred alignment in gravity waves depend on the parameter F = k L_x² / h-bar compared to a critical value based on bending stiffness.

Reference graph

Works this paper leans on

37 extracted references · 37 canonical work pages · cited by 1 Pith paper

  1. [1]

    sinc cψlx 2 + 12 l2x ∂2 ∂ψ 2 sinc cψlx 2 # =− 6sψ lx j1 cψlx 2

    The coefficientsA, Bare fixed by the boundary conditions, that lead to the linear systems   j2 cosh jlx 2lD j∗2 cosh j∗lx 2lD j3 sinh jlx 2lD j∗3 sinh j∗lx 2lD   A A∗ =   l2 Dc2 ψ l4 Dc4 ψ+1 cos cψlx 2 − l3 Dc3 ψ l4 Dc4 ψ+1 sin cψlx 2   (33a) and   j2 sinh jlx 2lD j∗2 sinh j∗lx 2lD j3 cosh jlx 2lD j∗3 cosh j∗lx 2lD   B B∗ =   l2 Dc2 ψ l4 Dc4...

    work page

  2. [2]

    J. N. Newman, Marine hydrodynamics (The MIT press, 2018)

    work page 2018

  3. [3]

    C. H. Kim, Nonlinear waves and offshore structures, Vol. 27 (World Scientific Publishing Company, 2008)

    work page 2008

  4. [4]

    Molin, Offshore Structure Hydrodynamics (Cambridge University Press, 2023)

    B. Molin, Offshore Structure Hydrodynamics (Cambridge University Press, 2023)

    work page 2023

  5. [5]

    R. E. D. Bishop and W. G. Price, Hydroelasticity of Ships (Cambridge University Press, 1979)

    work page 1979

  6. [6]

    Montiel, F

    F. Montiel, F. Bonnefoy, P. Ferrant, L. G. Bennetts, V. A. Squire, and P. Marsault, Hydroelastic response of floating elastic discs to regular waves. Part 1. Wave basin experiments, Journal of Fluid Mechanics723, 604 (2013). 24

    work page 2013

  7. [7]

    Montiel, L

    F. Montiel, L. G. Bennetts, V. A. Squire, F. Bonnefoy, and P. Ferrant, Hydroelastic response of floating elastic discs to regular waves. Part 2. Modal analysis, Journal of Fluid Mechanics723, 629 (2013)

    work page 2013

  8. [8]

    Wang and B

    C. Wang and B. Wang, Large Floating Structures Technological Advances (Springer, 2015)

    work page 2015

  9. [9]

    Meylan and V

    M. Meylan and V. A. Squire, The response of ice floes to ocean waves, Journal of Geophysical Research 99, 891 (1994)

    work page 1994

  10. [10]

    Squire, Ocean wave interactions with sea ice: a reappraisal, Annu

    V. Squire, Ocean wave interactions with sea ice: a reappraisal, Annu. Rev. Fluid Mech.52, 37–60 (2020)

    work page 2020

  11. [11]

    Watanabe, T

    E. Watanabe, T. Utsunomiya, and C. Wang, Hydroelastic analysis of pontoon-type vlfs: a literature survey, Engineering structures26, 245 (2004)

    work page 2004

  12. [12]

    Ocean sun, https://oceansun.no (2024)

    work page 2024

  13. [13]

    Isobe, Research and development of mega-float, inProceedings of the 3rd international workshop on very large floating structures (1999) pp

    E. Isobe, Research and development of mega-float, inProceedings of the 3rd international workshop on very large floating structures (1999) pp. 7–13

    work page 1999

  14. [14]

    H. C. Mozaf, M. Ghiasi, and P. Ghadimi, Performance assessment of the innovative wave line magnet wave energy converter, Energy337, 138547 (2025)

    work page 2025

  15. [15]

    Malenica, Q

    S. Malenica, Q. Derbanne, F.-X. Sireta, F. Bigot, E. Tiphine, G. De-Hauteclocque, and X.-B. Chen, Homer-integrated hydro-structure interactions tool for naval and off-shore applications, in RINA, International Conference on Computer Applications in Shipbuilding (2013) pp. 209–221

    work page 2013

  16. [16]

    Zhang and S

    M. Zhang and S. Schreier, Review of wave interaction with continuous flexible floating structures, Ocean Engineering264, 112404 (2022)

    work page 2022

  17. [17]

    Tavakoli, M

    S. Tavakoli, M. Singh, S. Hosseinzadeh, Z. Hu, Y. Shao, S. Wang, L. Huang, A. Grammatikopoulos, Y. P. Li, D. Khojasteh, J. Liu, A. Dolatshah, H. Cheng, and S. Hirdaris, A review of flexible fluid- structure interactions in the ocean: Progress, challenges, and future directions, Ocean Engineering342, 122545 (2025)

    work page 2025

  18. [18]

    Timoshenko and S

    S. Timoshenko and S. Woinowsky-Krieger, Theory of Plates and Shells, 2nd ed. (McGraw-Hill, New York, 1959)

    work page 1959

  19. [19]

    L. D. Landau and E. M. Lifshitz, Theory of Elasticity, 3rd ed., Course of Theoretical Physics, Vol. 7 (Pergamon Press, Oxford, 1986)

    work page 1986

  20. [20]

    J. N. Newman, The drift force and moment on ships in waves, Journal of ship research11, 51 (1967)

    work page 1967

  21. [21]

    Veritas, Hydrostar for experts user manual, Bureau Veritas (2016)

    B. Veritas, Hydrostar for experts user manual, Bureau Veritas (2016)

    work page 2016

  22. [22]

    Kashiwagi, A new solution method for hydroelastic problems of a very large floating structure in waves, in Proc 17th Int Conf Offshore Mech and Arctic Eng, ASME, 1998 (1998)

    M. Kashiwagi, A new solution method for hydroelastic problems of a very large floating structure in waves, in Proc 17th Int Conf Offshore Mech and Arctic Eng, ASME, 1998 (1998)

    work page 1998

  23. [23]

    Y. Miao, X. Chen, H. Shen, X. Wei, K. Lu, and G. Wu, Analysis of the second order wave forces acted on a floating pontoon, in 11th International Workshop on Ship and Marine Hydrodynamics (IWSH2019) (2019)

    work page 2019

  24. [24]

    T. S. van den Bremer and O. Breivik, Stokes drift, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences376, 20170104 (2018)

    work page 2018

  25. [25]

    S. G. Monismith, Stokes drift: theory and experiments, Journal of Fluid Mechanics884, F1 (2020)

    work page 2020

  26. [26]

    A. W. K. Law, Wave-induced surface drift of an inextensible thin film, Ocean Engineering , 24 (1999)

    work page 1999

  27. [27]

    P. C. Y. Wong and A. W.-K. Law, Wave-induced drift of an elliptical surface film, Ocean Engineering 30, 413 (2003)

    work page 2003

  28. [28]

    K. H. Christensen and J. E. Weber, Wave-induced drift of large floating sheets, Geophysical & Astro- physical Fluid Dynamics99, 433 (2005)

    work page 2005

  29. [29]

    A. W.-K. Law and G. Huang, Observations and measurements of wave-induced drift of surface inex- tensible film in deep and shallow waters, Ocean Engineering34, 94 (2007)

    work page 2007

  30. [30]

    Kostikov, M

    V. Kostikov, M. Hayatdavoodi, and R. C. Ertekin, Drift of elastic floating ice sheets by waves and current, part i: single sheet, Proc. R. Soc. A.477, 20210449 (2021)

    work page 2021

  31. [31]

    Skejic and O

    R. Skejic and O. M. Faltinsen, A unified seakeeping and maneuvering analysis of ships in regular waves, Journal of marine science and technology13, 371 (2008)

    work page 2008

  32. [32]

    Suyehiro, The yawing of ships caused by the oscillation amongst waves., Journal of Zosen Kiokai 1920, 23 (1921)

    K. Suyehiro, The yawing of ships caused by the oscillation amongst waves., Journal of Zosen Kiokai 1920, 23 (1921)

    work page 1920

  33. [33]

    Le Boulluec, B

    M. Le Boulluec, B. Forest, and E. Mansuy, Steady drift of floating objects in waves - experimental and numerical investigations, Proceedings of the ASME 27th International Conference on Offshore Mechanics and Arctic Engineering (2008)

    work page 2008

  34. [34]

    Herreman, B

    W. Herreman, B. Dhote, L. Danion, and F. Moisy, Preferential orientation of floaters drifting in water waves, J. Fluid Mech. (in press) (2024), arXiv:2401.03254 [physics.flu-dyn]

    work page arXiv 2024

  35. [35]

    Dhote, F

    B. Dhote, F. Moisy, and W. Herreman, Flexible floaters align with the direction of wave propagation, Physical Review Fluids10, 074801 (2025). 25

    work page 2025

  36. [36]

    M. Kashiwagi, A time-domain green function method for transient problems of a pontoon-type vlfs, in Proceedings of the 3rd International Workshop on Very Large Floating Structures, Honolulu, Vol. 1 (1999) pp. 97–104

    work page 1999

  37. [37]

    J. N. Newman, The drift force and moment on floating and submerged bodies in long waves, Journal of Fluid Mechanics1032, A19 (2026)

    work page 2026