Pith. sign in

REVIEW 2 major objections 3 minor 38 references

Surface Waves Alter Air Entrainment During Water Entry

T0 review · 2 major / 3 minor · reviewed 2026-08-01 · deepseek-v4-flash

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

Pith's one-line read When a sphere falls into wavy water, the local slope of the wave at the sphere's radius determines how much air gets dragged under, and this single geometric parameter collapses experiments across wave phase, frequency, and amplitude.

desk verdict Careful experiments and a genuinely new collapse parameter, but the 'fully described' claim outruns the evidence — worth refereeing, with a request for a direct slope check. read the letter →

arxiv 2607.20067 v1 pith:HKZUG4EX submitted 2026-07-22 physics.flu-dyn

Chase T. Gabbard , Mario Ibrahim , Joseph Quinton , Eli Silver , Jesse Belden , Daniel M. Harris This is my paper
classification physics.flu-dyn
keywords waterentryairentrainmentsurfacewavescavityclosuresplashcurtaindeepsealWebernumber
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

This paper asks whether the shape of a wavy water surface changes how much air a falling sphere entrains. The answer is yes: the effect can be dramatic, enough to nearly double the maximum cavity volume or shift the closure mode between deep seal and surface seal. The authors show that all their measurements across wave phase, drive amplitude, and frequency collapse onto a single curve when plotted against m ≈ AR/λ², the local wave slope at the sphere radius. The mechanism is geometric: waves alter the trajectory of the splash curtain, not the early submarine cavity expansion. If correct, this adds one dimensionless number to the classical Weber and Bond numbers for predicting air entrainment on unsteady, real-world interfaces.

What carries the argument

The central object is m ≈ AR/λ², a dimensionless local interface slope at the impactor radius R. It is derived from an assumed axisymmetric standing wave field h(r,t)=A0J0(kr)sin(ωt+ϕ), whose slope is ∂h/∂r = −A0k J1(kr)sin(ωt+ϕ); for R ≪ λ, this reduces to m ∼ AR/λ² and can be interpreted as the ratio of the sphere radius to the local radius of curvature of the interface. The parameter does the work of separating the wave's geometric effect from the impact dynamics: the interface appears frozen on the R/U timescale, so the instantaneous slope at the impactor scale sets the initial conditions of the ejecta sheet and splash curtain, ultimately controlling whether the cavity closes deep or at

What would settle it

Measure the free-surface slope directly at r=R at the instant of impact—for example, with a second high-speed camera profiling the interface or laser profilometry—across the same drive amplitudes and frequencies, then replot maximum cavity volume against the measured slope. If the data no longer collapse, or if two wavefields with the same modeled m but different true local geometry give different volumes, the claim that m alone captures the wave effect is falsified.

Watch

Extended reading notes

Core claim

The paper's central claim is that for a hydrophobic sphere entering an axisymmetric standing wave field, the influence of the waves on air entrainment is fully described by the non-dimensional local wave slope m ∼ AR/λ² evaluated at the sphere radius. Impacts on crests (positive m) widen the splash curtain, delay surface seal, and can nearly double the maximum cavity volume, shifting the deep-seal-to-surface-seal transition to higher Weber numbers; impacts on troughs (negative m) have a weaker opposing effect. Plotting V*/Vs against m collapses all data for fixed We and Bo regardless of wave phase, frequency, or driving amplitude, and the same parameter also captures pinchoff depth and time.

Load-bearing premise

The load-bearing premise is that the local wave slope at the sphere radius equals the value computed from a modeled single-mode axisymmetric standing wave h=A0J0(kr)sin(ωt+ϕ) with deep-water dispersion; if the real instantaneous surface near the impact point is not well described by that assumed shape, the parameter m assigned to each impact is systematically wrong and the reported collapse could be partly an artifact.

Editorial extensions

If this is right

  • For fixed Weber and Bond numbers, air entrainment in a wavy bath can be predicted from a single local geometric measurement of the free surface at the impactor scale, rather than from the detailed wave state.
  • Crest impacts extend the deep-seal regime to higher Weber numbers, meaning a wavy surface can allow air entrainment to exceed the quiescent-water maximum; trough impacts reduce it.
  • Because the wave acts through the splash curtain rather than the submarine cavity expansion, the effect is additive with other mechanisms such as ambient pressure and splash guards.
  • The same slope parameter collapses not only maximum cavity volume but also pinchoff depth and time, so the framework describes the whole cavity evolution.
  • The scaling is hypothesized to extend to drops and to three-dimensional interfaces described by two principal curvatures plus a mean surface slope.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • Inference: If the collapse holds for broadband, non-axisymmetric seas, field practitioners could estimate m from wave spectra at the body scale and bypass detailed impact experiments for air-entrainment estimates.
  • Inference: The frozen-interface assumption implies a regime boundary: waves with periods comparable to or shorter than R/U should break the single-parameter description. Mapping that boundary would define the framework's validity.
  • Inference: If the mechanism is purely geometric via ejecta angle, the same m parameter may apply to non-hydrophobic impactors or flat-faced bodies, though the functional form of V*(m) could differ. This is a testable extension the paper does not make.
  • Inference: The paper's reliance on a modeled rather than directly measured slope leaves room for a direct experimental check: measuring the instantaneous surface slope at r=R would confirm the collapse or reveal that part of it is an artifact of the assumed wave form.
Share X Bluesky LinkedIn Reddit HN

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

2 major / 3 minor

Summary. The paper reports controlled experiments on hydrophobic spheres impacting an axisymmetric, ring-generated standing wave field at a water surface. By varying wave phase, driving frequency, driving amplitude, Weber number, and Bond number, the authors show that surface waves can substantially change the volume of entrained air and can shift the cavity between deep-seal and surface-seal closure. They propose that the influence of the wave is captured by a single non-dimensional local slope parameter m ~ A R / lambda^2 evaluated at the sphere radius, and demonstrate that, at fixed (We,Bo), V* collapses onto a single curve as a function of m across the tested wave parameters. The paper is clearly written, the experiments are carefully repeated (three trials per condition), and the data are made openly available. However, the central conclusion that the wave influence is 'fully described' and 'universally captured' by m is broader than the evidence, chiefly because m is inferred from an assumed analytic waveform rather than directly validated, and because the experimental scope is limited to centered impacts on a single axisymmetric wave mode.

Significance. If the m-collapse survives direct slope validation, this would be a valuable and transferable result: it would reduce the wave influence to a local geometric quantity, connecting a longstanding idealized problem to wavy interfaces and potentially informing naval and multiphase-flow applications. The paper's strengths are its controlled parametric isolation of interface geometry, the clear physical mechanism (splash-curtain modulation rather than cavity expansion), the three-trial repeats with error bars, and the open data/movies. The proposed parameter is not a fitted free parameter, so the collapse is not guaranteed by construction. Nevertheless, the unsupported model dependence of m and the overgeneralization to open-ocean conditions are load-bearing issues that must be addressed before the stronger claims can be accepted.

major comments (2)
  1. [Eq. (2) and Fig. 4] The collapsing parameter m is not measured directly but inferred from the assumed linear Bessel wavefield h(r,t)=A0 J0(kr) sin(omega t + phi) and the deep-water dispersion relation. Even if the central amplitude A is measured at r=0, the slope at r=R is a model output. The paper does not validate this slope with a direct measurement of the interface tangent at the sphere radius, nor does it demonstrate that higher radial modes, meniscus effects, and nonlinearity are negligible at the largest Ad and f. Because m is the sole wave parameter used for the collapse, a systematic error in m could artificially tighten Fig. 4. The assumption R << lambda is only marginally satisfied (R/lambda up to ~0.2), so the small-argument approximation J1(kR) ≈ kR/2 involves ~20% errors in the slope at the largest R/lambda. Please validate the waveform by direct image-based measurement of h(r) near r=R at the
  2. [Abstract and Conclusion] The claims that wave influence is 'fully described' and 'universally captured' by m extend beyond the evidence. The experiments cover centered impacts on a ring-generated axisymmetric standing wavefield, and the m-collapse is demonstrated at only two Weber numbers and two Bond numbers (Fig. 4). Real open-ocean surfaces involve broadband, directional, nonlinear waves and off-axis impact points, none of which are tested here. The later statement that the framework 'may be adaptable' to more complex interfaces is appropriate; the abstract and conclusion should be tempered to the axisymmetric standing-wave regime and to state extension to ocean surfaces as a hypothesis rather than as an established predictive framework.
minor comments (3)
  1. [Fig. 4 caption] All three panels are labeled '(a)' in the caption; they should be (a), (b), and (c).
  2. [Section 'Experimental setup' / Fig. S6] The text says the central amplitude A is 'determined by the drive amplitude Ad and the impact phase phi', but later mentions measured A/R values. Please clarify whether A is measured from images or inferred from the drive parameters, and describe the measurement if used.
  3. [Discussion of Fig. 3(b)] The claim that the measured wave amplitude A remains nearly constant with frequency is supported by Fig. S6 but not shown with error bars in the main text; adding uncertainty information for A would strengthen the interpretation.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the wave-slope parameter m is a measured geometric input, not fitted to the cavity-volume data it is used to collapse.

full rationale

The paper's central claim is that the dimensionless maximum cavity volume V* collapses onto a single curve as a function of m ~ AR/lambda^2 for fixed Weber and Bond numbers. Walking the derivation chain, m is constructed from Eq. (2), which is obtained from the linear axisymmetric standing-wave model h(r,t) = A0 J0(kr) sin(omega t + phi) via the small-argument form of the Bessel derivative. The inputs to m are the measured central wave amplitude A (set by drive amplitude and impact phase), the sphere radius R, and the wavelength lambda determined by the imposed frequency and the gravity-capillary dispersion relation. None of these inputs are fitted to, or derived from, the measured cavity volume V*. The collapse in Fig. 4 is therefore not guaranteed by construction: m is an independently varied geometric parameter, and the observed collapse is an empirical result. No equation in the paper reduces the prediction to its inputs, and no fitted parameter is later renamed as a prediction. The paper does lean on some works by the same authors — [27] for wavemaker/meniscus context, [31] for the hydrophobic-coating protocol, [33] for a related droplet-splashing scaling — but these citations are contextual or methodological, not load-bearing for the central wave-slope parameterization. The claimed uniqueness of the proposed framework is not based on a self-citation; it is based on the experimental collapse over phase, frequency, amplitude, Weber number, and Bond number. The model-dependent nature of m (e.g., reliance on a single linear Bessel mode and the assumption R << lambda, which is only marginally satisfied) is a legitimate scientific caveat about the accuracy of the inferred slope, but it is not evidence of circularity: an imperfect proxy can weaken an empirical claim without making the claim equivalent to its input. Therefore, no circular step satisfying the quoted-reduction standard is present, and the appropriate finding is 'no significant circularity.'

Assumptions & free parameters 0 free parameters · 4 assumptions · 0 invented entities

No free parameters are fitted to the cavity-volume data; m is a measured grouping of amplitude, radius, and wavelength. The main input assumptions are the standing-wave profile form, the dispersion relation, the small-R Bessel expansion, and the frozen-interface timescale separation.

assumptions (4)
  • domain assumption The ring-generated wavefield is an axisymmetric linear standing wave h(r,t)=A0J0(kr)sin(ωt+ϕ).
    Used to derive Eq. (1) and the scaling m ∼ AR/λ²; the actual radial mode shape is not directly validated against a surface-height measurement for every drive condition.
  • domain assumption The deep-water gravity-capillary dispersion relation maps forcing frequency f to wavelength λ.
    Wavelength λ enters m, but λ is computed from f rather than measured simultaneously with impact.
  • standard math R ≪ λ, so J1(kR) ≈ kR/2, giving the AR/λ² estimate for the local slope.
    Small-argument Bessel expansion stated just before Eq. (2); this is a standard mathematical approximation.
  • domain assumption The splash curtain emerges on a timescale R/U much shorter than the wave period 1/f, so the interface is frozen during ejecta formation.
    The authors report a two-orders-of-magnitude timescale separation; this justifies replacing wave dynamics with static interface geometry in the mechanism.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Surface Waves Alter Air Entrainment During Water Entry." pith.science (2026). https://pith.science/paper/HKZUG4EX

@misc{pith2026260720067,
  author       = {Pith},
  title        = {Pith review of: Surface Waves Alter Air Entrainment During Water Entry},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/HKZUG4EX}},
  note         = {Machine review of arXiv:2607.20067}
}
read the original abstract

When a sphere crosses an air-water interface it can entrain a significant volume of air, a process relevant to numerous naval, industrial, and environmental settings. While air entrainment through sphere impact onto quiescent baths has been extensively studied, real-world interfaces are inherently unsteady, and the influence of surface waves is less understood. In this Letter, we systematically investigate the effect of interfacial geometry on the air entrained by impacting hydrophobic spheres onto an axisymmetric wavefield. By analyzing the resulting cavity across a wide parameter space, including wave phase, driving amplitude, and frequency, we reveal that local interface deformation dramatically alters air entrainment. This effect is driven by a geometric modulation of the splash curtain, which shifts the transition between cavity closure modes. We demonstrate that the influence of the waves is fully described by the local wave slope at the radius of the sphere, which alongside the Weber number We and Bond number Bo, establishes a foundational parametric framework for predicting air entrainment and cavity metrics across highly dynamic, real-world surfaces like the open ocean.

Figures

Figures reproduced from arXiv: 2607.20067 by the authors.

Figure 1
Figure 1. FIG. 1: Schematic of the experimental setup, including the (1) drop tower, (2) electromagnet, (3) heaving cylindrical [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2: (a) Dimensionless maximum cavity volume [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3: Dimensionless maximum cavity volume [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figures from the paper (1 more)
Figure 4
Figure 4. Figure 4: FIG. 4: Dimensionless maximum cavity volume [PITH_FULL_IMAGE:figures/full_fig_p005_4.png]

Discussion (0). Sign in to comment.

Reference graph

Works this paper leans on

38 extracted references · 1 linked inside Pith

  1. [1]

    C. Duez, C. Ybert, C. Clanet, and L. Bocquet, Making a splash with water repellency, Nat. Phys.3, 180 (2007)

    2007

  2. [2]

    A. M. Worthington and R. S. Cole, Iv. impact with a liquid sur- face studied by the aid of instantaneous photography. paper ii, Philos. Trans. R. Soc. Lond. A194, 175 (1900)

    1900

  3. [3]

    Zhao, X.-P

    M.-H. Zhao, X.-P. Chen, and Q. Wang, Wetting failure of hy- drophilic surfaces promoted by surface roughness, Sci. Rep.4, 5376 (2014)

    2014

  4. [4]

    Marston, I

    J. Marston, I. U. Vakarelski, and S. T. Thoroddsen, Cavity for- mation by the impact ofleidenfrost spheres, J. Fluid Mech.699, 465 (2012)

    2012

  5. [5]

    Speirs, M

    N. Speirs, M. M. Mansoor, R. C. Hurd, S. I. Sharker, W. Robin- son, B. Williams, and T. T. Truscott, Entry of a sphere into a water-surfactant mixture and the effect of a bubble layer, Phys. Rev. Fluids3, 104004 (2018)

    2018

  6. [6]

    D. A. Watson, J. L. Stephen, and A. K. Dickerson, Jet ampli- fication and cavity formation induced by penetrable fabrics in hydrophilic sphere entry, Phys. Fluids30(2018)

    2018

  7. [7]

    L. B. Smolka and C. K. McLaughlin, Sphere entry through an oil lens floating on water, Phys. Rev. Fluids4, 044001 (2019)

    2019

  8. [8]

    D. A. Watson, S. Anzola, F. A. Zeas, K. B. Smith, and A. A. Cruz, Compound cavity formation and splash crown suppres- sion by water entry through proximally adjacent polystyrene beads, Phys. Fluids36(2024)

    2024

Show all 38 references
  1. [9]

    T. T. Truscott, B. P. Epps, and J. Belden, Water entry of projec- tiles, Annu. Rev. Fluid Mech.46, 355 (2014)

    2014

  2. [10]

    A. M. Worthington and R. S. Cole, V . impact with a liquid sur- face, studied by the aid of instantaneous photography, Philos. Trans. R. Soc. Lond. A , 137 (1897)

  3. [11]

    V on Karman,The impact on seaplane floats during land- ing, Tech

    T. V on Karman,The impact on seaplane floats during land- ing, Tech. Rep. (National Advisory Committee for Aeronautics, 1929)

    1929

  4. [12]

    Gilbarg and R

    D. Gilbarg and R. A. Anderson, Influence of atmospheric pres- sure on the phenomena accompanying the entry of spheres into water, J. Appl. Phys.19, 127 (1948)

    1948

  5. [13]

    May,Water entry and the cavity-running behavior of mis- siles, Tech

    A. May,Water entry and the cavity-running behavior of mis- siles, Tech. Rep. (1975)

    1975

  6. [14]

    I. U. Vakarelski, J. O. Marston, D. Y . C. Chan, and S. T. Thoroddsen, Drag reduction by leidenfrost vapor layers, Phys. Rev. Lett.106, 214501 (2011)

    2011

  7. [15]

    Ropert-Coudert, D

    Y . Ropert-Coudert, D. Grémillet, P. Ryan, A. Kato, Y . Naito, and Y . Le Maho, Between air and water: the plunge dive of the cape gannet morus capensis, Ibis146, 281 (2004)

    2004

  8. [16]

    K. B. Miller and J. Bergsten,Diving beetles of the world: Sys- tematics and biology of the Dytiscidae(JHU Press, 2016)

    2016

  9. [17]

    Glasheen and T

    J. Glasheen and T. McMahon, A hydrodynamic model of loco- motion in the basilisk lizard, Nat.380, 340 (1996)

    1996

  10. [18]

    J. W. Bush and D. L. Hu, Walking on water: biolocomotion at the interface, Annu. Rev. Fluid Mech.38, 339 (2006)

    2006

  11. [19]

    J. M. Aristoff and J. W. Bush, Water entry of small hydrophobic spheres, J. Fluid Mech.619, 45 (2009)

    2009

  12. [20]

    Duclaux, F

    V . Duclaux, F. Caillé, C. Duez, C. Ybert, L. Bocquet, and C. Clanet, Dynamics of transient cavities, J. Fluid Mech.591, 1 (2007)

    2007

  13. [21]

    J. O. Marston, T. T. Truscott, N. B. Speirs, M. M. Mansoor, and S. T. Thoroddsen, Crown sealing and buckling instability during water entry of spheres, J. Fluid Mech.794, 506 (2016)

    2016

  14. [22]

    Eshraghi, S

    J. Eshraghi, S. Jung, and P. P. Vlachos, To seal or not to seal: The closure dynamics of a splash curtain, Phys. Rev. Fluids5, 104001 (2020)

    2020

  15. [23]

    M. M. Mansoor, J. O. Marston, I. U. Vakarelski, and S. T. Thoroddsen, Water entry without surface seal: extended cavity formation, J. Fluid Mech.743, 295 (2014)

    2014

  16. [24]

    May,The cavity after vertical water entry, Tech

    A. May,The cavity after vertical water entry, Tech. Rep. (1968)

    1968

  17. [25]

    A. H. Moalemi, H. Bredmose, A. Ghadirian, and T. Kristiansen, Cylinder water entry on a perturbed water surface, J. Fluid Mech.965, A16 (2023)

    2023

  18. [26]

    G. L. Siscoe and Z. Levin, Water-drop-surface-wave interac- tions, J. Geophys. Res.76, 5112 (1971)

    1971

  19. [27]

    X. Shao, C. T. Gabbard, J. B. Bostwick, and J. R. Saylor, On the role of meniscus geometry in capillary wave generation, Exp. Fluids62, 59 (2021)

    2021

  20. [28]

    C. T. Gabbard, M. Ibrahim, J. Quinton, E. Silver, J. Belden, and D. M. Harris, WavyWaterEntry GitHub repository,https:// github.com/harrislab-brown/WavyWaterEntry(2026)

    2026

  21. [29]

    C. Zhao, Q. Wang, H. Lu, and H. Liu, Vertical water entry of a hydrophobic sphere into waves: Numerical computations and experiments, Phys. Fluids35(2023)

    2023

  22. [30]

    L. Yi, S. Li, H. Jiang, D. Lohse, C. Sun, and V . Mathai, Water entry of spheres into a rotating liquid, J. Fluid Mech.912, R1 (2021)

    2021

  23. [31]

    C. A. Galeano-Rios, R. Cimpeanu, I. A. Bauman, A. MacEwen, P. A. Milewski, and D. M. Harris, Capillary-scale solid re- bounds: experiments, modelling and simulations, J. Fluid Mech.912, A17 (2021)

    2021

  24. [32]

    N. B. Speirs, J. L. Belden, and A. M. Hellum, The capture of airborne particulates by rain, J. Fluid Mech.958, A40 (2023)

    2023

  25. [33]

    T. C. Sykes, L. F. L. Alventosa, J. R. Castrejon-Pita, R. Cimpeanu, D. M. Harris, and A. A. Castrejon-Pita, Fast droplet impact onto slowly moving deep pools, arXiv preprint arXiv:2511.03682 (2025)

    2025 arXiv

  26. [34]

    J. M. Aristoff, T. T. Truscott, A. H. Techet, and J. W. Bush, The water entry of decelerating spheres, Phys. Fluids22(2010)

    2010

  27. [35]

    Gregorio, E

    E. Gregorio, E. Balaras, and M. C. Leftwich, Air cavity defor- mation by single jointed diver model entry bodies, Experiments in Fluids64, 168 (2023)

    2023

  28. [36]

    J. T. Antolik, J. L. Belden, N. B. Speirs, and D. M. Harris, For- mation of undulatory cavities during hydroelastic water entry, Phys. Rev. Fluids9, 110503 (2024)

    2024

  29. [37]

    Belden, N

    J. Belden, N. Speirs, A. Hellum, G. Loubimov, and T. T. Tr- uscott, Water impact: when a sphere becomes flat, Phys. Rev. Lett.133, 034002 (2024)

    2024

  30. [38]

    Rabbi, N

    R. Rabbi, N. B. Speirs, A. Kiyama, J. Belden, and T. T. Truscott, Impact force reduction by consecutive water entry of spheres, J. Fluid Mech.915, A55 (2021)

    2021

Pith tools

Reviewed August 1, 2026 · model on record in the stance chip above.