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REVIEW 3 major objections 6 minor 50 references

A two-dimensional analytical model of vertical water entry for asymmetric bodies with flow separation

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Pith's one-line read A two-dimensional analytical model with fictitious flat-plate continuations gives reliable slamming-load estimates for asymmetric water entry, including after flow separation.

desk verdict A solid, honest extension of the FBC model to asymmetric water entry with useful benchmarks; the pre-calibrated continuation angles are the main caveat, but the paper flags them itself. read the letter →

arxiv 1908.09201 v2 pith:7C7T2KLV submitted 2019-08-24 physics.flu-dyn physics.ao-ph

Romain Hascoët (1) , Nicolas Jacques (1) , Yves-Marie Scolan (1) , Alan Tassin (2) ((1) IRDL-CNRS , ENSTA Bretagne , (2) IFREMER) This is my paper · ORCID
classification physics.flu-dynphysics.ao-ph MSC 76B1076B07
keywords waterentryflowseparationslammingloadsFictitiousBodyContinuationWagnermodelModifiedLogvinovichasymmetricfoilimpact
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

The paper tries to show that the Fictitious Body Continuation (FBC) idea, previously used for symmetric bodies, also gives reliable estimates of slamming loads when a two-dimensional body enters water asymmetrically and flow separates at different times on its two sides. The model glues fictitious flat plates onto the real body after separation and applies the classical Wagner flat-plate solution to the composite shape, computing pressure with the Modified Logvinovich Model and integrating only over the real wetted surface. For an inclined flat plate, the FBC prediction matches a fully nonlinear self-similar solution to about 10% for inclinations between $5^\circ$ and $30^\circ$. For a thick foil, with no adjustment of the two continuation angles, the predicted vertical force and moment agree well with CFD for inclinations between about $-28^\circ$ and $20^\circ$, including accelerated entries. If the claim holds, slamming loads on complex asymmetric sections can be obtained almost instantly during design instead of running expensive CFD.

What carries the argument

The central device is the Fictitious Body Continuation: after flow separates, the real contour is extended by flat fictitious plates so that Wagner's flat-plate solution can still be applied to the composite body, with the separated cavity flow represented by those plates. The pressure is then evaluated with the Modified Logvinovich Model, which uses the exact Bernoulli equation along the body contour and removes negative-pressure regions near the contact points, and the load is integrated only over the real part. The continuation angles $\alpha_1$ and $\alpha_2$ are the parameters that carry the model's predictive power: they set where and at what slope the fictitious plates attach, hence when separation occurs and how fast the cavity widens. A modified added-mass term with min operators interpolates between the two separation heights, which is what lets the model survive the asymmetric phase when only one side has separated.

What would settle it

Run the FBC model with the standard angles, $60^\circ$ at a smooth separation and $47^\circ$ at a chine, against CFD or experiment for an asymmetric body outside the calibration family, for example a wedge or foil at an inclination beyond the tested $-30^\circ$ to $20^\circ$ range, and check whether force and moment stay within about 10%; a single clear miss would refute the generic-angle claim. Alternatively, measure the initial cavity opening angle in a water-entry experiment and compare it with the fictitious plate angle.

Watch

Extended reading notes

Core claim

On its own terms, the paper's discovery is that a single pair of continuation angles can represent separated cavity flow for asymmetric bodies: $\alpha=60^\circ$ at a smooth leading edge, the value calibrated for a circular cylinder, and $\alpha=47^\circ$ at a chine, the value calibrated for a flat plate. With those fixed values, the FBC model reproduces the CFD-computed vertical slamming force $F_y$ and moment $M_z$ on a 28%-thick foil for initial inclinations from $\theta=-28.1^\circ$ to $\theta=20^\circ$, and captures the order of separation events. In the intermediate phase when separation has occurred on only one side, the model still works because the added-mass term is modified to interpolate between the two separation heights; the loads during this phase are set by the competition between the local pressure drop and continued wetted-area growth. The horizontal force estimate is less accurate, but its magnitude is small for moderate deadrise angles, so the practical load picture remains reliable.

Load-bearing premise

The model's usefulness depends on the a-priori choice of the two continuation angles, inherited from a cylinder and a flat plate; if those angles are not generic across body shapes and inclinations, the claimed reliability collapses.

Editorial extensions

If this is right

  • Slamming loads on asymmetric sections can be estimated analytically in near-real time, making FBC a practical screening tool before detailed CFD.
  • Two pre-calibrated continuation angles, one for smooth-body separation and one for chine separation, transfer across different body shapes without per-case tuning, at least within the tested range of inclinations.
  • The model captures separation timing and the vertical force and moment evolutions, including the peak loads reached when trailing-edge separation finally occurs.
  • For accelerated entries, the modified added-mass term keeps the added-mass force estimate within about 10% of CFD for the moment peak, so early-stage acceleration loads are also covered.
  • Horizontal slamming force is not predicted as reliably; users should treat $F_x$ as indicative only, relying on $F_y$ and $M_z$ for structural load estimates.

Reading between the lines

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

  • If the continuation angles are truly generic, the same two-angle FBC recipe could be embedded in strip-theory ship-slamming or ditching tools, replacing expensive two-dimensional CFD at each station with a few seconds of algebra.
  • The fact that calibrated angles cluster near $47^\circ$--$60^\circ$ across very different shapes suggests they may encode a property of the separated jet itself rather than of the body; measuring the initial cavity-opening angle in experiments across shapes would test that interpretation.
  • The model's known weakness in $F_x$ points at the jet-root region, where nonlinearity is strongest; a local correction for the jet-root pressure distribution could improve the horizontal load without changing the FBC structure.
  • One testable extension is to vary the entry velocity over a wider range to check whether the continuation angles depend on impact speed, which the current constant-velocity calibrations leave open.
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Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

3 major / 6 minor

Summary. The paper extends the Fictitious Body Continuation (FBC) concept to two-dimensional vertical water entry of asymmetric bodies with flow separation. It combines linearised Wagner theory with the Modified Logvinovich Model, introduces a generalised added-mass term (Eq. 18) for non-simultaneous separation on the two sides, and validates the approach against a nonlinear self-similar model for an inclined flat plate (Section 3) and against ABAQUS/Explicit CFD for a NACA 0028 foil at several inclination angles and accelerations (Section 4). The reported agreement is good for the vertical force Fy and moment Mz, while Fx is less accurate; the paper also presents slamming-load maps for foils of different thicknesses (Section 4.4).

Significance. If the central claim is accepted, the FBC model provides a fast, semi-analytical tool for estimating slamming loads on asymmetric bodies with separated flow, a configuration not covered by Tassin et al. (2014). The paper's strengths are its use of external benchmarks (nonlinear model and CFD), its explicit handling of the added-mass term in asymmetric configurations, and its candid discussion of the model's limitations. However, the predictive claim hinges on two continuation angles (alpha1=60°, alpha2=47°) inherited from earlier calibration for a circular cylinder and a flat plate; the paper does not demonstrate sensitivity to these angles or transferability to other body shapes. The validation is limited to one foil shape and a flat-plate benchmark that degrades for theta above about 20°. These issues make the general 'reliable estimates' conclusion premature, although the model appears promising for the specific configurations tested.

major comments (3)
  1. [Section 5 and Section 3.2] The central claim that the FBC model provides reliable slamming-load estimates for asymmetric bodies rests on the a priori continuation angles alpha1=60° and alpha2=47°, inherited from calibrations for a circular cylinder and a flat plate. Section 5 states that 'the critical point in the model is the choice, a priori, of the continuation angles', and Section 3.2 shows that for an inclined flat plate the agreement with the nonlinear model holds only for theta in [5°, 30°] with alpha=47°, with divergence for theta larger than about 20°. The foil validation uses fixed alpha1 and alpha2 across the whole range of theta, but only one foil shape. Thus the paper demonstrates that the chosen angles work for the tested configurations, not that they are generic; the abstract's claim of reliable estimates is stronger than the evidence supports.
  2. [Section 4.3.2, Figs. 6-8] No quantitative error metrics are reported; the statements 'agree very well' for Fy and Mz are based on visual inspection of curves. Given that the paper's conclusion is about reliability, the authors should provide a normalized error (e.g., L2 or maximum relative error over the reported penetration range) for Fy, Mz, and Fx, and ideally as a function of the inclination angle. This is especially important because Section 4.3.4 shows that the free surface in the FBC model deviates significantly from CFD once separation occurs, so the good load agreement is not self-evident from the flow solution.
  3. [Section 4.2, Fig. 5] The mesh-convergence study is presented only for the vertical force Fy at a single inclination (theta=20°). The horizontal force Fx is explicitly identified in Section 4.3.2 as sensitive to the contact region, and the moment Mz and the separation times (Section 4.3.1) are also key outputs. Without a grid-dependence check for these quantities, the CFD reference used for validation is not fully characterised, which weakens the quantitative support for the FBC predictions.
minor comments (6)
  1. [Eq. (18) and Eq. (28)] The notation min(λ1,l1) and min(λ2,l2) in Eq. (18) is not fully explained; state which side each quantity refers to and specify the integration limits in Eq. (28) in terms of these min-operators.
  2. [Section 3.2, Eq. (22)] The normalisation Cfp = (tan²θ/h) Fy/(ρ ḣ²) is unusual; the tan²θ factor is introduced 'to limit the range of values' and deserves a brief justification or a reference.
  3. [Section 4.2] The CFD simulations use a speed of sound of 500 m/s, which is lower than physical water; the artificial compressibility effect is discussed only through Eq. (27). Please quantify the resulting error in the reported load coefficients or cite a previous verification for this parameter choice.
  4. [Appendix A, Eq. (32)] The factor 1/β in the gravity-neglect criterion is justified by a hand-wavy argument ('the gravity component acting along streamlines'); this could be derived more rigorously or removed.
  5. [Section 4.4] The slamming-load maps for foil thicknesses w=0.05 and w=0.1 are computed with FBC without direct CFD or experimental validation for those cases; the text should state explicitly that these are extrapolations.
  6. [Fig. 9] The statement that, after separation from both sides, the agreement on loads remains good despite the free-surface deviation is purely qualitative. Adding the integrated pressure difference between FBC and CFD would make the point quantitative.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the FBC load predictions are tested against independent nonlinear-model and CFD benchmarks, and the pre-calibrated continuation angles are model parameters, not fitted outputs of this paper.

full rationale

The derivation chain is self-contained once the FBC ansatz is adopted: Wagner's linearized problem (Eqs. 1-10) determines the wetted region, the MLM pressure formula (Eq. 16) supplies the loads, and the FBC extension (Eqs. 17-19) handles separated flow. The continuation angles are fixed in Section 4.1 from prior calibration (alpha1 = 60 deg from Tassin et al. 2014 for a circular cylinder, alpha2 = 47 deg for a flat plate) and are then held constant. The central claim that the FBC model gives reliable slamming loads is not circular because the paper validates it against independent external results: the nonlinear self-similar model of Faltinsen and Semenov for the inclined flat plate (Section 3.2) and ABAQUS/Explicit CFD for the NACA 0028 foil (Section 4.3), including constant-velocity and constant-acceleration cases. No force or moment result in the paper is constructed by fitting to these benchmark outputs; the agreements are genuine comparisons with fixed parameters. The self-citation to Tassin et al. (2014) supplies the FBC concept and calibrated constants, but the present claim is re-tested here against data that are independent of those fitted values, so the citation is not load-bearing in a circular way. The paper's own caveat that the continuation angles are chosen a priori and that comparative studies on other bodies are needed to delimit their genericness (Section 5) is a robustness and transferability limitation, not a circularity. No equation reduces by construction to its inputs, and no fitted parameter is renamed as a prediction.

Assumptions & free parameters 2 free parameters · 6 assumptions · 1 invented entities

The central claim rests on a chain of standard Wagner linearization assumptions, ad hoc regularization of the MLM pressure, and heuristic continuation angles calibrated in earlier work. The only free parameters are the two continuation angles, and the fictitious body is an invented modeling entity without independent physical evidence.

free parameters (2)
  • α1 = 60° continuation angle at smooth leading edge (foil) = 60°
    Inherited from Tassin et al. (2014) circular-cylinder calibration; used as a generic constant for separation on the smooth part of the foil contour in Section 4.1.
  • α2 = 47° continuation angle at chine / trailing edge (foil and inclined plate) = 47°
    Inherited from Tassin et al. (2014) flat-plate calibration and confirmed for the inclined plate in Section 3; used as a generic constant for separation at a chine.
assumptions (6)
  • domain assumption Potential flow, inviscid, incompressible, irrotational, with gravity and surface tension neglected.
    Standard Wagner-theory assumptions stated in Section 2.1 and discussed in Appendix A.
  • domain assumption Small deadrise angles and projection of the body onto a flat plate (Wagner linearization).
    Used to formulate Eqs. (1)-(7) and the simplified pressure model; validity is limited to moderate deadrise angles.
  • ad hoc to paper Negative MLM pressure regions close to contact points are ignored.
    Section 2.2 states this condition 'lacks a physically grounded justification'; it is needed to regularize the non-integrable quadratic pressure term.
  • ad hoc to paper A fictitious flat-plate continuation can mimic the separated cavity flow after flow separation.
    Core FBC modeling assumption from Tassin et al. (2014), adopted here; discussed in Sections 2.3 and 5.
  • ad hoc to paper The modified added-mass pressure (Eqs. 17-18) with min operators and linear interpolation f̃ is valid after separation.
    Introduced in Section 2.3 with 'We suggest to use'; it is a modeling prescription rather than a derived result.
  • domain assumption Separation on a smooth body occurs at the point where the local deadrise angle equals the continuation angle, with a tangential connection.
    Section 4.1 states the tangential connection is motivated by experiments and numerical results; the separation location is not solved from a physical criterion.
invented entities (1)
  • Fictitious flat plates continuing the real body beyond separation points
    purpose: To allow the Wagner model to be applied to the composite real-plus-fictitious body and to mimic the separated cavity flow for the pressure calculation.
    The fictitious body is a mathematical construct with no direct observable; it is validated only indirectly through integrated force and moment comparisons with CFD and nonlinear theory.

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Cite this review

Pith. "Pith review of A two-dimensional analytical model of vertical water entry for asymmetric bodies with flow separation." pith.science (2026). https://pith.science/paper/7C7T2KLV

@misc{pith2026190809201,
  author       = {Pith},
  title        = {Pith review of: A two-dimensional analytical model of vertical water entry for asymmetric bodies with flow separation},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/7C7T2KLV}},
  note         = {Machine review of arXiv:1908.09201}
}
read the original abstract

The vertical water entry of asymmetric two-dimensional bodies with flow separation is considered. As long as there is no flow separation, linearised Wagner's theory combined with the Modified Logvinovich Model has been shown to provide computationally fast and reliable estimates of slamming loads during water entry. Tassin et al. (2014) introduced the Fictitious Body Continuation (FBC) concept as a way to extend the use of Wagner's model to separated flow configurations, but they only considered symmetric bodies. In the present study, we investigate the ability of the FBC concept to provide accurate estimates of slamming loads for asymmetric bodies. In this case, flow separation may not occur simultaneously on both sides of the body. During an intermediate phase, slamming loads are governed by a competition between the local drop in pressure due to partial flow separation and the ongoing expansion of the wetted area. As a first benchmark for the model, we consider the water entry of an inclined flat plate and compare the FBC estimates with the results of a nonlinear model. Then, we consider the case of a foil and compare the FBC results with Computational Fluid Dynamics predictions. In both cases, we find that the FBC model is able to provide reliable estimates of the slamming loads.

Figures

Figures reproduced from arXiv: 1908.09201 by the authors.

Figure 1
Figure 1. Illustration of Wagner’s model for vertical water entry. The boundary conditions [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 2
Figure 2. Vertical water entry of a flat plate – illustration. The flat plate is inclined by an [PITH_FULL_IMAGE:figures/full_fig_p008_2.png] view at source ↗
Figure 3
Figure 3. Vertical water entry of an inclined flat plate at constant velocity: normalised [PITH_FULL_IMAGE:figures/full_fig_p009_3.png] view at source ↗
Figures from the paper (8 more)
Figure 4
Figure 4. Figure 4: (a): Initial conditions of impact when the foil first touches the water. The initial [PITH_FULL_IMAGE:figures/full_fig_p011_4.png]
Figure 5
Figure 5. Figure 5: The effect of mesh resolution on ABAQUS simulations. The quantity shown is [PITH_FULL_IMAGE:figures/full_fig_p013_5.png]
Figure 6
Figure 6. Figure 6: Vertical water entry of a NACA 0028 foil at constant velocity. CFD and FBC [PITH_FULL_IMAGE:figures/full_fig_p014_6.png]
Figure 7
Figure 7. Figure 7: Same as Fig. 6 for two other inclination angles: [PITH_FULL_IMAGE:figures/full_fig_p015_7.png]
Figure 8
Figure 8. Figure 8: Vertical water entry of a NACA 0028 foil (chord length, [PITH_FULL_IMAGE:figures/full_fig_p016_8.png]
Figure 9
Figure 9. Figure 9: Free surface of the flow induced by the vertical water entry of a NACA 0028 foil. [PITH_FULL_IMAGE:figures/full_fig_p017_9.png]
Figure 10
Figure 10. Figure 10: Slamming loads on foils during a vertical water entry at constant velocity. The [PITH_FULL_IMAGE:figures/full_fig_p019_10.png]
Figure 11
Figure 11. Figure 11: Same as Fig. 10 for different foil thicknesses: [PITH_FULL_IMAGE:figures/full_fig_p020_11.png]

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Pith tools

Reviewed August 14, 2026 · model on record in the stance chip above.