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arxiv: 1907.11279 · v1 · pith:324X4RNMnew · submitted 2019-07-25 · 🌊 nlin.PS · physics.flu-dyn

Asymmetric behavior of surface waves induced by an underlying interfacial wave

Shixiao W. Jiang , Gregor Kova\v{c}i\v{c} , Douglas Zhou This is my paper

Pith reviewed 2026-05-24 15:32 UTC · model grok-4.3

classification 🌊 nlin.PS physics.flu-dyn
keywords asymmetric surface wavesinterfacial solitary wavestwo-layer fluidsweakly nonlinear modelray-based theoriesocean internal wavesgroup velocitywave broadening
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The pith

A weakly nonlinear model captures the asymmetric behaviors of surface waves induced by an underlying interfacial solitary wave.

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

The authors develop a weakly nonlinear model for surface and interfacial waves in a two-layer fluid. This model reproduces the broadening of large-amplitude internal waves commonly seen in the ocean. It also generates three specific asymmetries in the surface waves: shorter wavelengths and higher amplitudes at the leading edge of the interfacial wave, longer wavelengths and lower amplitudes at the trailing edge, along with differing group velocities. These patterns are explained through ray-based theories. The model's simplicity makes it useful for understanding how internal waves appear on the ocean surface.

Core claim

We develop a weakly nonlinear model to study the spatiotemporal manifestation and the dynamical behavior of surface waves in the presence of an underlying interfacial solitary wave in a two-layer fluid system. Interfacial solitary-wave solutions of this model capture the ubiquitous broadening of large-amplitude internal waves in the ocean. The model captures three asymmetric behaviors of surface waves that can be quantified in the theoretical framework of ray-based theories: surface waves become short in wavelength at the leading edge and long at the trailing edge, propagate towards the trailing edge with a relatively small group velocity and towards the leading edge with a relatively large,

What carries the argument

The weakly nonlinear model for the two-layer fluid system that produces interfacial solitary waves and the associated surface wave asymmetries quantified via ray-based theories.

Where Pith is reading between the lines

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

  • Observations of surface wave patterns could be used to infer properties of subsurface interfacial waves without direct measurement.
  • The approach might apply to other stratified fluid systems where one wave influences another.
  • Testing the model against full nonlinear simulations would reveal the limits of the weak nonlinearity assumption.

Load-bearing premise

The weakly nonlinear approximation suffices to capture the essential spatiotemporal and dynamical features of the surface waves without needing higher-order terms.

What would settle it

If laboratory experiments or ocean measurements show no difference in surface wave wavelength or amplitude between the leading and trailing edges of an internal solitary wave, the model's predictions would be falsified.

Figures

Figures reproduced from arXiv: 1907.11279 by Douglas Zhou, Gregor Kova\v{c}i\v{c}, Shixiao W. Jiang.

Figure 1
Figure 1. Figure 1: Sketch of the two-layer fluid system [see text]. [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: (Color online) Comparison of interfacial solitary-wave solutions among our [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: (Color online) (a) Pure linear dispersion relations Ωk for slow-mode waves [Eq. (3.31)] and ωk for fast-mode waves [Eq. (3.32)]. (b) Phase velocities Cp for slow-mode waves and cp for fast-mode waves. MCC solutions become much broader than the KdV solutions. The maximum amplitude of our TWN model is approximately (h1 −h2)/2. Beyond the maximum amplitude, no solitary waves can exist for IWs. 3.2 Dispersion … view at source ↗
Figure 4
Figure 4. Figure 4: (Color online) Spatiotemporal evolution of the interfacial solitary-wave so [PITH_FULL_IMAGE:figures/full_fig_p009_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: (Color online) Numerical convergence examination of the scheme in time and [PITH_FULL_IMAGE:figures/full_fig_p011_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: (Color online) (a) Spatiotemporal evolution of SWs’ profile ξ1 in the near field for 0≤T ≤10000 and −100≤ X ≤100, and snapshot of the interfacial solitary wave at T = 0. The amplitude of the interfacial solitary wave is −0.976. The yellow line corresponds to the group velocity of the left-moving fast-mode SW packet that is not trapped in the near field. The red (blue) line corresponds to the negative (post… view at source ↗
Figure 7
Figure 7. Figure 7: (Color online) (a) The logarithmic modulus, log10 |ξb1(k,ν)| 2 , of SWs’ pro￾file ξ1 for 3181≤T ≤4000 and −150≤ X ≤150. For comparison, also plotted are the pure linear dispersion relation νk (red dashed-dotted curve) and the modulated disper￾sion relation νk (black solid curve). The green rectangle corresponds to the range of wavenumbers and frequencies predicted by the ray-based theories [see text and pa… view at source ↗
Figure 8
Figure 8. Figure 8: (Color online) (a) Comparison of the phase velocity for fast-mode waves cp , the group velocity for fast-mode waves cg, and the phase velocity for slow-mode waves Cp, with the parameters (h1,h2,g,ρ1,ρ2) = (1,3,1,1,1.003). The resonant wavenumber kres satisfies the triad resonance condition (2.50) (b) Zoomed-in version of panel (a). ηb1 =h1 +ξb1 −ξb2, ηb2 =h2 +ξb2, Mc1 =ub1 − 1 3 h 2 1ub1XX − 1 2 h1  H2ub2… view at source ↗
read the original abstract

We develop a weakly nonlinear model to study the spatiotemporal manifestation and the dynamical behavior of surface waves in the presence of an underlying interfacial solitary wave in a two-layer fluid system. We show that interfacial solitary-wave solutions of this model can capture the ubiquitous broadening of large-amplitude internal waves in the ocean. In addition, the model is capable of capturing three asymmetric behaviors of surface waves: (i) Surface waves become short in wavelength at the leading edge and long at the trailing edge of an underlying interfacial solitary wave. (ii) Surface waves propagate towards the trailing edge with a relatively small group velocity, and towards the leading edge with a relatively large group velocity. (iii) Surface waves become high in amplitude at the leading edge and low at the trailing edge. These asymmetric behaviors can be well quantified in the theoretical framework of ray-based theories. Our model is relatively easily tractable both theoretically and numerically, thus facilitating the understanding of the surface signature of the observed internal waves.

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

2 major / 1 minor

Summary. The paper develops a weakly nonlinear model for a two-layer fluid to describe surface waves modulated by an underlying interfacial solitary wave. It claims that the model's interfacial solitary-wave solutions reproduce the observed broadening of large-amplitude internal waves in the ocean, and that the model captures three specific asymmetric surface-wave behaviors (wavelength shortening at the leading edge and lengthening at the trailing edge; group-velocity differences directing propagation toward the trailing edge with smaller velocity and leading edge with larger velocity; amplitude increase at the leading edge and decrease at the trailing edge). These asymmetries are quantified within ray-based theories, and the model is presented as tractable for both analysis and numerics.

Significance. If the central claims hold under the stated approximation, the work supplies a simplified, analytically and numerically accessible framework for interpreting surface signatures of internal waves, with potential relevance to ocean remote sensing. The explicit linkage to ray theory for quantifying the asymmetries is a constructive element when the underlying model is shown to be reliable.

major comments (2)
  1. [Model derivation and results sections] The central claim that the weakly nonlinear model captures both the broadening of large-amplitude interfacial waves and the three quantified surface-wave asymmetries rests on the assumption that higher-order nonlinear and dispersive terms remain negligible. No comparison to the full Euler equations or to a higher-order asymptotic model is supplied to test this assumption in the large-amplitude regime invoked for ocean observations.
  2. [Abstract and numerical/theoretical results] The abstract states that the model captures the behaviors and broadening, yet the supplied text contains no equations, error analysis, or validation data against observations or full simulations; this absence prevents evaluation of whether the reported asymmetries are robust or truncation artifacts.
minor comments (1)
  1. [Introduction and model setup] Notation for the two-layer depths, density ratio, and small parameters should be introduced with explicit definitions and ranges of validity at first use.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive feedback on our manuscript. We address the major comments point by point below, acknowledging limitations where appropriate and outlining planned revisions.

read point-by-point responses

  1. Referee: [Model derivation and results sections] The central claim that the weakly nonlinear model captures both the broadening of large-amplitude interfacial waves and the three quantified surface-wave asymmetries rests on the assumption that higher-order nonlinear and dispersive terms remain negligible. No comparison to the full Euler equations or to a higher-order asymptotic model is supplied to test this assumption in the large-amplitude regime invoked for ocean observations.

    Authors: We agree that the absence of direct comparisons to the full Euler equations or higher-order models represents a limitation when invoking the large-amplitude regime relevant to ocean observations. Our model is derived under the standard weakly nonlinear and dispersive assumptions for two-layer fluids, and the reported behaviors (including broadening) emerge consistently within this framework and align with ray-theory predictions. However, performing such comparisons would require substantial additional computational work outside the paper's focus on a tractable reduced model. In revision, we will expand the discussion section to explicitly delineate the regime of validity, estimate the magnitude of neglected terms for typical ocean parameters, and note this as a direction for future validation. revision: partial

  2. Referee: [Abstract and numerical/theoretical results] The abstract states that the model captures the behaviors and broadening, yet the supplied text contains no equations, error analysis, or validation data against observations or full simulations; this absence prevents evaluation of whether the reported asymmetries are robust or truncation artifacts.

    Authors: The full manuscript contains the model derivation (including the governing equations), numerical simulations of the interfacial solitary waves, and explicit quantification of the three asymmetries via ray theory. The abstract is a concise summary. To improve clarity, we will revise the abstract to reference the weakly nonlinear derivation and ray-theory framework more explicitly. We will also add a short subsection on truncation error estimates and the robustness of the asymmetries within the model's assumptions, drawing on the existing numerical results. revision: yes

Circularity Check

0 steps flagged

No circularity; derivation chain not exhibited in text

full rationale

The provided abstract and description state that a weakly nonlinear model is developed to study surface waves over an interfacial solitary wave, with claims that its solutions capture broadening and three asymmetric behaviors quantifiable by ray theory. No equations, derivation steps, parameter fits, or self-citations are quoted that reduce any prediction to an input by construction, self-definition, or load-bearing prior work by the authors. The model is presented as tractable for understanding observed phenomena without shown reductions to fitted values or ansatzes smuggled via citation. This is the normal case of a self-contained presentation against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract-only review yields no explicit free parameters, axioms, or invented entities; full text would be required to audit the model equations for fitted scales or domain assumptions.

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Reference graph

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