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Dispersive shock waves in gravity-capillary free-surface flows.

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Title: Dispersive shock waves in gravity-capillary free-surface flows.
Authors: Zhao, Wangyang1,2 (AUTHOR), Wang, Zhan1,2,3 (AUTHOR) zwang@imech.ac.cn, Hu, Lei1,3 (AUTHOR)
Source: Journal of Fluid Mechanics. 2/10/2026, Vol. 1028, p1-33. 33p.
Subjects: Capillary waves, Euler equations, Nonlinear waves, Theory of wave motion, Solitons, Bond number (Chemistry), Shock waves, Euler, Leonhard, 1707-1783, Modulation theory
Abstract: This paper explores dispersive shock waves (DSWs) of gravity-capillary waves within the framework of the two-dimensional, fully nonlinear Euler equations. In this system, initial wave profiles characterised by a smooth step function evolve into modulated wavetrains that connect different constant states, a phenomenon arising from the interplay between nonlinear and dispersive effects. The Bond number, which quantifies the relative significance of gravity compared to surface tension, is crucial in determining the behaviour of the DSW solution. As the Bond number increases from zero, solutions traverse four distinct zones: the radiating DSW region, an unstable crossover region, the travelling DSW region, and the inverse radiating DSW region. The propagation velocities of DSWs can be estimated using the DSW fitting method alongside numerical results from travelling waves. Particular attention is given to travelling DSWs, which are characterised by a uniform wavetrain followed by an oscillatory decaying wavepacket. Notably, the high platform and its extended periodic wavetrain can be part of a specific type of gravity-capillary solitary wave that features an oscillatory pulse, with the number of oscillations at the core potentially increasing indefinitely. The Whitham modulation theory for the Euler equations is employed to describe the modulation parameters – such as wavenumber, amplitude and wave mean – in the travelling DSW region. Finally, we discuss the bifurcation mechanism of solitary waves with oscillatory pulses in the Euler equations, along with analyses of their stability. It is also demonstrated that for relatively small Bond numbers, a series of trapped bubbles can occur along the bifurcation curves, representing the limiting configuration of this type of solitary wave. [ABSTRACT FROM AUTHOR]
Copyright of Journal of Fluid Mechanics is the property of Cambridge University Press and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
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DbLabel: Engineering Source
An: 191814644
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PubTypeId: academicJournal
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  Data: Dispersive shock waves in gravity-capillary free-surface flows.
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  Data: <searchLink fieldCode="AR" term="%22Zhao%2C+Wangyang%22">Zhao, Wangyang</searchLink><relatesTo>1,2</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Wang%2C+Zhan%22">Wang, Zhan</searchLink><relatesTo>1,2,3</relatesTo> (AUTHOR)<i> zwang@imech.ac.cn</i><br /><searchLink fieldCode="AR" term="%22Hu%2C+Lei%22">Hu, Lei</searchLink><relatesTo>1,3</relatesTo> (AUTHOR)
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  Data: <searchLink fieldCode="JN" term="%22Journal+of+Fluid+Mechanics%22">Journal of Fluid Mechanics</searchLink>. 2/10/2026, Vol. 1028, p1-33. 33p.
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– Name: Abstract
  Label: Abstract
  Group: Ab
  Data: This paper explores dispersive shock waves (DSWs) of gravity-capillary waves within the framework of the two-dimensional, fully nonlinear Euler equations. In this system, initial wave profiles characterised by a smooth step function evolve into modulated wavetrains that connect different constant states, a phenomenon arising from the interplay between nonlinear and dispersive effects. The Bond number, which quantifies the relative significance of gravity compared to surface tension, is crucial in determining the behaviour of the DSW solution. As the Bond number increases from zero, solutions traverse four distinct zones: the radiating DSW region, an unstable crossover region, the travelling DSW region, and the inverse radiating DSW region. The propagation velocities of DSWs can be estimated using the DSW fitting method alongside numerical results from travelling waves. Particular attention is given to travelling DSWs, which are characterised by a uniform wavetrain followed by an oscillatory decaying wavepacket. Notably, the high platform and its extended periodic wavetrain can be part of a specific type of gravity-capillary solitary wave that features an oscillatory pulse, with the number of oscillations at the core potentially increasing indefinitely. The Whitham modulation theory for the Euler equations is employed to describe the modulation parameters – such as wavenumber, amplitude and wave mean – in the travelling DSW region. Finally, we discuss the bifurcation mechanism of solitary waves with oscillatory pulses in the Euler equations, along with analyses of their stability. It is also demonstrated that for relatively small Bond numbers, a series of trapped bubbles can occur along the bifurcation curves, representing the limiting configuration of this type of solitary wave. [ABSTRACT FROM AUTHOR]
– Name: AbstractSuppliedCopyright
  Label:
  Group: Ab
  Data: <i>Copyright of Journal of Fluid Mechanics is the property of Cambridge University Press and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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RecordInfo BibRecord:
  BibEntity:
    Identifiers:
      – Type: doi
        Value: 10.1017/jfm.2026.11169
    Languages:
      – Code: eng
        Text: English
    PhysicalDescription:
      Pagination:
        PageCount: 33
        StartPage: 1
    Subjects:
      – SubjectFull: Capillary waves
        Type: general
      – SubjectFull: Euler equations
        Type: general
      – SubjectFull: Nonlinear waves
        Type: general
      – SubjectFull: Theory of wave motion
        Type: general
      – SubjectFull: Solitons
        Type: general
      – SubjectFull: Bond number (Chemistry)
        Type: general
      – SubjectFull: Shock waves
        Type: general
      – SubjectFull: Euler, Leonhard, 1707-1783
        Type: general
      – SubjectFull: Modulation theory
        Type: general
    Titles:
      – TitleFull: Dispersive shock waves in gravity-capillary free-surface flows.
        Type: main
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      – PersonEntity:
          Name:
            NameFull: Zhao, Wangyang
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          Name:
            NameFull: Wang, Zhan
      – PersonEntity:
          Name:
            NameFull: Hu, Lei
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          Dates:
            – D: 10
              M: 02
              Text: 2/10/2026
              Type: published
              Y: 2026
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            – Type: volume
              Value: 1028
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            – TitleFull: Journal of Fluid Mechanics
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