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Modulational instability of multiphase capillary wavetrains on deep water.

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Title: Modulational instability of multiphase capillary wavetrains on deep water.
Authors: Mukherjee, Suman1, Dhar, A. K.1 asoke.dhar@gmail.com
Source: Journal of Fluid Mechanics. 2/25/2026, Vol. 1029, p1-26. 26p.
Subjects: Modulational instability, Capillary waves, Nonlinear evolution equations, Water waves, Theory of wave motion
Abstract: The stability analysis of multiphase capillary wavetrains on water of infinite depth is performed using two coupled fourth-order nonlinear evolution (NLE) equations. We have investigated analytically the influence of a second wavetrain travelling in a different direction to the first wavetrain. The propagation of multiphase modes is studied for the case when group velocity projections of two wavetrains overlap. Criteria are derived for capillary Stokes wave instabilities and for the existence of a multiphase solitary envelope solution. We have exhibited that the weakly nonlinear multiphase capillary wavetrains in deep water is unstable to oblique disturbances and presented that the dominant modulational instability is two-dimensional in deep water. It is found that the growth rate of modulational instability increases with the increase of the angle of interaction between two wavetrains. The existing fourth-order analysis provides significant deviations on the stability results when compared with the third-order analysis. [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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  Data: Modulational instability of multiphase capillary wavetrains on deep water.
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  Data: <searchLink fieldCode="JN" term="%22Journal+of+Fluid+Mechanics%22">Journal of Fluid Mechanics</searchLink>. 2/25/2026, Vol. 1029, p1-26. 26p.
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  Data: <searchLink fieldCode="DE" term="%22Modulational+instability%22">Modulational instability</searchLink><br /><searchLink fieldCode="DE" term="%22Capillary+waves%22">Capillary waves</searchLink><br /><searchLink fieldCode="DE" term="%22Nonlinear+evolution+equations%22">Nonlinear evolution equations</searchLink><br /><searchLink fieldCode="DE" term="%22Water+waves%22">Water waves</searchLink><br /><searchLink fieldCode="DE" term="%22Theory+of+wave+motion%22">Theory of wave motion</searchLink>
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  Data: The stability analysis of multiphase capillary wavetrains on water of infinite depth is performed using two coupled fourth-order nonlinear evolution (NLE) equations. We have investigated analytically the influence of a second wavetrain travelling in a different direction to the first wavetrain. The propagation of multiphase modes is studied for the case when group velocity projections of two wavetrains overlap. Criteria are derived for capillary Stokes wave instabilities and for the existence of a multiphase solitary envelope solution. We have exhibited that the weakly nonlinear multiphase capillary wavetrains in deep water is unstable to oblique disturbances and presented that the dominant modulational instability is two-dimensional in deep water. It is found that the growth rate of modulational instability increases with the increase of the angle of interaction between two wavetrains. The existing fourth-order analysis provides significant deviations on the stability results when compared with the third-order analysis. [ABSTRACT FROM AUTHOR]
– Name: AbstractSuppliedCopyright
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  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:
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      – Type: doi
        Value: 10.1017/jfm.2026.11243
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      – Code: eng
        Text: English
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      Pagination:
        PageCount: 26
        StartPage: 1
    Subjects:
      – SubjectFull: Modulational instability
        Type: general
      – SubjectFull: Capillary waves
        Type: general
      – SubjectFull: Nonlinear evolution equations
        Type: general
      – SubjectFull: Water waves
        Type: general
      – SubjectFull: Theory of wave motion
        Type: general
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      – TitleFull: Modulational instability of multiphase capillary wavetrains on deep water.
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              Text: 2/25/2026
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              Y: 2026
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              Value: 1029
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