Acoustic-gravity wave triad resonance in compressible flow: a dynamical systems approach
The classical water-wave theory often neglects water compressibility effects, assuming acoustic and gravity waves propagate independently due to their disparate spatial and temporal scales. However, nonlinear interactions can couple these wave modes, enabling energy transfer between them. This study...
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| Vydané v: | Journal of fluid mechanics Ročník 1013 |
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| Hlavní autori: | , , , |
| Médium: | Journal Article |
| Jazyk: | English |
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Cambridge, UK
Cambridge University Press
16.06.2025
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| Abstract | The classical water-wave theory often neglects water compressibility effects, assuming acoustic and gravity waves propagate independently due to their disparate spatial and temporal scales. However, nonlinear interactions can couple these wave modes, enabling energy transfer between them. This study adopts a dynamical systems approach to investigate acoustic–gravity wave triads in compressible water flow, employing phase-plane analysis to reveal complex bifurcation structures and identify steady-state resonant configurations. Through this framework, we identify specific parameter conditions that enable complete energy exchange between surface and acoustic modes, with the triad phase (also known as the dynamical phase) playing a crucial role in modulating energy transfer. Further, incorporating spatial dependencies into the triad system reveals additional dynamical effects that depend on the wave velocity and resonance conditions: we observe that travelling-wave solutions emerge, and their stability is governed by the Hamiltonian structure of the system. The phase-plane analysis shows that, for certain velocity regimes, the resonance dynamics remains similar to the spatially independent case, while in other regimes, bifurcations modify the structure of resonant interactions, influencing the efficiency of energy exchange. Additionally, modulated periodic solutions appear, exhibiting changes in wave amplitudes over time and space, with implications for wave-packet stability and energy localisation. These findings enhance the theoretical understanding of acoustic–gravity wave interactions, offering potential applications in geophysical phenomena such as oceanic microseisms. |
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| AbstractList | The classical water-wave theory often neglects water compressibility effects, assuming acoustic and gravity waves propagate independently due to their disparate spatial and temporal scales. However, nonlinear interactions can couple these wave modes, enabling energy transfer between them. This study adopts a dynamical systems approach to investigate acoustic–gravity wave triads in compressible water flow, employing phase-plane analysis to reveal complex bifurcation structures and identify steady-state resonant configurations. Through this framework, we identify specific parameter conditions that enable complete energy exchange between surface and acoustic modes, with the triad phase (also known as the dynamical phase) playing a crucial role in modulating energy transfer. Further, incorporating spatial dependencies into the triad system reveals additional dynamical effects that depend on the wave velocity and resonance conditions: we observe that travelling-wave solutions emerge, and their stability is governed by the Hamiltonian structure of the system. The phase-plane analysis shows that, for certain velocity regimes, the resonance dynamics remains similar to the spatially independent case, while in other regimes, bifurcations modify the structure of resonant interactions, influencing the efficiency of energy exchange. Additionally, modulated periodic solutions appear, exhibiting changes in wave amplitudes over time and space, with implications for wave-packet stability and energy localisation. These findings enhance the theoretical understanding of acoustic–gravity wave interactions, offering potential applications in geophysical phenomena such as oceanic microseisms. |
| Author | Bustamante, Miguel D. Andrade, David Stuhlmeier, Raphael Kadri, Usama |
| Author_xml | – sequence: 1 givenname: David orcidid: 0000-0002-9486-8200 surname: Andrade fullname: Andrade, David organization: School of Sciences and Engineering, Universidad del Rosario, Bogota, Colombia – sequence: 2 givenname: Miguel D. orcidid: 0000-0003-3360-0304 surname: Bustamante fullname: Bustamante, Miguel D. organization: School of Mathematics and Statistics, University College Dublin, Belfield, Dublin 4, Ireland – sequence: 3 givenname: Usama orcidid: 0000-0002-5441-1812 surname: Kadri fullname: Kadri, Usama email: usama.kadri@gmail.com organization: School of Mathematics, Cardiff University, Cardiff, UK – sequence: 4 givenname: Raphael orcidid: 0000-0002-6568-1543 surname: Stuhlmeier fullname: Stuhlmeier, Raphael organization: School of Engineering Computing & Mathematics, University of Plymouth, Plymouth, UK |
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| Keywords | compressible flows surface gravity waves nonlinear dynamical systems |
| Language | English |
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| References | 2009; 85 2023; 35 2017; 3 2023; 101 2024; 109 1969; 55 1964; 20 2016; 788 2012; 17 2015; 767 2019; 887 2020; 884 2018; 849 2020; 883 2008; 464 2024; 36 2016; 39 1991; 8 2014; 113 2016; 55 2004; 113 2022; 4 2013; 735 2018; 850 2013; 50 2024; 9 2022; 34 2023; 116 2024; 130 2016; 794 2022; 609 1950; 243 2025; 1008 2023; 956 2007; 40 1985; 78 2012; 710 2023; 958 |
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| Title | Acoustic-gravity wave triad resonance in compressible flow: a dynamical systems approach |
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