Acoustic-gravity wave triad resonance in compressible flow: a dynamical systems approach

Andrade, David, Bustamante, Miguel, Kadri, Usama ORCID: https://orcid.org/0000-0002-5441-1812 and Stuhlmeier, Raphael 2025. Acoustic-gravity wave triad resonance in compressible flow: a dynamical systems approach. Journal of Fluid Mechanics Item availability restricted.

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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 (a.k.a. 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 phase22 plane analysis shows that for certain velocity regimes, the resonance dynamics remain 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.

Item Type:	Article
Status:	In Press
Schools:	Schools > Mathematics
Publisher:	Cambridge University Press
ISSN:	0022-1120
Date of First Compliant Deposit:	3 June 2025
Date of Acceptance:	11 May 2025
Last Modified:	12 Jun 2025 13:00
URI:	https://orca.cardiff.ac.uk/id/eprint/178699

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