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Two-dimensional resonant triad interactions in a two-layer system

Published online by Cambridge University Press:  18 November 2020

Wooyoung Choi Open the ORCID record for Wooyoung Choi [Opens in a new window] ,
Malik Chabane  and
Tore Magnus A. Taklo
Wooyoung Choi*
Affiliation:
Department of Mathematical Sciences, New Jersey Institute of Technology, Newark, NJ07102-1982, USA
Malik Chabane
Affiliation:
Department of Mathematical Sciences, New Jersey Institute of Technology, Newark, NJ07102-1982, USA
Tore Magnus A. Taklo
Affiliation:
Department of Mathematical Sciences, New Jersey Institute of Technology, Newark, NJ07102-1982, USA
*
†Email address for correspondence: [email protected]
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Abstract

We consider resonant triad interactions between surface and internal gravity waves propagating in two horizontal dimensions in a two-layer system with a free surface. As the system supports both surface and internal wave modes, two different types of resonant triad interactions are possible: one with two surface and one internal wave modes and the other with one surface and two internal wave modes. The resonance conditions are studied in detail over a wide range of physical parameters (density and depth ratios). Explicitly identified are the spectral domains of resonance whose boundaries represent one-dimensional resonances (class I–IV). To study the nonlinear interaction between two-dimensional surface and internal waves, a spectral model is derived from an explicit Hamiltonian system for a two-layer system after decomposing the surface and interface motions into the two wave modes through a canonical transformation. For both types of resonances, the amplitude equations are obtained from the reduced Hamiltonian of the spectral model. Numerical solutions of the explicit Hamiltonian system using a pseudo-spectral method are presented for various resonance conditions and are compared with those of the amplitude equations.

JFM classification

Geophysical and Geological Flows: Stratified flows Geophysical and Geological Flows: Internal waves Waves/Free-surface Flows: Surface gravity waves
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 907 , 25 January 2021 , A5
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Copyright
© The Author(s), 2020. Published by Cambridge University Press

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References

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