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

Document Type

Article

Publication Date

1-1-2020

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.

Identifier

85087283670 (Scopus)

Publication Title

Journal of Fluid Mechanics

External Full Text Location

https://doi.org/10.1017/jfm.2020.824

e-ISSN

14697645

ISSN

00221120

Volume

907

Grant

DMS-1517456

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