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

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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.

Original languageEnglish (US)
Article numberA5
JournalJournal of Fluid Mechanics
Volume907
DOIs
StatePublished - 2020

All Science Journal Classification (ASJC) codes

  • Condensed Matter Physics
  • Mechanics of Materials
  • Mechanical Engineering

Keywords

  • internal waves
  • stratified flows
  • surface gravity waves

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