# Excitation of interfacial waves via near---resonant surface---interfacial wave interactions

## TL;DR

This paper develops a Hamiltonian-based formalism to analyze resonant interactions between surface and interfacial waves in a two-layer system, revealing energy transfer mechanisms influenced by wind and wave spectra.

## Contribution

It introduces a novel Hamiltonian framework for coupled surface-interfacial wave interactions, including spectral energy transfer and growth rate calculations.

## Key findings

- Energy transfer from surface to interfacial waves can occur over hours.
- Most effective energy transfer at wind speeds near sea capping.
- Interfacial waves can be generated oblique to wind direction.

## Abstract

We consider interactions between surface and interfacial waves in the two layer system. Our approach is based on the Hamiltonian structure of the equations of motion, and includes the general procedure for diagonalization of the quadratic part of the Hamiltonian. Such diagonalization allows us to derive the interaction crossection between surface and interfacial waves and to derive the coupled kinetic equations describing spectral energy transfers in this system. Our kinetic equation allows resonant and near resonant interactions. We find that the energy transfers are dominated by the class III resonances of \cite{Alam}. We apply our formalism to calculate the rate of growth for interfacial waves for different values of the wind velocity. Using our kinetic equation, we also consider the energy transfer from the wind generated surface waves to interfacial waves for the case when the spectrum of the surface waves is given by the JONSWAP spectrum and interfacial waves are initially absent. We find that such energy transfer can occur along a timescale of hours; there is a range of wind speeds for the most effective energy transfer at approximately the wind speed corresponding to white capping of the sea. Furthermore, interfacial waves oblique to the direction of the wind are also generated.