Effect of long internal waves on the evolution of deep-water surface gravity waves

Equations describing the resonant interaction between long internal waves and short surface waves are derived and represented in wavenumber space. Various evolution equations can arise depending on the slopes of the two wave fields and the ratio of their wavelengths. The existence of the internal waves will affect the stability of a short surface plane wave. A coupled set of transport equations is derived for deterministic internal waves and Gaussian random surface waves. The amplification rate of perturbations can be analyzed for a range of spectral bandwidths.