| Abstract: | Energy transfer via resonance in a stratified fluid with a constant Brunt–Väisälä frequency is studied through the Manley–Rowe relation and direct numerical simulations. The objectives of this study are two-fold. One is to determine if there is a limitation on the lengthscale of small-scale waves to which primary energy can be effectively transferred. The other is to study factors affecting the growth of parametric subharmonic instability. Resonantly interacting modes are classified into three groups: local sum modes, quasi-subharmonic modes and remote parametric subharmonic instability modes (characterized by interaction with very small-scale waves). The latter two involve energy transfer from a primary wave to secondary waves with half the frequency. Most energy transfer is through local sum resonant modes and quasi-subharmonic modes. Energy cannot effectively transfer to higher wavenumber modes since dynamical systems are altered as wavenumbers of excited modes increase. In the remote modes, the solution is sinusoidal with high angular frequency and very small energy capacity. As a consequence, these modes are inactive in energy transfer despite their high energy growth rates. Effects of non-uniform white noise amplitude and primary mode propagation angle on the quasi-subharmonic modes are also investigated. Implications for energy transfer in the ocean are discussed. |
