Energy cascade due to nonlinear interactions of internal gravity waves

The kinetic energy spectra of oceanic internal gravity waves (IGWs) from recent field measurements exhibit large variability, deviating from the standard Garrett-Munk (GM) models. However, the current finescale parameterization of turbulent dissipation is based on the GM76 model, which does not consider general spectral shapes. Thus an improved estimate of turbulent dissipation for different spectra is needed for better parameterization of ocean mixing for global circulation and climate models. The rate of turbulent dissipation occurring at small scales can be inferred from knowledge of energy transfer due to nonlinear wave-wave interactions at intermediate scales. In this work, we conduct direct calculation of energy transfer based on the wave kinetic equation in the wave turbulence theory and compare the energy flux across a critical vertical wavenumber that provides energy available for dissipation with the estimate from finescale parameterization. Three representative spectra, i.e., the GM75 and GM76 models as well as a spectrum fitted from observation, are analyzed. Key mechanisms, i.e., local and three non-local interactions (parametric subharmonic instability, elastic scattering and induced diffusion) are identified with their contribution to the energy transfer quantified. This will shed light on a new formulation of finescale parameterization incorporating varying spectral forms of IGWs and a realistic ocean environment.