Energy Pathways of the Internal Gravity Wave Field in the Ocean driven by Wave–Mean Flow and Wave–Wave Interactions

Abstract

Internal gravity waves (IGWs) mediate key pathways in the ocean’s energy cycle, redistributing energy across a broad range of scales due to interactions with their environment shaped by, inter alia, mean flows, other waves, topography, and turbulence. Through these interactions, IGWs transfer energy to smaller scales, inducing density mixing that is essential to maintain the global overturning circulation. Yet diagnosing and quantifying these pathways remains challenging due to complex IGW generation, interaction, and dissipation processes. This thesis examines energy pathways driven by wave-mean flow and wave-wave interactions under representative oceanic conditions. Theory, numerical modeling, and observation-based analyses are integrated to provide a unified understanding of IGW dynamics. IGWs evolve within an inhomogeneous environment; their scale separation gives rise to dynamically distinct interaction regimes. When fast, small-scale IGWs interact with slowly varying background flows, IGWs evolve according to WKBJ-ray tracing theory. Within this regime, the first part of the thesis investigates IGW evolution in a coherent mesoscale eddy using a novel Internal Wave Energy Model based on the six-dimensional radiative transfer equation. Simulations initialized with the Garrett–Munk spectrum (GM76) and an observation-inspired eddy and stratification from the Canary Current System show that vertical shear drives wave energy loss at the rim, whereas lateral shear drives wave energy gain outside the eddy through anisotropy development. Vertical refraction produces surface-intensified dissipation at the eddy rim with diffusivities of O(1e-7) to O(1e-5) m^2/s. As scale separation diminishes and waves interact with similar scales, weakly nonlinear effects dominate their evolution. The second part of the thesis develops a unified theoretical foundation for wave-wave and wave-vortex triad interactions. The kinetic equations or scattering integrals are derived from both Euler and Lagrange formulations of the rotating, stratified, non-hydrostatic Boussinesq system. Both formulations generally differ, as energy is strictly quadratic in the Eulerian framework but is an infinite series in amplitude powers in the Lagrangian. However, under resonant conditions, both kinetic equations reduce to quadratic form and are equal. In horizontally isotropic conditions, only resonant interactions contribute to energy transfers, while in anisotropic conditions, so far unconsidered non-resonant interactions may contribute through the imaginary part of the time response function. Based on this theoretical framework, the third part of the thesis develops the novel numerical framework Scattering Integral for Nonlinear Energy Transfers to evaluate the scattering integral across typical oceanic IGW spectra. These methods resolve long-standing issues regarding weak-interaction consistency and convergence of the scattering integral. When applied to the GM76 spectrum, the scattering integral diverges unless modified by steeper slopes or smooth transitions to turbulence, suggesting that the canonical GM76 spectrum is not universally self-consistent. The computed energy transfers are dominated by non-local interactions rather than local interactions. Parametric subharmonic instability drives an inverse energy cascades in frequency; induced diffusion drives bidirectional energy transfers in frequency; and elastic scattering weak forward transfers. Two new mechanisms are identified: Third parametric generation is the main driver of forward energy cascades, and horizontal diffusion drives strong energy transfers at high frequencies. Together, these studies offer an integrated view of how IGW energy is redistributed by mesoscale flows and weakly nonlinear interactions. By combining theoretical and numerical advances with observation-based configurations, the thesis provides a quantitative description of the complex energy pathways of the full IGW field at unprecedented high resolution. The findings establish a robust physical foundation for parameterizing IGW processes in ocean circulation models and open new paths for future research on IGW energetics.