Spectral and Vertical Decomposition of Oceanic Eddy Energy Pathways

Abstract

The oceanic meso-scale eddy field, characterized by spatial scales of 10-200 km, is critical to the transport of heat, carbon, and momentum. It is well established that meso-scale energy is primarily generated via baroclinic instability and subsequently undergoes an inverse cascade toward larger horizontal scales, moving energy away from the small scale where dissipation takes place at O(10^{-2}). Consequently, a significant scale-gap exists between the energy-containing and dissipation scales, and how this scale is bridged remains uncertain. Energy-equation-based frameworks, like the Lorenz energy cycle, have proven valuable for deepening the understanding of energy reservoirs, conversions and transfers across scales. This study utilizes such frameworks in a hierarchy of ocean models to address the scale-gap conundrum and the uncertainties regarding meso-scale energy reservoirs and pathways in the ocean.

The first part of this thesis examines the spectral characteristics of the oceanic Lorenz energy cycle, focusing on the baroclinic conversion term. The analysis reveals a dipolar structure in spectral space, where baroclinic conversion acts as a source of eddy kinetic energy (EKE) at small horizontal scales and a sink at larger scales, partly balancing the inverse cascade of EKE. In realistic global simulations, this large-scale EKE sink is found predominantly poleward of 30° latitude in regions of eastward mean flow. In idealized models, the EKE sink appears in eastward mean flow and is absent for westward mean flow, confirming the link between the EKE sink and mean flow direction. Furthermore, the EKE sink disappears when $\beta$ is set to zero, indicating that planetary Rossby waves are essential for its existence. These findings are explained by linear stability analysis, which confirms that the EKE sink only appears at large scales for beta unequal and further reveals how the vertical structure of this sink is tied to the mean flow direction: In eastward mean flow, the EKE sink appears in the upper half of the water column, while it is found near the bottom for westward mean flow. Since EKE and baroclinic conversion are surface-intensified, the EKE sink near the bottom in westward flows is damped, whereas in eastward flows it is intensified, explaining the results found in the numerical models.

The second part of the thesis shifts the focus to analyzing the vertical structure of EKE using vertical Sturm--Liouville eigenmodes. Across all model configurations, and given sufficient resolution, most EKE is contained by the barotropic and first baroclinic mode, and the fundamental energy pathway remains consistent: EKE is produced by baroclinic instability in the baroclinic modes, while barotropic production remains weak. Subsequently, EKE is transferred to the barotropic mode by non-linear transfers, which are non-local in modal space, with EKE transferred directly from higher modes to the barotropic mode. The presence of a pycnocline shifts baroclinic generation and non-linear transfer origins to higher modes and increases the complexity of these transfers, by introducing an energy loop between the first and higher baroclinic modes that operates alongside the direct transfer to the barotropic mode. Within model configurations incorporating a rough bottom, topographic scattering of EKE can be locally significant, but remains small in the global integral and is of secondary importance relative to baroclinic generation and non-linear transfers. Applying a spectral decomposition of the modal EKE conversions and transfers reveals that while the baroclinic modes facilitate the large-scale EKE sink via negative baroclinic conversion, such a sink is absent in the barotropic mode. Simultaneously, non-linear transfers in modal and spectral space accumulate barotropic large-scale EKE. Consequently, the removal of large-scale barotropic EKE and its route to dissipation must rely on alternative processes. Finally, horizontal wavenumber spectra of modal eddy energy exhibit slopes that vary significantly with vertical mode and latitude, typically ranging between -2 and -5. The analysis reveals that a clear scale separation between energy sources and sinks is absent, leading to a violation of classical inertial range assumptions and explaining the non-universality of the observed spectral slopes. By integrating modal and spectral perspectives, this work provides an unprecedentedly detailed analysis of meso-scale eddy energy pathways, representing a significant advancement in our fundamental understanding of the global ocean circulation.