Spectral Decomposition and Energy Transfer in Rotating Stratified Flows Using Normal Mode Methods

Abstract

Spectral energy transfer in rotating stratified flows underpins many of the dynamic processes observed in the atmosphere and oceans. We present a refined normal mode decomposition that separates geostrophic and ageostrophic components, applied to a non-hydrostatic simulation of a baroclinic life cycle in a doubly-periodic domain. By projecting the flow onto Sturm-Liouville vertical eigenmodes, we reveal distinct spectral signatures and energy cascades associated with balanced and unbalanced motions. Our results highlight fundamental differences from classical Helmholtz- based approaches, particularly the enhanced role of available potential energy at mesoscale wavelengths. This study offers new insights into multiscale energy dynamics and establishes a mathematically rigorous framework for interpreting turbulent processes in rotating stratified environments.