Spectral Decomposition and Energy Transfer in Rotating Stratified Flows Using Normal Mode Methods - Syed Ibrahim; Roohi Laila (Spectrum of Engineering Sciences, 2025)
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.