Ekaterina Bagaeva

• This thesis addresses the challenge of accurately representing oceanic dynamics characterized by a multitude of interacting processes in numerical models. Specifically, it focuses on the simulation of oceanic circular patterns ranging from 10 to 100 km in diameter, known as mesoscale eddies. These eddies play a critical role in transporting energy, water properties, and nutrients across the ocean. This research uses grid resolutions that directly capture some larger mesoscale eddies (resolved) while employing advanced mathematical techniques to represent the effects of smaller, unresolved eddies. The primary aim of the thesis is to develop and incorporate novel mathematical and numerical approaches into the Finite Volume Sea Ice-Ocean Model (FESOM2) to improve the representation of mesoscale eddies while maintaining manageable computational costs. To bridge the gap between low-resolution and high-resolution simulations, the study enhances the mesoscale eddy modeling framework formulated by Juricke et al. (2019) through the implementation of new components that address unresolved dynamics. This includes the addition of an advection-based component to capture nonlinear interactions between resolved and unresolved eddies, which demonstrates positive performance. Furthermore, stochastic elements are introduced into the governing equations to better represent small-scale variability missing from deterministic formulations. In parallel, the thesis explores alternative and complementary parameterization strategies, offering fresh perspectives on modeling at partially resolved scales. Each enhancement is rigorously evaluated using a suite of diagnostic tools — many developed as part of this work — with a particular focus on spectral analysis and energy pathways. Overall, the thesis proposes an integrated approach to mesoscale eddy modeling, advancing the accuracy and consistency of ocean simulations across eddy-permitting resolutions.