On flow decomposition in realistic ocean models

Decomposing oceanic flow fields into slow and fast evolving components is necessary to understand processes like mesoscale eddy dissipation and spontaneous wave emission. To study these processes, the decomposition in a geostrophic (slow) and a non-geostrophic (fast) component is not precise enough. A part of the non-geostrophic component, the slaved mode, evolves slowly and thus belongs to the slow component. More precise decomposition methods that capture the slaved mode exist, such as optimal balance and nonlinear normal mode decomposition, but their application is limited to idealized model settings that neither include topography nor a varying Coriolis parameter. Here, I present a new modification of the optimal balance method such that it is applicable to more realistic ocean model setups. The new modification uses a time-averaging procedure to project onto the linear geostrophic component. This approach eliminates the necessity for the Fourier transformation that was previously required in the original method. To test and compare the different balancing methods, I used a scaled rotating shallow water model in various dynamical regimes, with Rossby numbers ranging from 0.03 to 0.5. In all tested configurations, the imbalances obtained with the new method converges towards the imbalances obatained with the  original method. Although, in theory, the new method is applicable to ocean models that include topography and a varying Coriolis parameter, I only test it in models without these settings, which highlights the need of further research.