Decomposing Realistic Oceanic Flow in Balanced and Unbalanced Parts Using a Novel Balancing Approach

Decomposing oceanic flow fields into its slowly evolving geostrophic component and the fast wave mode is necessary to understand processes like mesoscale eddy dissipation and spontaneous wave emission. The application of existing decomposition methods, such as nonlinear normal mode decomposition or optimal balance is limited to idealized model settings that neither include topography nor a varying Coriolis parameter. To overcome these limitations, we propose a new approach that combines optimal balance with a time-averaging procedure. This approach eliminates the necessity for the Fourier transformation that is required in the original optimal balance method. We tested and compared the new  variation of optimal balance with the original method in 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 obtained with the original method. We further show that the convergence rate can be improved by doing multiple short time averages instead of a single long one. The new method is applicable to realistic ocean scenarios that include topography and a varying Coriolis parameter and shows promising results in decomposing complex flow fields.