Climate models require increased resolution in order to resolve mesoscale processes which are often parameterized. Coupled global climate models typically use structured (i.e. rectangular) grids for which eddy-permitting resolution is prohibitive since resolution must be increased globally. The Model for Prediction Across Scales (MPAS) Ocean is the ocean component of the Energy Exascale Earth System Model (E3SM), and employs an unstructured mesh that allows resolution -- and therefore computational resources -- to be focused on specific regions. Here we test of the model's variable-resolution simulation quality in three experiments: (1) global 60 km resolution, (2) global 15 km resolution, and (3) 60 km resolution with a 15 km refined-resolution in the Southern Ocean. To quantify model skill we focus on eddy kinetic energy and find that the variable-resolution model generates similar Southern Ocean eddy kinetic energy compared to the 15 km resolution model. This finding motivates the future application of this grid-refinement approach to additional key regions such as western boundary currents and coastal upwelling zones. By exploiting the ocean's non-uniform distribution of kinetic energy, we can focus our resources on resolving the regions where fine-scale processes have the largest effects on the climate system.