Submesoscale processes play a key role in the ocean's energy cycle, linking large-scale balanced motions to small-scale dissipation. Their small spatial scales impose stringent demands on numerical models, making sub-kilometer resolution essential for resolving these processes. In this talk, we present high-resolution simulations of an idealized double-gyre system conducted with OMARE (Ocean Modeling with Adaptive REsolution). The experiments span a hierarchy of horizontal resolutions, focusing on 2 km-resolution, submesoscale-capable runs and 400 m-resolution, submesoscale-resolving runs. Both spectral analysis and the coarse-graining (CG) method are applied for the diagnosis of cross-scale KE fluxes in the wavenumber-frequency space. The consequent KE flux estimates are inter-compared to assess the influence of the diagnostic method. The sensitivity of the choice of window functions is also evaluated for the spectral method. Results show that, compared with the 2 km runs, the 400 m simulations exhibit a substantially stronger forward cascade which also extends to smaller spatial scales. These differences suggest that the O(1 km) grid spacing commonly used in high-resolution global ocean simulations is insufficient to fully resolve submesoscale dynamics and the associated cross-scale energy transfers. In addition, the diagnosed KE flux shows similar results, but quantitative differences with respect to the analysis method. Future work will focus on evaluating the potential of OMARE's adaptive mesh refinement capability for studying submesoscale energy cascades, leveraging its computational efficiency and localized grid refinement.