Seasonal evolution of both surface signature and subsurface structure of a Mediterranean mesoscale anticyclones is assessed using the CROCO high-resolution numerical model with realistic background stratification and fluxes. In good agreement with remote-sensing and in-situ observations, our numerical simulations capture the seasonal cycle of the anomalies, induced by the anticyclone, both in the sea surface temperature (SST) and the mixed layer depth (MLD). The eddy signature on the SST shifts from warm-core in winter to cold-core in summer, while the MLD deepens significantly in the core of the anticyclone in late winter. Our sensitivity analysis shows that these dynamical properties can be accurately reproduced only if the resolution is high enough (~1km for the horizontal with 100 vertical levels in a Mediterranean stratification) and if the atmospheric forcing contains high-frequency. In this configuration the deformation radius is explicitly resolved and the vertical mixing parametrized by the k-ε closure scheme is three times higher inside the eddy than outside the eddy. This differential mixing is explained by near-inertial waves, triggered by the high-frequency atmospheric forcing.Near-inertial waves propagate more energy inside the eddy because of the lower effective Coriolis parameter in the anticyclonic core. In addition to these high spatial and temporal resolution, SST retroaction on air-sea fluxes appears to be necessary to obtain marked eddy mixed layer depth anomaly.