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 in 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 the eddy SST anomaly can be accurately reproduced only if the vertical resolution is high enough (~4m in near surface) and if the atmospheric forcing contains high-frequency. In summer with this configuration, the vertical mixing parameterized by the k-epsilon closure scheme is three times higher inside the eddy than outside the eddy, and leads to an anticyclonic cold core SST anomaly. 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 anticyclone core. On the other hand, eddy MLD anomaly appears more sensitive to horizontal resolution, and requires SST retroaction on air-sea fluxes. These results detail the need of high frequency forcing, high vertical and horizontal resolutions to accurately reproduce the evolution of a mesoscale eddy.