A numerical solution for an idealized double-gyre is used to investigate the sensitivity of ocean dynamics and passive tracer advection to horizontal resolution (Δx) in a mesoscale eddy rich regime. In agreement with previous studies, we find that ocean dynamical solutions are strongly sensitive to grid resolution. With mesoscale resolution (Δx~O(10) km), eddies are marginally resolved and their impact on tracer transport is not well represented. At submesoscale resolution (Δx~O(1) km), the number of mesoscale eddies and their energy is increased, due to the resolved submesoscales. The changes are mostly seen in the vorticity and vertical velocity fields, and are less obvious in the temperature field. In contrast, we demonstrate that the offline transport of passive tracer is not altered when the finest scales (O(1) km) present in the dynamical solutions are discarded. We do so by showing that dynamical solutions obtained with Δx~O(1) km can be degraded (following a flux preserving procedure) down to resolutions Δx~O(10) km without significantly impacting passive tracer solutions. The reason for this stems from the level of dissipation/diffusion required during the integration of the dynamical model which smoothes variance at wavelength smaller than at least 5-10 Δx. This result is used to derive a method which alleviates data storage needs and accelerates tracer advection simulations, with a gain of the order of 10³ in computing time. The method involves three steps: (1) on-line resolution of the dynamics with Δx~O(1) k), (2) degradation of the 3D velocity field on a Δx~O(10) km grid and (3) off-line tracer transport with the degraded velocity on the ΔX grid. It opens promising perspectives for submesoscale bio-physical modelling at reduced numerical cost.