The increase of computational capabilities led recent studies to implement very high resolution simulations that gave access to new scale interaction processes, particularly those associated with the transfer of energy from the oceanic mesoscales to smaller scales through an interior route to dissipation which is still under-explored. In this context, we study spin down simulations of a mesoscale interior vortex, unstable to a mixed baroclinic-barotropic instability. Even though the global energy is almost conserved, some energy is transferred down to dissipation scales during the development of instabilities. However, in our parameter regime, there is no substantial forward energy cascade sustained by unbalanced dynamics. Rather than exploring the physical parameter range, we clarify numerical discretization issues that can be detrimental to the physical solutions and our interpretation of fine scale dynamics. Special care is given to determining the effective resolution of the different simulations. We improve it by a factor of 2 in our PE finite-difference model (CROCO) by implementing a 5th-order accurate horizontal advection scheme. We also explore a range of grid aspect ratios dx/dz and find that energy spectra converge for aspect ratios that are close to N/ f . However, convergence is not reached in the PE model when using a fourth-order centered scheme for vertical tracer advection (standard in ROMS-family codes). The scheme produces dispersion errors that triggers baroclinic instabilities and generates spurious submesoscale horizontal features. This spurious instability shows great impact on submesoscale production and energy cascade, emphasizing the significance of numerical settings in oceanic turbulence studies.