A host of studies has recognized that truncation errors of the discretized advection terms lead to spurious mixing and dissipation (Fig. 1) and may interact nonlinearly with turbulent mixing and transport. To investigate the impacts of spurious mixing and dissipation, we implemented some of the most novel advection schemes into the coastal ocean model GETM. We quantified spurious dissipation [Klingbeil, 2014] and mixing of the advection schemes (Fig. 3) in idealized experiments of baroclinic instabilities (Fig. 2) ranging from mesoscales (small Rossby number) to sub-mesoscales (order-one Rossby number). The processes at submesosales are distinct from mesoscale by their contribution to restratification of the mixed layer. Such analyses (Fig. 4) help to choose between highly accurate but complex schemes and lower-order less complex schemes balancing accuracy and computational costs. The major outcome of the present study is that both, numerically induced dissipation (leading to a decrease of kinetic energy) and numerically induced mixing (leading to an increase of background potential energy), artificially delay the restratification process [Mohammadi-Aragh, 2015], an effect that needs to be taken into account if parameterizations for eddy-induced mixing and dissipation are compared with numerical model simulations.