The first scenario is a case where the horizontal resolution is fine enough to resolve all of the SI modes

necessary to restratify the mixed layer to a marginally stable state (Ri=1Ri=1 and q=0q=0), but where the horizontal viscosity is large enough to damp out some of the modes needed to reach this state. The end ZD1839 nmr result is that the model equilibrates at a state that is unstable to SI (Ri<1Ri<1 and q<0q<0). The second scenario is similar to the first but where the model resolution is coarse enough that some of the SI modes are unresolved. Linear theory predicts that this case would occur when the grid spacing is too coarse to resolve the most-restratifying mode. Finally, the

third scenario features an unphysical numerical instability that arises when νv≠νh. In this case the flow becomes too stratified (Ri>1Ri>1 and q>0q>0) as a result of numerical artifacts. This occurs even when the grid resolution is sufficient to directly resolve the shear instability, and so is attributed here to the use of anisotropic viscosity. It is likely that this effect is not isolated to the flow scenarios depicted here, for which further investigation may be warranted. It is important to note that the scenarios above are not necessarily tied to the explicit model viscosity; that is, the numerical viscosity can just as easily affect SI restratification in cases where it dominates the model viscosity. see more Given that the relationship between the numerical viscosity and model viscosity is

affected by the choice of advection scheme, these scenarios could occur in idealized models or models running with extremely low model viscosity as either well as larger-scale GCMs. Inclusion of other parameterizations such as KPP (Large et al., 1994) or viscous closures would also strongly affect the SI dynamics in the model, as they could induce large mixed layer viscosities that could quash the growth of SI modes. It is of interest to submesoscale modelers to know at what resolution SI begins to become resolved at the gridscale, and what effect it would have upon the mixed layer stratification once it becomes present. Fig. 4 demonstrates that the linear growth rate can be used to predict the wavelength of the largest SI modes when the mixed layer N2N2 and M2M2 are uniform and slowly varying in time. A prediction made in this way would require knowledge of the model viscosity and diffusivity, and would be improved by accounting for contributions to each of these by other parameterizations such as KPP. For a more dynamically evolving mixed layer the simple, if unsatisfying, answer is that the necessary resolution depends heavily on the local flow parameters.