Modelling of partially-resolved oceanic symmetric instability

- Ocean models can fail to resolve some symmetric instability (SI) modes due to coarse resolution.
- Viscosity can suppress SI modes as well, limiting the maximum potential restratification.
- SI extracts energy from the background flow field differently depending on the slope of the mode.
- The use of anisotropic viscosity can lead to gridscale noise and excessive restratification.
- The resolution threshold for SI can be approximated when the stratification varies slowly in time.

A series of idealized numerical models have been developed to investigate the effects of partially resolved symmetric instability (SI) in oceanic general circulation models. An analysis of the energetics of symmetric instability is used to argue that the mixed layer can be at least partially restratified even when some SI modes are absent due to either large horizontal viscosity or coarse model resolution. Linear stability analysis reveals that in the idealized models the amount of restratification can be predicted as a function of the grid spacing and viscosity. The models themselves are used to demonstrate these predictions and reveal three possible outcomes in steady-state: (1) incomplete restratification due to viscosity, (2) incomplete restratification due to resolution, and (3) excessive restratification due to anisotropy of the viscosity. The third outcome occurs even on a high-resolution isotropic grid and in two separate numerical models, and thus appears to be a sort of robust numerical feature. The three outcomes are used to recommend criteria that a successful SI parameterization should satisfy.