##### The study of submesoscale dynamics can help to improve future climate and ocean state predictions through the development of eddy parameterizations, which aim to represent the effects of unresolved turbulence in numerical fluid flow simulations. This is an ever-evolving problem, as improvements in both theory and the computing power with which to run General Circulation Models (GCM’s) introduce new opportunities for parameterization development. Parameterizing submesoscale turbulence is but one frontier of this effort.

##### Next-generation GCM’s are expected to routinely resolve dynamics at 1/4◦ or smaller, so that these models are entering a regime where the unresolved turbulence is less constrained by planetary rotation. The resolution of these GCM’s will soon become fine enough that submesoscale turbulence will be the largest, most energetic, and dynamically relevant type of unresolved turbulence. This is especially important because submesoscale turbulence plays a leading role in setting the stratification of the surface mixed layer, and is of primary importance in coupling the dynamics of the ocean and atmosphere. Because of its role in air-sea coupling, it is hypothesized to exert significant influence on the global climate on long timescales.

##### The SMILES numerical modelling group has developed a submesoscale parameterization which focuses on a special type of fluid instability for which no parameterization has previously been developed: symmetric instability (SI). This parameterization is dependent on external forcing by either surface buoyancy loss (i.e. atmospheric cooling or precipitation) or down-front winds (which blow parallel to regions where the fluid density changes in the horizontal), which lead to conditions favorable for SI. Previously-developed theory of SI has been leveraged to estimate the rates of momentum, buoyancy, and passive tracer mixing appropriate for this type of turbulence. With this parameterization the mixing rates of these quantities in GCM’s are then adjusted to reflect this “missing” turbulence. Early testing of the new SI parameterization has shown strong agreement with very high-resolution turbulence models, and efforts are now underway to further test and improve the scheme.

###### S.D. Bachman, B. Fox-Kemper, J.R. Taylor, L.N. Thomas, 2017. Parameterization of Frontal Symmetric Instabilities. I: Theory for Resolved Fronts, Ocean Modelling, 109,72-95.

**Link:
https://doi.org/10.1016/j.ocemod.2016.12.003 **

**Figure 1.** Schematic of a symmetrically-unstable mixed layer flow. A combination of surface buoyancy loss (B0 > 0; curvy arrows) and winds directed parallel to the lateral density gradient (τw; block arrow) lead to the presence of dense water over light water. Instead of leading to purely vertical convection, the rotation of the Earth and lateral density gradient modify the resulting turbulence and manifest dynamics which are unique to SI. A primary effect of these dynamics is to tilt surfaces of constant density (colored planes) toward the horizontal via an overturning circulation (elliptical arrows).

##### The numerical modelling team has also produced a realistic re-creation of the sea state during the observational campaign. While simulations like these are excellent tools for assessing and comparing against the cruise observations, many technical challenges remain in ensuring such models produce accurate, high-fidelity solutions. Chief among these challenges is the representation of turbulence which is too small to be resolved by the model grid, but which significantly influences the fluid flow. Three papers have been written which propose solutions to the "turbulence closure" problem, each of which focuses on a different aspect of the subgridscale physics. The added skill of numerical models which employ these closures will help to ensure that future ocean state predictions benefit from the state-of-the-science in ocean modelling techniques.

###### S.D. Bachman, D.P. Marshall, J.R. Maddison, J. Mak, 2017. Evaluation of a scalar eddy transport coefficient based on geometric constraints, Ocean Modelling, 109, 44-54.

**Link:
https://doi.org/10.1016/j.ocemod.2016.12.004 **

**Figure 2.** Schematic of Eady model configuration and diagnostic procedure. The shear and stratification at time t = 0 are constant, and the initial tracer profiles vary sinusoidally in y and z as in Bachman and Fox-Kemper (2013). At later times after the front goes baroclinically unstable, the tracer concentrations are zonally averaged, their meridional gradients and eddy fluxes are calculated, and a solution for κ is obtained by pseudoinverting the ensemble flux-gradient relationship at each point on the yz-plane. The overall value for κ at each output interval is taken as the domain average of these solutions. In the inset panels the tracer gradients and fluxes may vary beyond the given color scale, but the color limits are chosen to be suitable for all tracers shown.

###### S.D. Bachman, B. Fox-Kemper, B. Pearson, 2017. A scale-aware subgrid model for quasi-geostrophic turbulence, Journal of Geophysical Research Oceans, doi: 10.1002/2016JC012265.

**Link:
http://onlinelibrary.wiley.com/doi/10.1002/2016JC012265/full **