Applied Mathematics seminar | Gualtiero Badin, On the representation of submesoscale dynamics

Observational and numerical works show that the ocean displays a significant presence of dynamics at scales smaller than the mesoscale, i.e. passing from horizontal scales of O (100 km) to scales of O (1-10 km). Understanding the properties of these dynamics and their role in the turbulent transfer and mixing of properties such as heat, nutrients and pollutants is important for the correct parameterization of mixing in climate models. In this study we show how submesoscale dynamics can be represented in two different models. The first model is a three-layer quasi geostrophic model. Linear stability analysis shows that the interplay of the relative shear between the upper and lower layers creates shortwave instabilities. Results show that the probability density functions (PDFs) of the vorticity show large deviation from Gaussian distributions, which are reflected in anomalous fluxes of potential vorticity. The second model is a surface semi-geostrophic model, that result in the solution of a nonlinear Monge-Ampere equation. Results show this model is able to reproduce skewed PDFs with non-zero mean, associated to a cyclone-anticyclone asymmetry as observed in the real ocean and due to the presence of ageostrophic dynamics.