Lagrangian tracer spreading in surface ocean turbulence with ageostrophic dynamics

Ocean submesoscales are characterized by horizontal scales smaller than approximately 10 km that evolve with timescales of O(1) day. Due to their small size and rapid temporal evolution, they are notoriously difficult to measure. In particular, the associated velocity field is not resolved in current satellite altimetry products. At these scales, surface ocean flows are populated by small eddies, and filaments linked with strong gradients of physical properties, such as temperature. Several recent studies indicate that submesoscale fronts are associated with important vertical velocities, thus playing a significant role in vertical transport. On that account, these fine-scale flows are key to the dynamical coupling between the interior and the surface of the ocean, as well as to plankton dynamics and marine ecology. In spite of their importance, the understanding of submesoscale ocean dynamics is still incomplete. In particular, a relevant open question concerns the role played by the ageostrophic components of the surface velocity field that manifest at these scales.By means of numerical simulations, we investigate ocean submesoscale turbulence in the SQG+1 model, which accounts for ageostrophic motions generated at fronts, and which is obtained as a small-Rossby-number approximation of the primitive equations. In the limit of vanishing Rossby number, this system gives surface quasi-geostrophic (SQG) dynamics. In this study, we explore the effect of the ageostrophic flow components on the spreading process of Lagrangian tracer particles on the horizontal. We particularly focus on the characterization of pair-dispersion regimes and particle clustering, as a function of the Rossby number, using different indicators. The observed Lagrangian behaviours are further related to the structure of the underlying turbulent flow. We find that relative dispersion is essentially unaffected by the ageostrophic flow components. However, these components are found to be responsible for (temporary) particle aggregation in cyclonic frontal regions. These results appear interesting for the modelling of submesoscale dynamics and for comparison purposes with the new high-resolution surface current data that will be soon provided by the satellite SWOT.