Submesoscale processes, characterized by O(1km) horizontal scale and O(1) Rossby number, are ubiquitous in the world ocean and play an important role in the vertical flux of mass, buoyancy and tracers in the upper ocean. However, they have not been intensively studied due to the requirement of uniquely high spatial and temporal resolution in the observation and computer modeling. In this thesis, using a suite of high-resolution numerical experiments in the northwestern Gulf of Mexico, where rich submesoscale structures are accompanied by the strong mesoscale Loop Current eddies, the impact of resolving submesoscales on the tracer distribution and 3-D transport was extensively examined. It was concluded that, submesoscale dynamics aggregated the surface tracers and formed characteristic patterns at scales of kilometers near the ocean surface by enhanced convergence/divergence zones associated with strong ageostrophic processes. This distinctive phenomenon was evident in recent ocean color satellite images which showed similar extensive lines and spirals of floating Sargassum in the western Gulf of Mexico. In addition, better-resolved submesoscale activities increased the horizontal resolution dramatically and elevated local vertical velocity both within and below the mixed layer while leaving the horizontal component almost unaltered. The vertical dispersion increased by several fold with the largest difference close to the surface. Considering the pervasive presence of submesoscale structures at the surface ocean, these models predict that submesoscale processes may serve as an important nutrient supply mechanism in the upper ocean and potentially make a significant contribution on balancing the global biogeochemical tracer budget.

Ocean submesoscales are the subject of increasing focus in the oceanographic literature; with instrumentation now more capable of observing them in situ and numerical models now able to reach the resolution required to more fully capture them. Submesoscales are typified by horizontal spatial scales of O(1 − 10) km, vertical scales O(100) m and time-scales of O(1) day and are known to be associated with regions of high vertical velocity and vorticity. Occurring most commonly at density fronts at the ocean surface they can control mixed layer restratification and provide an important control on fluxes between the atmosphere and the deep ocean. This thesis sets out to better understand the fundamental physical processes underpinning submesoscale instabilities using a number of idealised process models. Linear stability analysis complemented by non-linear, high-resolution simulations will be used initially to explore the ways in which submesoscale instabilities in the mixed layer may compete and interact with one another. In particular, we will investigate the way in which symmetric and ageostrophic baroclinic instabilities interact when simultaneously present in a flow, with focus on the growth rates and energetic pathways of previously unexplored dynamic instabilities that arise in this paradigm; three-dimensional, mixed symmetric-baroclinic instabilities. Further, these non-linear simulations will allow us to investigate the transition to dissipative scales that can occur in the classical Eady model via a multitude of small-scale secondary instabilities that result from primary submesoscale instabilities. Finally, observational data, taken aboard the SMILES project cruise to the Southern Ocean, helps to motivate the consideration of a new dynamical paradigm; the Eady model with superimposed high amplitude barotropic jet. Non-linear simulations investigate the extent to which the addition of such a jet is capable of damping submesoscale growth. The causes of this damping are then investigated using linear analysis. With this approach eventually demonstrated as being unable to fully explain growth rate reductions, we introduce a new framework combining potential vorticity mixing by submesoscale instabilities with geostrophic adjustment, which relaxes the flow back to a geostrophic balanced state. This framework will help to explain, conceptually, how non-linear eddies control the linear stability of the flow.