The ocean mixed layer (OML) is a significant and dynamically active part of the ocean which plays an important role in climate variability. Here, atmospheric processes such as winds, heat fluxes or density differences drive the generation of small-scale, three-dimensional turbulence and mixing of oceanic waters. These turbulent flows govern the distribution of buoyant materials including oil droplets and microplastics, which have significant implications for marine life and safety. However, turbulent flow structures are often too small to be resolved by global or regional circulation models, and observations at these scales remain limited. The focus of this thesis is to use numerical simulations to improve our understanding of the small-scale, three-dimensional turbulent processes in the OML and examine their role on transporting and accumulating buoyant material.

We use high resolution large eddy simulations (LES) and direct numerical simulations (DNS), and model non-inertial, buoyant particles using a combination of buoyant tracers and three-dimensional Lagrangian particles. Surface cooling drives convection, and under this regime persistent convective vortices form which trap and accumulate buoyant particles. We test the resilience of convective vortices under the additional presence of wind, and find that in weak winds, convective vortices survive but are less effective at trapping buoyant material. With sufficiently strong wind forcing, convective vortices are no longer visible, but some clustering occurs in downwelling regions associated with longitudinal wind rolls.

Despite their small size, the convective vortices exhibit a bias towards cyclonic vorticity which has not been reported previously. We independently vary the Coriolis acceleration and surface buoyancy flux, and using Lagrangian particles, we find that the large convective vortices develop through the merger of many small unbiased convective vortices. We propose a statistical theory to predict the cyclonic bias of large convective vortices and test the theory using LES results. We apply the theory to typical convective conditions and find that convective vortices in OML are expected to exhibit a bias, but convective vortices in the terrestrial and Martian atmospheres are expected to be largely unbiased.

Finally, motivated by accumulation of buoyant material observed at surface fronts in the SUNRISE field campaign in the Gulf of Mexico, we run simulations of a highly idealised front under geostrophic adjustment. By varying the balanced Rossby number, we show that strong fronts develop a three-dimensional instability which generates turbulence near the top and bottom boundaries. We describe the physical mechanisms at play and the energy pathways as the front evolves over time. In the case of the most turbulent dynamics, we additionally model the movement of buoyant particles. Shear instabilities drive turbulence which enhances mixing, and strongly buoyant particles are carried out of the front during the first inertial period, which segregates the particles and leaves a large void in the centre of the front. In contrast, weakly buoyant particles are quickly subducted into the interior, and subsequently move according to the inertial oscillations of the front.