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Persian Gulf Water and Red Sea Water are salty and dense waters flowing at intermediate depths in the Gulf of Oman and the Gulf of Aden, respectively. Their spreading pathways are influence by mesoscale eddies that dominate the surface flow in both semi-enclosed basins. In situ measurements combined with altimetry indicate that Persian Gulf Water is stirred in the form of filaments and submesoscale structures by mesoscale eddies. In this paper, we study the formation and the life cycle of intense submesoscale vortices and their potential impact on the spreading of Persian Gulf Water and Red Sea Water. We use a primitive-equation three-dimensional hydrostatic model at a submesoscale-resolving resolution to study the evolution of submesoscale vortices. Our configuration idealistically mimics the dynamics in the Gulf of Oman and the Gulf of Aden: a zonal row of mesoscale vortices interacting with north and south topographic slopes. Intense submesoscale vortices are generated in the simulations along the continental slopes due to two different mechanisms. First, intense vorticity filaments are generated over the continental slope due to frictional interactions of the background flow with the sloping topography. These filaments are shed into the ocean interior and undergo horizontal shear instability that leads to the formation of submesoscale coherent vortices. The second mechanism is inviscid and features baroclinic instabilities arising at depth due to the weak stratification. Submesoscale vortices subsequently drift away, merge and form larger vortices. They can also pair with opposite-signed vortices and travel across the domain. They eventually dissipate their energy via several mechanisms, in particular fusion into the larger eddies or erosion on the topography. Since no submesoscale flow clearly associated with the fragments of Persian Gulf Water was observed in situ, we modeled Persian Gulf Water as Lagrangian particles. Particle patches are advected and sheared by vortices and are entrained into filaments. Their size first grows as the square root of time: a signature of the merging processes. Then, it increases linearly with time, corresponding to their ballistic advection by submesoscale eddies. On the contrary, without intense submesoscale eddies, particles are mainly advected by mesoscale eddies; this implies a weaker dispersion of particles than in the previous case. This shows the potentially important role of submesoscale eddies in spreading Persian Gulf Water and Red Sea Water.

This work focuses on buoyant tracers floating on the ocean surface and treats the geostrophic and ageostriphic surface velocities as the 2D solenoidal (non-divergent) and potential (divergent) flow components, respectively. We consider a random kinematic flow model and study the process of clustering, that is, aggregation of tracers in localized spatial patches. An asymptotic theory exists only for strongly divergent velocity fields and predicts complete clustering, that is, emergence in the large-time limit of spatial singularities containing all available tracers. To extend the theory, we consider combinations of the solenoidal and potential velocity components and explore the corresponding regimes of the clustering process. We have found that, even for weakly divergent flows complete clustering still persists but occurs at a significantly slower rate. For a wide range of parameters, we have analyzed this process, as well as the other type of clustering, referred to as fragmentation clustering, and the coarse-graining effects on clustering, and interpreted the results.For the analyses we have considered ensembles of Lagrangian particles representing the tracer, then, introduced and applied the methodology of statistical topography, which paves the way for systematic studies of clustering in progressively more complicated flows, and for both passive and floating tracers.

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