Floating contaminants in the marine environment, such as buoyant microplastic particles, are of increasing concern. This is due to the rapid rate at which they are being introduced to the ocean, and observations that they can accumulate on the oceanic gyres, where they form dense clusters. There is reason to believe that microplastic particles could have severe effects on previously isolated ocean ecosystems. Prior modelling of the flow of floating material has been limited by the available data of convergent surface ocean currents. In this thesis, we will construct idealised models of floating tracers from first principles. We will then use these models to explore the dynamics of cluster formation in kinematic and quasigeostrophic ocean velocity fields, with applications to the flow of microplastics, inertial Lagrangian drifters, and organic material. These idealised models will further serve as a test-bed for clustering metrics that can be used to make quantitative comparisons between clustering models. The insights derived from these metrics will motivate best practices which can improve the methodology of clustering models in more realistic scenarios.