Oceans are responsible for about half of the oxygen production on Earth. Inside the oceans, the primary production of organic compounds from dissolved carbon dioxide is provided by phytoplankton, mostly unicellular organisms with sizes between few to hundreds of micrometers. Phytoplankton distribution is known to be heterogeneous due to hydrodynamic and chemical processes. The small-scale concentration of phytoplankton has many consequences on the oceanic ecosystem, including basic processes such as nutrient uptake, predator-prey dynamics and reproduction. In last decades, it has been shown that numerical simulations of turbulence can be successfully adapted to treat the effect of fluctuations on simple biophysical systems. Here we study the dynamics of small floating particles transported by stratified turbulence as a simple model for the confinement and the accumulation of plankton in the ocean. By means of direct numerical simulations we investigate the statistical distribution of floaters. We characterize the vertical confinement and the small-scale fractal clustering, depending on the dimensionless parameters of the system. Finally, the implications of our findings for the formation of thin phytoplankton layers are discussed.