We use a conceptual mathematical reaction-diffusion model to investigate the mechanisms of spatial structure formation and complex temporal dynamics of plankton in a heterogeneous environment. We take into account basic trophic interactions, namely, "prey-predator" interactions between phytoplankton, zooplankton, and fish in upper layers of natural waters. We consider plankton as a passive contaminant in turbulent waters. We show that plankton structure formation can result from the difference in phytoplankton growth rate in neighboring habitats. Phytoplankton and zooplankton biomass is shown to undergo both regular and chaotic oscillations. The fish predation rate substantially affects the spatial and temporal dynamics of plankton in a heterogeneous environment.