This paper is devoted to the study of a predator-prey model in a patchy environment.The model represents the interactions between phytoplankton and zooplankton in the water column.Two patches are considered with respect to light availability: one patch is associated to thesurface layer, the second patch describes the bottom layer. We show that this spatial heterogeneitymay destabilize the predator-prey system, even in oligotrophic system where the nutrient is lowenough to avoid ”paradox-enrichment” phenomenon. Indeed, in this case, an heterogeneity indexcan be used as a bifurcation parameter, leading to a Hopf bifurcation. Moreover, we assume that individualscan be dispersed in both patches via hydrodynamism processes, like in a mixed layer. Theeffect of mixing intensity is analysed as well as interactions between dispersion and enrichment.We also show that, in some cases, spatial heterogeneity has a stabilizing effect. These contrastedresults are examined by considering the non linear interaction between heterogeneity, dispersal andenrichment and some mechanisms leading to stabilization/destabilization are exhibited.