By supplying nutrients to the ocean surface, submesoscale vertical motions can have a strong impact on phytoplankton growth and phytoplankton distributions. To study this impact, we model a phytoplankton population in a baroclinically unstable submesoscale eddy using a phytoplankton model coupled to a three-dimensional hydrodynamic model. In the eddy, strong vertical transports are generated as a consequence of baroclinic instability. The resulting plankton distributions turn out to depend strongly on the light intensity and local vertical transport. To analyze these distributions in detail, we use more idealized coupled hydrodynamic-biological models and we extend the critical turbulence concept to three dimensions.