The emergence of spatial and spatio-temporal patterns in a minimal non
linear interaction-diffusion-advection model of phytoplankton-zooplank
ton dynamics is considered. Conditions for the formation of spatial pa
tterns after the diffusive instability of a uniform species distributi
on are derived and numerical results of diffusive as well as shear-dif
fusive patterning are presented on a two-dimensional spatial cross-sec
tion. The variability of phytoplankton growth due to its light sensiti
vity is considered in a linear approximation.