We examine the influence of mesoscale turbulence and random growth rate fields upon phytoplankton patchiness, on length scales from 1 km to 100 km and time scales from 1 day to 100 days. We consider phytoplankton concentrations with quite general nonlinear growth rate functions, such that the concentration is bounded for all time. We use, and justify the use of, particle separation statistics to deduce variance spectra of nonlinearly transformed concentration. Two growth rate models are examined: an advected field, and a locally specified field. Both lead to initial patchiness in the concentration, correlated with the growth rate field. The advected growth rate field leads to a temporal peak in the patchiness before the mesoscale turbulence causes the concentration variance to cascade to a "noisy" spatial distribution that retains no correlation with either the motion field, or the growth rate field. We outline numerical experiments to test these results, in particular the occurrence of the peak in patchiness and the time scales associated with its formation and decay.