Oceanic plankton plays an important role in the marine food chain and through its significant contribution to the global carbon cycle can also influence the climate. Plankton bloom is a sudden rapid increase of the population. It occurs naturally in the North Atlantic as a result of seasonal changes. Ocean fertilization experiments have shown that supply of iron, an important trace element, can trigger a phytoplankton bloom in oceanic regions with low natural phytoplankton density. Here we use a simple mathematical model of the combined effects of stirring by ocean eddies and plankton evolution to consider the impact of a transient local perturbation, e.g. in the form of iron enrichment as in recent 'ocean fertilization' experiments. The model not only explains aspects of the bloom observed in such experiments but predicts the unexpected outcome of a large scale bloom that in its extent could be comparable to the spring bloom in the North Atlantic.