We use a Lagrangian particles dispersal method to track where free floating material (fish larvae, algae, phytoplankton, zooplankton...) present in the sea water near the damaged Fukushima Daiichi nuclear power station plant could have gone since the earthquake on March 11th. THIS IS NOT A REPRESENTATION OF THE RADIOACTIVE PLUME CONCENTRATION. Since we do not know exactly how much contaminated water and at what concentration was released into the ocean, it is impossible to estimate the extent and dilution of the plume. However, field monitoring by TEPCO showed concentration of radioactive Iodine and Cesium higher than the legal limit during the next two months following the event (with a peak at more than 100 Bq/cm3 early April 2011 for I-131 as shown by the following picture).