A one dimensional Lagrangian model of random walk is presented to study the distribution of phytoplankton in the Antarctic Ocean. Since little is known about mixed layer dynamics in the Antarctic Ocean, we estimate the depth of the mixed layer and its turbulence intensity from an Ekman layer model. Available CTD data suggest that the mixing in the upper layer is less than what we expected. However, the effect on the dynamics is vital, affecting the distribution of particles in the upper ocean.