Mathematical models used to represent plankton dynamics often display limit-cycle behavior in a range of realistic parameter values. However, experimental data do not show evidence of plankton oscillations besides externally driven seasonal blooms, casting doubts on the validity of the models themselves. In this work we show that spatial-temporal variability, coupled with advection by mesoscale turbulence, can disguise limit-cycle behavior to the point that it cannot be detected in fixed-point measurements of plankton abundance. The results presented here have more general implications as they indicate that the behavior of ecosystem models in the presence of advection can be very different from that occurring for homogeneous conditions. Care should thus be exercised in drawing general conclusions from the analysis of homogeneous ecosystem models.