Diatoms are among the most efficient marine organisms for primary production and carbon sequestration, absorbing at least 10 billion tonnes of carbon dioxide every year. Yet, the spatial distributions of these planktonic organisms remain puzzling and the underlying physical processes poorly known. Here we investigate what dynamical conditions are conductive to episodic diatom blooms in oligotrophic waters based on Lagrangian diagnosis and satellite-derived phytoplankton functional types and ocean currents. The Lagrangian coherence of the flow is diagnosed in space and time simultaneously to identify which structures favor diatom growth. Observations evidence that flow structures with a high degree of coherence (40 days or longer) in high turbulent kinetic energy and vorticity sustain high concentrations of diatoms in the sunlite layers. Our findings show that the integration of Eulerian kinematic variables into a Lagrangian frame allows revealing new dynamical aspects of geophysical turbulence and unveil transport properties having large biological impacts.