Simulation of light-limited algae growth in homogeneous turbulence

A study is performed of the effect of turbulent mixing on algae growth rate under light-limiting conditions. In order to isolate the effect of light fluctuations and to eliminate possible effects of mass transfer and other side effects of mixing, a numerical model of algae growth is employed. The study examines three aspects of turbulent mixing using models of increasing complexity. First, mixing increases the depth of the “mixed layer”—the layer of approximately uniform algae concentration—spreading the algae produced near the surface over a thicker fluid region. We demonstrate that mixed layer depth has no effect on the net algae production rate. Second, mixing causes motion of algae cells across the optical gradient. A single-frequency harmonic model is used to demonstrate the influence of periodic motion on algae production rate for different frequencies and concentration values. The model results explain previous apparently contradictory experimental observations. Significant enhancement of algae production rate with mixing is observed for small values of the ratio of illuminated layer depth to total fluid depth; however, growth rate enhancement saturates beyond a certain mixing frequency. Third, turbulent mixing involves a broad range of fluid time and length scales. A direct numerical simulation of homogeneous turbulence coupled to the algae growth model is used to show that the main conclusions of the single-frequency model can be carried over to a more realistic turbulent flow by appropriate choice of the mixing time scale.