  We investigate the effects of turbulent fluctuations on the Lagrangian
statistics of absorption of a scalar field by tracer particles, as a model for
nutrient uptake by suspended non-motile microorganisms. By means of extensive
direct numerical simulations of an Eulerian-Lagrangian model we quantify, in
terms of the Sherwood number, the increase of the scalar uptake induced by
turbulence and its dependence on the Peclet and Reynolds numbers. Numerical
results are compared with classical predictions for a stationary shear flow
extended here to take into account the presence of a restoring scalar flux. We
find that mean field predictions agree with numerical simulations at low Peclet
numbers but are unable to describe the large fluctuations of local scalar
uptake observed for large Peclet numbers. We also study the role of velocity
fluctuations in the local uptake by looking at the temporal correlation between
local shear and uptake rate and we find that the latter follows fluid velocity
fluctuations with a delay given by Kolmogorov time scale. The relevance of our
results for aquatic microorganisms is also discussed.
