  Communities of swimming microorganisms often thrive near liquid-air
interfaces. We study how such `active carpets' shape their aquatic environment
by driving biogenic transport in the water column beneath them. The
hydrodynamic stirring that active carpets generate leads to diffusive upward
fluxes of nutrients from deeper water layers, and downward fluxes of oxygen and
carbon. Combining analytical theory and simulations, we examine the biogenic
transport by studying fundamental metrics, including the single and pair
diffusivity, the first passage time for particle pair encounters, and the rate
of particle aggregation. Our findings reveal that the hydrodynamic fluctuations
driven by active carpets have a region of influence that reaches orders of
magnitude further in distance than the size of the organisms. These
nonequilibrium fluctuations lead to a strongly enhanced diffusion of particles,
which is anisotropic and space-dependent. Fluctuations also facilitate
encounters of particle pairs, which we quantify by analysing their velocity
pair correlation functions as a function of distance between the particles. We
found that the size of the particles plays a crucial role in their encounter
rates, with larger particles situated near the active carpet being more
favourable for aggregation. Overall, this research broadens our comprehension
of aquatic systems out of equilibrium and how biologically driven fluctuations
contribute to the transport of fundamental elements in biogeochemical cycles.
