The effect of turbulent motion on the diffusion of microorganisms

The effect of turbulent fluid motion on the diffusion of simple organisms is discussed. The net reproduction rate and the turbulent flow are assumed to be Gaussian-correlated random variables. For homogeneous istropic turbulence, simple equations for the average concentration of the organisms are derived in terms of the energy density of the fluid. It is shown that the effective diffusivity generated by the motion is positive-definite, and is independent of the helicity of the flow.