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Analytical models for predator-prey contact and capture rates in turbulent environments

Scaling laws for planktonic contact and capture rates in turbulent environments are obtained in terms of basic parameters for the problem. Enhanced turbulence levels increase the encounter rate but can, on the other hand, also be too large by reducing the capture probability. The results thus indicate an optimum intermediate turbulence level for the predator capture rate. Probability densities of some basic parameters entering the scaling laws were found by numerical simulations. We consider cases where the capture range of an organism is comparable to or smaller than the Kolmogorov length scale, as well as the opposite limit of large capture ranges. The reference model assumes spherical contact surfaces, but it is demonstrated that the results remain basically valid also for the case where the contact volumes are hemispherical or conical: the consequences of the conical shape can be accounted for by an empirical scaling factor, which depends solely on the opening angle of the cone.