Predator–prey encounter and capture rates for plankton in turbulent environments

Turbulence plays an important role for predator–prey interactions in aquatic environments. In one sense turbulence benefits the predator by increasing its encounter rate with prey, but on the other hand it can benefit the prey by making them more difficult to catch. In the present study of this problem, a turbulent flow field is obtained by direct numerical solution of the Navier–Stokes equation. The analysis includes the effects of the turbulence on the encounter rate between passively moving predators and prey, and at the same time also models the capture probability depending on the relative turbulent motions of predator and prey. Analytical results for scaling laws for planktonic encounter and capture rates in turbulent environments are obtained in terms of the basic parameters for the problem, and the results are compared with related findings reported in the literature. For large values of the specific energy dissipation rates ϵ the turbulence reduces the capture probability significantly, in part also because the effective capture range reduces for increasing turbulence intensity. The results presented here predict the parameters for an optimum turbulence level for the predator capture rate. For enhanced turbulence levels sudden bursts in the space–time varying velocity field contribute to a noise level that can reduce the probability for capturing prey. We consider cases where the capture range of an organism is comparable to or smaller than the effective Kolmogorov length scale, as well as the opposite limit of larger capture ranges in the inertial range of the turbulence. The reference model assumes spherical interception volumes, but it is demonstrated that the results remain basically valid also for the case where these volumes are hemispherical or conical: the consequences of having a shape of the interception surface deviating from a sphere can be accounted for by an empirical scaling factor, which depends solely on the opening angle of the cone.