Planktonic Contact Rates in Homogeneous Isotropic Turbulence: Theoretical Predictions and Kinematic Simulations

The key role played by turbulence in the environment of plankton and larval fish populations has become appreciated in recent years. In particular, the turbulent enhancement of encounter rates between different species of microorganisms, either swimming or passively advected by the flow, is well established. However, most of the current modelling approaches are rather ad hoc, giving rise to ambiguities in the specification of certain key parameters. In this paper, the encounter problem in a turbulent flow of large Reynolds number is re-examined from first principles and a number of new formulae will be established for different swimming strategies. The key innovation is the proposal of a model form for the conditional joint probability density function of predator and prey velocities when the organisms are separated by their given contact radius, R. Particular attention will be paid to the case when a microorganism follows a random trajectory, due to a combination of its own swimming and the action of the flow. The theoretical predictions are subsequently tested against corresponding quantities derived from a series of kinematic simulations of a turbulent-like flow field. Good agreement is demonstrated between the predictions and simulations.