Numerical studies of turbulent particle fluxes into perfectly absorbing spherical surfaces

Abstract

With reference to studies of the influence of turbulence on the feeding process of aquatic micro-organisms, we analyze particle fluxes into absorbing surfaces in turbulent flows by numerical simulations. The simultaneous trajectories of many point particles are followed in time in a fully three-dimensional solution of the turbulent flow described by the Navier–Stokes equation. Selecting one of these points to represent a predator, while the others are considered as prey, we obtain estimates for the time variation of the statistical average of particle fluxes into a co-moving “sphere of interception”. The essential restriction in the model, when applied to aquatic micro-organisms, is that self-induced motions are ignored. Particles are assumed to be absorbed when crossing the surface. In this sense, the problem can be analyzed as the one involving a perfectly absorbing surface. The variation of the particle flux with the radius in the absorbing sphere, as well as the variation with basic flow parameters is well described by a simple scaling law, expressed in terms of the radius of the sphere and the energy dissipated per mass unit. The results also agree well with experimental results. In the present study, we obtain a unique signal-to-noise ratio in the estimates. The analysis is extended by inclusion of another dataset, with a somewhat smaller Reynolds number. The scaling laws obtained by a simple dimensional reasoning agree well for the two datasets. The numerical simulations refer to two different Reynolds numbers, but the scaling laws verified for these conditions can then be applied generally for other flows, provided the basic assumptions are fulfilled: the turbulence has to be fully developed so that a universal subrange exists, and the spatial scales defined by the radii of the absorbing spherical surfaces have to be restricted to this subrange.

Acknowledgements

Two of the authors (HLP and JT) were in part supported by the ECOBE project, Norwegian National Science Foundation under contract NFR-136030/431. The authors acknowledge the hospitality of the Norwegian Centre for Advanced Studies, under the project “Turbulence in Fluids and Plasmas”. We thank Jakob Mann and Søren Ott for valuable discussions.