Turbulent particle fluxes to perfectly absorbing surfaces: a numerical study

Abstract

The motion of small absorbing surfaces is modeled by numerical simulations of turbulent flows with realistic Reynolds numbers. We obtain empirical models for the encounter rate of particles, and in particular the turbulent particle fluxes to given surfaces following the flow. Particular attention is given to the limit, where the particle separations are in the viscous limit, where the scale size of the absorbing surfaces are comparable to or smaller the Kolmogorov length scale. Spherical surfaces represent a special limiting case, but more general shapes are considered as well. The relevance of the problem to the feeding rate of small planktonic organisms in turbulent environments is pointed out in particular, but the results have wider applications. Based on analytical results, we obtain first an empirical expression for the particle flux to a reference spherical surface of interception. This result covers ranges in the universal as well as the viscous subrange. The analysis is then generalized to conical surfaces of interception. We demonstrate the applicability of the results for a wide range of radii, and opening angles of the cones, as well as for two values of turbulence Reynolds numbers. We present also analytical models that account for finite size of particles being transported by a turbulent flow. These latter effects are important for cases where the particles are comparable to the Kolmogorov length in size.

Keywords:

• Turbulent mixing
• Relative diffusion
• Zooplankton

Acknowledgements

We thank Guido Boffetta for helping us to access the database from the numerical simulations, and for his interest and comments. The data can be freely downloaded from the web address http://cfd.cineca.it/. Conditions for usage are given at http://cfd.cineca.it/cfd/repository/folder.2006-01-20.4761556357/document.2006-01-20.5299514280/ The supercomputing center Cineca (Bologna, Italy) is acknowledged for hosting the data. Valuable discussions with Svein Sundby, Jan Erik Stiansen, Øyvind Fiksen, Jakob Mann and SØren Ott are gratefully acknowledged. The authors were in part supported by the “Effects of North Atlantic Climate Variability on the Barents Sea Ecosystem” (ECOBE) project. The present study was initiated while the authors were affiliated with the Norwegian Center for Advanced Studies. We are grateful to the staff at this institute for creating unique conditions for our work.