Abstract
The motion of point-particles is studied by numerical simulations. We analyze the turbulent particle fluxes to perfectly absorbing spheres, which are moving with the flow. Particular attention is given to the effect of viscosity for the case where the radius of the sphere is comparable to or smaller than the Kolmogorov length scale. By relatively simple model arguments, we arrive at analytical expressions which give a very good agreement with the observed scalings.
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References
Batchelor, G. K. 1952, Diffusion in a field of homogeneous turbulence II. The relative motion of particles. Proc. Cambridge Philos. Soc. (London), 48, 345–362.
Roberts, P. H. 1961, Analytical theory of turbulent diffusion. J. Fluid Mech., 11, 257–283.
Sundby, S. and Fossum, P. 1990, Feeding conditions of arcto-norwegian cod larvae compared with the Rothschild-Osborn theory on small-scale turbulence and plankton contact rates. J. Plankton Res., 12, 1153–1162.
Kiørboe, T. and Saiz, E. 1995, Planktivorous feeding in calm and turbulent environments, with emphasis on copepods. Mar. Ecol. Prog. Ser., 122, 135–145.
Muelbert, J. H., Lewis, M. R. and Kelley, D. E. 1994, The importance of small-scale turbulence in the feeding of herring larvae. J. Plankton Res., 16, 927–944.
Rothschild, B. J. and Osborn, T. R. 1988, Small-scale turbulence and plankton contact rates. J. Plankton Res., 10, 465–474.
Osborn, T. 1996, The role of turbulent diffusion for copepods with feeding currents. J. Plankton Res., 18, 185–195.
Mann, J., Ott, S., Pécseli, H. L., and Trulsen, J. 2005, Turbulent particle flux to a perfectly absorbing surface. J. Fluid Mech., 534, 1–21.
Mann, J., Ott, S., Pécseli, H. L. and Trulsen, J. 2006, Laboratory studies of predator-prey encounters in turbulent environments: effects of changes in orientation and field of view. J. Plankton Res., 28, 509–522.
Blaxter, J. H. S. and Staines, M. E. 1971, Food searching potential in marine fish larvae. In D. J. Crisp, editor, Proceedings of the 4th European Marine Biology Symposium, pages 467–485. Cambridge University Press.
Lewis, D. M. and Pedley, T. J. 2000, Planktonic contact rates in homogeneous isotropic turbulence: theoretical predictions and kinematic simulations. J. Theor. Biol., 205, 377–408.
Hinze, J. O. 1975, Turbulence. McGraw-Hill, New York, 2 edition.
Mann, J. and Ott, S. 2006, Private communications: Recent laboratory experiments at the Risø National Laboratory has also demonstrated an r 2-variation for the viscous subrange of the velocity structure function.
Biferale, L., Boffetta, G., Celani, A., Lanotte, A., and Toschi, F. 2005, Particle trapping in three-dimensional fully developed turbulence. Phys. Fluids, 17, 021701.
Boffetta, G., Pécseli, H. L., and Trulsen, J. 2006, Numerical studies of turbulent particle fluxes into perfectly absorbing spherical surfaces. J. Turbulence, 7(22), 1–16 doi:10.1080/14685240600573138.
Lohse, D. and Müller-Groeling, A. 1996, Anisotropy and scaling corrections in turbulence. Phys. Rev. E, 54, 395–405.
Dobler, W., Haugen, N. E. L., Yousef, T. A., and Brandenburg, A. 2003, Bottleneck effect in three-dimensional turbulence simulations. Phys. Rev. E, 68, 026304.
Woodward, P. R., Porter, D. H., Edgar, B. K., Anderson, S., and Bassett, G. 1995, Parallel computation of turbulent fluid-flow. Comp. Appl. Math., 14, 97–105.
Chandrasekhar, S. 1957, The theory of turbulence. J. Madras Univ. B, 27, 251–275.
Buckingham, E. 1914, On physically similar systems; illustrations of the use of dimensional equations. Phys. Rev., 4, 345–376.
Davidson, P. A. Turbulence. An introduction for scientists and engineers. Cambridge University Press, UK, 2004.
Richardson, L. F. 1926, Atmospheric diffusion shown as a distance-neighbour graph. Proc. Roy. Soc. London, Ser. A, 6, 709–737.
Pigolotti, S., Jensen, M. H., and Vulpiani, A. 2006, Absorbing processes in Richardson diffusion: Analytical results. Phys. Fluids, 18, 048104.
Mann, K. H. and Lazier, J. R. N. 1996. Dynamics of Marine Ecosystems. Blackwell Science, UK, 2. edition.
Delichatsios, M. A. and Probstein, R. F. 1975, Coagulation in turbulent flow-theory and experiment. J. Colloid Interface Sci., 51, 394–405.
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PĂ©cseli, H.L., Trulsen, J. (2007). Numerical studies of viscous effects for particle fluxes to perfectly absorbing spherical surfaces in turbulent environments: biological applications. In: Geurts, B.J., Clercx, H., Uijttewaal, W. (eds) Particle-Laden Flow. ERCOFTAC Series, vol 11. Springer, Dordrecht. https://doi.org/10.1007/978-1-4020-6218-6_19
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DOI: https://doi.org/10.1007/978-1-4020-6218-6_19
Publisher Name: Springer, Dordrecht
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