Stirring by swimming bodies |
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Authors: | Jean-Luc Thiffeault Stephen Childress |
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Institution: | a Department of Mathematics, University of Wisconsin - Madison, 480 Lincoln Dr., Madison, WI 53706, USA b Institute for Mathematics and Applications, University of Minnesota - Twin Cities, 207 Church Street S.E., Minneapolis, MN 55455, USA c Courant Institute of Mathematical Sciences, New York University, 251 Mercer Street, New York, NY 10012, USA |
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Abstract: | We consider the stirring of an inviscid fluid caused by the locomotion of bodies through it. The swimmers are approximated by non-interacting cylinders or spheres moving steadily along straight lines. We find the displacement of fluid particles caused by the nearby passage of a swimmer as a function of an impact parameter. We use this to compute the effective diffusion coefficient from the random walk of a fluid particle under the influence of a distribution of swimming bodies. We compare with the results of simulations. For typical sizes, densities and swimming velocities of schools of krill, the effective diffusivity in this model is five times the thermal diffusivity. However, we estimate that viscosity increases this value by two orders of magnitude. |
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Keywords: | Biomixing Chaotic mixing Enhanced diffusion |
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