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Stirring by multiple cylinders in potential flow

Published online by Cambridge University Press:  05 April 2016

Zhi Lin  and
Yuanzhao Zhang
Zhi Lin*
Affiliation:
School of Mathematical Sciences, Zhejiang University, Hangzhou, Zhejiang 310027, China
Yuanzhao Zhang
Affiliation:
Department of Engineering Sciences and Applied Mathematics, Northwestern University, Evanston, IL 60208-3125, USA
*
†Email address for correspondence: [email protected]
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Abstract

We consider the enhanced mixing due to multiple cylinders organised in schools moving synchronously in a potential flow. Here simple interactions between cylinders are modelled by the method of image doublets. This is an extension to Thiffeault & Childress’s work (Phys. Lett. A, vol. 374, 2010, pp. 3487–3490) where fluid particle displacements due to non-interacting swimmers were analysed to produce an effective diffusivity that may have a significant impact in ocean mixing. Our results show that schools of two cylinders induce nonlinearly boosted diffusivity compared with the non-interacting case for general configuration parameters, except when they move along a straight line with small separation. We attribute this phenomenon to two different physical mechanisms via which interacting cylinders cooperate to generate long particle drifts depending on their formation. Finally, the effective diffusivity of schools of three or more cylinders in various configurations are also discussed.

JFM classification

Biological Fluid Dynamics: Biological Fluid Dynamics Biological Fluid Dynamics: Micro-organism dynamics Mixing: Mixing
Type
Papers
Information
Journal of Fluid Mechanics , Volume 794 , 10 May 2016 , pp. 552 - 564
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Copyright
© 2016 Cambridge University Press 

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References

Acheson, D. J. 1990 Elementary Fluid Dynamics. Oxford University Press.Google Scholar
Blake, J. R. 1971 A spherical envelope approach to ciliary propulsion. J. Fluid Mech. 46, 199–208.CrossRefGoogle Scholar
Carpenter, L. H. 1958 On the motion of two cylinders in an ideal fluid. J. Res. Natl Bur. Stand. 61 (2), 83–87.Google Scholar
Crowdy, D. G. 2006 Analytical solutions for uniform potential flow past multiple cylinders. Eur. J. Mech. (B-Fluids) 25, 459–470.Google Scholar
Dalton, C. & Helfinstine, R. A. 1971 Potential flow past a group of circular cylinders. Trans. ASME J. Fluids Engng 93 (4), 636–642.Google Scholar
Darwin, C. G. 1953 Note on hydrodynamics. Proc. Camb. Phil. Soc. 49 (2), 342–354.CrossRefGoogle Scholar
Dewar, W. K., Bingham, R. J., Iverson, R. L., Nowacek, D. P., St Laurent, L. C. & Wiebe, P. H. 2006 Does the marine biosphere mix the ocean? J. Mar. Res. 64, 541–561.Google Scholar
Drescher, K., Leptos, K., Tuval, I., Ishikawa, T., Pedley, T. J. & Goldstein, R. E. 2009 Dancing volvox: hydrodynamic bound states of swimming algae. Phys. Rev. Lett. 102, 168101.CrossRefGoogle ScholarPubMed
Guasto, J. S., Johnson, K. A. & Gollub, J. P. 2010 Oscillatory flows induced by microorganisms swimming in two-dimensions. Phys. Rev. Lett. 105, 168102.Google Scholar
Huntley, H. E. & Zhou, M. 2004 Influence of animals on turbulence in the sea. Mar. Ecol. Prog. V 273, 65–79.Google Scholar
Ishikawa, T. & Pedley, T. J. 2007 Diffusion of swimming model micro-organisms in a semi-dilute suspension. J. Fluid Mech. 588, 437–462.Google Scholar
Johnson, E. R. & McDonald, N. R. 2004 The motion of a vortex near two circular cylinders. Proc. R. Soc. Lond. A 460, 939–954.Google Scholar
Katija, K. 2011 Biogenic inputs to ocean mixing. J. Expl. Biol. 215 (6), 1040–1049.Google Scholar
Katija, K. & Dabiri, J. O. 2009 A viscosity-enhanced mechanism for biogenic ocean mixing. Nature 460, 624–627.Google Scholar
Kunze, E., Dower, J. F., Beveridge, I., Dewey, R. & Bartlett, K. P. 2006 Observations of biologically generated turbulence in a coastal inlet. Science 313, 1768–1770.CrossRefGoogle Scholar
Leptos, K. C., Guasto, J. S., Gollub, J. P., Pesci, A. I. & Goldstein, R. E. 2009 Dynamics of enhanced tracer diffusion in suspensions of swimming eukaryotic microorganisms. Phys. Rev. Lett. 103, 198103.Google Scholar
Leshansky, A. M. & Pismen, L. M. 2010 Do small swimmers mix the ocean? Phys. Rev. E 82 (2), 025301.Google Scholar
Lighthill, M. J. 1952 On the squirming motion of nearly spherical deformable bodies through liquids at very small Reynolds numbers. Commun. Pure Appl. Maths 5, 109–118.CrossRefGoogle Scholar
Lin, Z., Thiffeault, J.-L. & Childress, S. 2011 Stirring by squirmers. J. Fluid Mech. 669, 167–177.CrossRefGoogle Scholar
Maxwell, J. C. 1869 On the displacement in a case of fluid motion. Proc. Lond. Math. Soc. s1–3 (1), 82–87.CrossRefGoogle Scholar
Munk, W. H. 1966 Abyssal recipes. Deep-Sea Res. 13, 707–730.Google Scholar
Pushkin, D. O. & Yeomans, J. M. 2013 Fluid mixing by curved trajectories of microswimmers. Phys. Rev. Lett. 111, 188101.CrossRefGoogle ScholarPubMed
Pushkin, D. O., Shum, H. & Yeomans, J. M. 2013 Fluid transport by individual microswimmers. J. Fluid Mech. 726, 5–25.Google Scholar
Thiffeault, J.-L. & Childress, S. 2010 Stirring by swimming bodies. Phys. Lett. A 374, 3487–3490.CrossRefGoogle Scholar
Underhill, P. T., Hernandez-Ortiz, J. P. & Graham, M. D. 2008 Diffusion and spatial correlations in suspensions of swimming particles. Phys. Rev. Lett. 100, 248101.Google Scholar
Visser, A. W. 2007 Biomixing of the oceans? Science 316, 838–839.Google Scholar
Wagner, G. L., Young, W. R. & Lauga, E. 2014 Mixing by microorganisms in stratified fluids. J. Mar. Res. 72, 47–72.Google Scholar