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Scale-dependent colocalization in a population of gyrotactic swimmers
Phys. Rev. E 95, 023108 – Published 17 February, 2017
DOI: https://doi.org/10.1103/PhysRevE.95.023108
Abstract
We study the small scale clustering of gyrotactic swimmers transported by a turbulent flow, when the intrinsic variability of the swimming parameters within the population is considered. By means of extensive numerical simulations, we find that the variety of the population introduces a characteristic scale in its spatial distribution. At scales smaller than the swimmers are homogeneously distributed, while at larger scales an inhomogeneous distribution is observed with a fractal dimension close to what observed for a monodisperse population characterized by mean parameters. The scale depends on the dispersion of the population and it is found to scale linearly with the standard deviation both for a bimodal and for a Gaussian distribution. Our numerical results, which extend recent findings for a monodisperse population, indicate that in principle it is possible to observe small scale, fractal clustering in a laboratory experiment with gyrotactic cells.
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References (31)
- R. G. Williams and M. J. Follows, Ocean Dynamics and the Carbon Cycle: Principles and Mechanisms (Cambridge University Press, Cambridge, 2011).
- J. Mitchell, H. Yamazaki, L. Seuront, F. Wolk, and H. Li, J. Mar. Syst. 69, 247 (2008).
- T. Kiørboe, A Mechanistic Approach to Plankton Ecology (Princeton University Press, Princeton, 2008).
- A. W. Visser and T. Kiørboe, Oecologia 148, 538 (2006).
- D. L. Mackas, K. L. Denman, and M. R. Abbott, Bull. Mar. Science 37, 652 (1985).
- A. Martin, Progr. Ocean. 57, 125 (2003).
- L. T. Mouritsen and K. Richardson, J. Plank. Res. 25, 783 (2003).
- E. Malkiel, O. Alquaddoomi, and J. Katz, Meas. Sci. Technol. 10, 1142 (1999).
- T. J. Pedley and J. O. Kessler, Proc. R. Soc. London B 231, 47 (1987); Annu. Rev. Fluid Mech. 24, 313 (1992).
- W. M. Durham, J. O. Kessler, and R. Stocker, Science 323, 1067 (2009).
- J. O. Kessler, Nature (London) 313, 218 (1985).
- G. J. Thorn and R. N. Bearon, Phys. Fluids 22, 041902 (2010).
- S. O'Malley and M. A. Bees, Bull. Math. Biol. 74, 232 (2012).
- D. M. Lewis, Proc. R. Soc. London A 459, 1293 (2003).
- W. M. Durham and R. Stocker, Annu. Rev. Mar. Sci. 4, 177 (2012).
- F. Santamaria, F. De Lillo, M. Cencini, and G. Boffetta, Phys. Fluids 26, 111901 (2014).
- W. M. Durham, E. Climent, M. Barry, F. De Lillo, G. Boffetta, M. Cencini, and R. Stocker, Nature Comm. 4, 2148 (2013).
- F. De Lillo, M. Cencini, W. M. Durham, M. Barry, R. Stocker, E. Climent, and G. Boffetta, Phys. Rev. Lett. 112, 044502 (2014).
- C. Zhan, G. Sardina, E. Lushi, and L. Brandt, J. Fluid Mech. 739, 22 (2013).
- K. Gustavsson, F. Berglund, P. R. Jonsson, and B. Mehlig, Phys. Rev. Lett. 116, 108104 (2016).
- K. Gustavsson and B. Mehlig, Advan. Phys. 65, 1 (2016).
- T. Pedley and J. Kessler, Annu. Rev. Fluid Mech. 24, 313 (1992).
- U. Frisch, Turbulence: The Legacy of AN Kolmogorov (Cambridge University Press, Cambridge, 1995).
- G. Paladin and A. Vulpiani, Phys. Rep. 156, 147 (1987).
- J. Bec, J. Fluid Mech. 528, 255 (2005).
- J. Bec, A. Celani, M. Cencini, and S. Musacchio, Phys. Fluids 17, 073301 (2005).
- L. Biferale, G. Boffetta, A. Celani, B. J. Devenish, A. Lanotte, and F. Toschi, Phys. Rev. Lett. 93, 064502 (2004).
- T. Pedley and J. Kessler, J. Fluid Mech. 212, 155 (1990).
- D. W. Sims, E. J. Southall, N. E. Humphries, G. C. Hays, C. J. Bradshaw, J. W. Pitchford, A. James, M. Z. Ahmed, A. S. Brierley, and M. A. Hindell, Nature (London) 451, 1098 (2008).
- R. Benzi, M. H. Jensen, D. R. Nelson, P. Perlekar, S. Pigolotti, and F. Toschi, Eur. Phys. J. Special Topics 204, 57 (2012).
- S. Pigolotti, R. Benzi, M. H. Jensen, and D. R. Nelson, Phys. Rev. Lett. 108, 128102 (2012).