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Active swimmers interacting with stratified fluids during collective vertical migration. (English) Zbl 1460.76988

Summary: Coordinated laboratory experiments and computational simulations are conducted that explore the collective vertical migration of a swarm of inertial swimmers through a stably stratified density interface. Values of the governing parameters such as the swimmer- and swarm-scale Reynolds numbers, the Richardson number, as well as the animal number density in the swarm closely match each other in the simulations and experiments. In addition to intense mixing at the swimmer scale, the experiments and simulations demonstrate that the hydrodynamic interaction of the individual swimmers produces a spatially coherent source of thrust that results in the formation of a swarm-scale jet in the direction opposite to the migration. The jet velocity is seen to increase monotonically with the animal number density, at a sublinear rate. For steadily moving dilute swarms, the jet velocity is well predicted by a simple analytical model that assumes spatially uniform jet and swimmer velocities. Experimental measurements demonstrate effective diffusivity values up to three orders of magnitude larger than the molecular value. Numerical results are consistent with these observations, although they employ a larger molecular diffusivity and, hence, yield a lower ratio. The effective diffusivity is seen to increase linearly with the volume fraction of the swimmers. A continuum model is proposed for the generation of the swarm-scale jet, based on an idealization of the swarm as a self-propelled porous sphere. This model suggests that large swarms generate most of their mixing through the coherent swarm-scale jet, rather than by processes at the scale of individual swimmers.

MSC:

76Z10 Biopropulsion in water and in air
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[1] Ardekani, A. M., Doostmohammadi, A. & Desai, N.2017Transport of particles, drops, and small organisms in density stratified fluids. Phys. Rev. Fluids2 (10), 100503.
[2] Ardekani, M. N., Asmar, L. A., Picano, F. & Brandt, L.2018Numerical study of heat transfer in laminar and turbulent pipe flow with finite-size spherical particles. Intl J. Heat Fluid Flow71, 189-199.
[3] Biegert, E., Vowinckel, B. & Meiburg, E.2017A collision model for grain-resolving simulations of flows over dense, mobile, polydisperse granular sediment beds. J. Comput. Phys.340, 105-127. · Zbl 1376.76069
[4] Blake, J. R.1971A spherical envelope approach to ciliary propulsion. J. Fluid Mech.46 (1), 199. · Zbl 0224.76031
[5] Catton, K. B., Webster, D. R., Kawaguchi, S. & Yen, J.2011The hydrodynamic disturbances of two species of krill: implications for aggregation structure. J. Expl Biol.214 (11), 1845-1856.
[6] Chisholm, N. G., Legendre, D., Lauga, E. & Khair, A. S.2016A squirmer across Reynolds numbers. J. Fluid Mech.796 (2016), 233-256.
[7] Dabiri, J. O2010Role of vertical migration in biogenic ocean mixing. Geophys. Res. Lett.37, L11602.
[8] Dewar, W. K., Bingham, R. J., Iverson, R. L., Nowacek, D. P., St. Laurent, L.C. & Wiebe, P. H.2006Does the marine biosphere mix the ocean?J. Mar. Res.64 (4), 541-561.
[9] Doostmohammadi, A., Stocker, R. & Ardekani, A. M.2012Low-Reynolds-number swimming at pycnoclines. Proc. Natl Acad. Sci. USA109 (10), 3856-3861.
[10] Gonzalez, R. C. & Woods, R. E.2002Digital Image Processing. Prentice Hall.
[11] Gualtieri, C., Angeloudis, A., Bombardelli, F., Jha, S. & Stoesser, T.2017On the values for the turbulent Schmidt number in environmental flows. Fluids2 (2), 17.
[12] Hamner, W. M., Hamner, P. P., Strand, S. W. & Gilmer, R. W.1983Behavior of antarctic krill, euphausia superba: chemoreception, feeding, schooling, and molting. Science220 (4595), 433-435.
[13] Houghton, I. A. & Dabiri, J. O.2019Alleviation of hypoxia by biologically generated mixing in a stratified water column. Limnol Oceanogr.64, 2161-2171.
[14] Houghton, I. A., Koseff, J. R., Monismith, S. G. & Dabiri, J. O.2018Vertically migrating swimmers generate aggregation-scale eddies in a stratified column. Nature556 (7702), 497-500.
[15] Huntley, M. E. & Zhou, M.2004Influence of animals on turbulence in the sea. Mar. Ecol. Prog. Ser.273, 65-79.
[16] Ishikawa, T., Simmonds, M. P. & Pedley, T. J.2006Hydrodynamic interaction of two swimming model micro-organisms. J. Fluid Mech.568, 119. · Zbl 1177.76477
[17] Katija, K. & Dabiri, J. O.2009A viscosity-enhanced mechanism for biogenic ocean mixing. Nature460 (7255), 624-626.
[18] Khair, A. S. & Chisholm, N. G.2014Expansions at small Reynolds numbers for the locomotion of a spherical squirmer. Phys. Fluids26, 011902.
[19] Lauga, E. & Powers, T. R.2009The hydrodynamics of swimming microorganisms. Rep. Prog. Phys.72 (9), 096601.
[20] Li, G. & Ardekani, A. M.2014Hydrodynamic interaction of microswimmers near a wall. Phys. Rev. E90 (1), 013010.
[21] Li, G., Ostace, A. & Ardekani, A. M.2016Hydrodynamic interaction of swimming organisms in an inertial regime. Phys. Rev. E94 (5), 053104.
[22] Lighthill, M. J.1952On the squirming motion of nearly spherical deformable bodies through liquids at very small Reynolds numbers. Commun. Pure. Appl. Maths5 (2), 109-118. · Zbl 0046.41908
[23] Magar, V. & Pedley, T. J.2005Average nutrient uptake by a self-propelled unsteady squirmer. J. Fluid Mech.539, 93-112. · Zbl 1076.76079
[24] Mittal, R. & Iaccarino, G.2005Immersed boundary methods. Annu. Rev. Fluid Mech.37 (1), 239-261. · Zbl 1117.76049
[25] Mitchell, J. G., Okubo, A. & Fuhrman, J. A.1990Gyrotaxis as a new mechanism for generating spatial heterogeneity and migration in microplankton. Limnol. Oceanogr.35 (1), 123-130.
[26] O’Brien, D. P.1988Surface schooling behaviour of the coastal krill Nyctiphanes australis (Crustacea: Euphausiacea) off Tasmania, Australia. Mar. Ecol. Prog. Ser.42, 219-233.
[27] Pak, O. S. & Lauga, E.2014Theoretical models of low-Reynolds-number locomotion. In Fluid-Structure Interactions in Low-Reynolds-Number Flows, chap. 4, pp. 100-167. Royal Society of Chemistry.
[28] Pond, D. W.2012The physical properties of lipids and their role in controlling the distribution of zooplankton in the oceans. J. Plankton Res.34 (6), 443-453.
[29] Thielicke, W. & Stamhuis, E. J.2014PIVlab – towards user-friendly, affordable and accurate digital particle image velocimetry in MATLAB. J. Open Res. Softw.2 (1).
[30] Visser, A. W.2007OCEAN SCIENCE: biomixing of the Oceans?Science316 (5826), 838-839.
[31] Wang, S. & Ardekani, A. M.2012Inertial squirmer. Phys. Fluids24 (10), 101902.
[32] Wang, S. & Ardekani, A. M.2015Biogenic mixing induced by intermediate Reynolds number swimming in stratified fluids. Sci. Rep.5, 17448.
[33] Wilhelmus, M. M. & Dabiri, J. O.2014Observations of large-scale fluid transport by laser-guided plankton aggregations. Phys. Fluids26 (10), 101302.
[34] Winters, K. B., Lombard, P. N., Riley, J. J. & D’Asaro, E. A.1995Available potential energy and mixing in density-stratified fluids. J. Fluid Mech.289, 115.
[35] Yuan-Hui, L. & Gregory, S.1974Diffusion of ions in sea water and in deep-sea sediments. Geochim. Cosmochim. Acta38 (5), 703-714.
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