Skip to main content Accessibility help

The instability of gyrotactically trapped cell layers

  • Smitha Maretvadakethope (a1), Eric E. Keaveny (a1) and Yongyun Hwang (a2)


Several metres below the coastal ocean surface there are areas of high ecological activity that contain thin layers of concentrated motile phytoplankton. Gyrotactic trapping has been proposed as a potential mechanism for layer formation of bottom-heavy swimming algae cells, especially in flows where the vorticity varies linearly with depth (Durham et al., Science, vol. 323(5917), 2009, pp. 1067–1070). Using a continuum model for dilute microswimmer suspensions, we report that an instability of a gyrotactically trapped cell layer can arise in a pressure-driven plane channel flow. The linear stability analysis reveals that the equilibrium cell-layer solution is hydrodynamically unstable due to negative microswimmer buoyancy (i.e. a gravitational instability) over a range of biologically relevant parameter values. The critical cell concentration for this instability is found to be $N_{c}\simeq 10^{4}~\text{cells}~\text{cm}^{-3}$ , a value comparable to the typical maximum cell concentration observed in thin layers. This result indicates that the instability may be a potential mechanism for limiting the layer’s maximum cell concentration, especially in regions where turbulence is weak, and motivates the study of its nonlinear evolution, perhaps, in the presence of turbulence.


Corresponding author

Email address for correspondence:


Hide All
Bees, M. & Hill, N. 1997 Wavelengths of bioconvection patterns. J. Expl Biol. 200 (10), 15151526.
Bees, M. A. & Hill, N. A. 1998 Linear bioconvection in a suspension of randomly swimming, gyrotactic micro-organisms. Phys. Fluids 10 (8), 18641881.10.1063/1.869704
Clifton, W., Bearon, R. N. & Bees, M. A. 2018 Enhanced sedimentation of elongated plankton in simple flows. IMA J. Appl. Maths 83 (4), 743766.
Croze, O. A., Ashraf, E. E. & Bees, M. A. 2010 Sheared bioconvection in a horizontal tube. Phys. Biol. 7 (4), 046001.10.1088/1478-3975/7/4/046001
Dekshenieks, M. M., Donaghay, P. L., Sullivan, J. M., Rines, J. E. B., Osborn, T. R. & Twardowski, M. S. 2001 Temporal and spatial occurrence of thin phytoplankton layers in relation to physical processes. Mar. Ecol. Prog. Ser. 223, 6171.
Durham, W. M., Clement, E., Berry, M., Lillio, F., De Boffetta, G., Cencini, M. & Stocker, R. 2013 Turbulence drives microscale patches of motile phytoplankton. Nat. Comm. 4, 2148.10.1038/ncomms3148
Durham, W. M., Kessler, J. O. & Stocker, R. 2009 Disruption of vertical motility by shear triggers formation of thin phytoplankton layers. Science 323 (5917), 10671070.10.1126/science.1167334
Durham, W. M. & Stocker, R. 2012 Thin phytoplankton layers: characteristics, mechanisms, and consequences. Annu. Rev. Marine Sci. 4, 177207.
Franks, P. J. S. 1995 Thin layers of phytoplankton: a model of formation by near-inertial wave shear. Deep-Sea Res. I 42 (1), 7591.10.1016/0967-0637(94)00028-Q
Ginzburg, M. & Ginzburg, B. Z. 1985 Influence of age of culture and light intensity on solute concentrations in two Dunaliella strains. J. Exp. Botany 36 (5), 701712.10.1093/jxb/36.5.701
Grünbaum, D. 2009 Peter principle packs a peck of phytoplankton. Science 323 (5917), 10221023.
Hill, N. A. & Bees, M. A. 2002 Taylor dispersion of gyrotactic swimming micro-organisms in a linear flow. Phys. Fluids 14 (8), 25982605.
Hwang, Y. & Pedley, T. J. 2014a Bioconvection under uniform shear: linear stability analysis. J. Fluid Mech. 738, 522562.
Hwang, Y. & Pedley, T. J. 2014b Stability of downflowing gyrotactic microorganism suspensions in a two-dimensional vertical channel. J. Fluid Mech. 749, 750777.10.1017/jfm.2014.251
Ishikawa, T. & Pedley, T. J. 2007 The rheology of a semi-dilute suspension of swimming model micro-organisms. J. Fluid Mech. 588, 399435.
Jiménez, F., Rodríguez, J., Bautista, B. & Rodríguez, V. 1987 Relations between chlorophyll, phytoplankton cell abundance and biovolume during a winter bloom in Mediterranean coastal waters. J. Exp. Mar. Bio. Ecol. 105 (2–3), 161173.10.1016/0022-0981(87)90169-9
Johnston, T. M. S. & Rudnick, D. L. 2009 Observations of the transition layer. J. Phys. Oceanogr. 39 (3), 780797.
Kessler, J. O. 1984 Gyrotactic buoyant convection and spontaneous pattern formation in algal cell cultures. In Nonequilibrium Cooperative Phenomena in Physics and Related Fields, pp. 241248. Springer.10.1007/978-1-4684-8568-4_14
Kessler, J. O. 1985 Hydrodynamic focusing of motile algal cells. Nature 313 (5999), 218220.10.1038/313218a0
Krivtsov, V., Bellinger, E. G. & Sigee, D. C. 2000 Changes in the elemental composition of Asterionella formosa during the diatom spring bloom. J. Plankton Res. 22 (1), 169184.10.1093/plankt/22.1.169
MacIntyre, J. G., Cullen, J. J. & Cembella, A. D. 1997 Vertical migration, nutrition and toxicity in the dinoflagellate Alexandrium tamarense . Mar. Ecol. Prog. Ser. 148, 201216.10.3354/meps148201
Moline, M. A., Benoit-Bird, K. J., Robbins, I. C., Schroth-Miller, M., Waluk, C. M. & Zelenke, B. 2010 Integrated measurements of acoustical and optical thin layers II: horizontal length scales. Cont. Shelf Res. 30 (1), 2938.
Nielsen, T. G., Kiørboe, T. & Bjørnsen, P. K. 1990 Effects of a Chrysochromulina polylepis subsurface bloom on the planktonic community. Mar. Ecol. Prog. Ser. 62, 2135.10.3354/meps062021
Osborn, T. 1998 Finestructure, microstructure, and thin layers. Oceanography 11, 3643.
Pedley, T. J. 2010 Instability of uniform micro-organism suspensions revisited. J. Fluid Mech. 647, 335359.10.1017/S0022112010000108
Pedley, T. J., Hill, N. A. & Kessler, J. O. 1988 The growth of bioconvection patterns in a uniform suspension of gyrotactic micro-organisms. J. Fluid Mech. 195, 223237.
Pedley, T. J. & Kessler, J. O. 1987 The orientation of spheroidal microorganisms swimming in a flow field. Proc. R. Soc. Lond. B 231 (1262), 4770.
Pedley, T. J. & Kessler, J. O. 1990 A new continuum model for suspensions of gyrotactic micro-organisms. J. Fluid Mech. 212, 155182.
Pedley, T. J. & Kessler, J. O. 1992 Hydrodynamic phenomena in suspensions of swimming microorganisms. Annu. Rev. Fluid Mech. 24 (1), 313358.10.1146/annurev.fl.24.010192.001525
Rusconi, R., Guasto, J. S. & Stocker, R. 2014 Bacterial transport suppressed by fluid shear. Nat. Phys. 10 (3), 212217.10.1038/nphys2883
Ryan, J. P., McManus, M. A. & Sullivan, J. M. 2010 Interacting physical, chemical and biological forcing of phytoplankton thin-layer variability in Monterey Bay, California. Cont. Shelf Res. 30 (1), 716.
Santamaria, F., De Lillo, F., Cencini, M. & Boffetta, G. 2014 Gyrotactic trapping in laminar and turbulent Kolmogorov flow. Phys. Fluids 26 (11), 111901.
Similä, A. 1988 Spring development of a chlamydomonas population in Lake Nimetön, a small humic forest lake in southern Finland. In Flagellates in Freshwater Ecosystems, pp. 149157. Springer.
Stacey, M. T., McManus, M. A. & Steinbuck, J. V. 2007 Convergences and divergences and thin layer formation and maintenance. Limnol. Oceanogr. 52 (4), 15231532.10.4319/lo.2007.52.4.1523
Steinbuck, J. V., Stacey, M. T., McManus, M. A., Cheriton, O. M. & Ryan, J. P. 2009 Observations of turbulent mixing in a phytoplankton thin layer: implications for formation, maintenance, and breakdown. Limnol. Oceanogr. 54 (4), 13531368.10.4319/lo.2009.54.4.1353
Sullivan, J. M., Donaghay, P. L. & Rines, J. E. B. 2010 Coastal thin layer dynamics: consequences to biology and optics. Cont. Shelf Res. 30 (1), 5065.
Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Journal of Fluid Mechanics
  • ISSN: 0022-1120
  • EISSN: 1469-7645
  • URL: /core/journals/journal-of-fluid-mechanics
Please enter your name
Please enter a valid email address
Who would you like to send this to? *

JFM classification


Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed