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The instability of gyrotactically trapped cell layers

Published online by Cambridge University Press:  15 April 2019

Smitha Maretvadakethope
Affiliation:
Department of Mathematics, Imperial College London, South Kensington, London SW7 2AZ, UK
Eric E. Keaveny
Affiliation:
Department of Mathematics, Imperial College London, South Kensington, London SW7 2AZ, UK
Yongyun Hwang
Affiliation:
Department of Aeronautics, Imperial College London, South Kensington, London SW7 2AZ, UK
Corresponding
E-mail address:

Abstract

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.

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JFM Rapids
Copyright
© 2019 Cambridge University Press 

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