The instability of gyrotactically trapped cell layers

• Published in: Journal of fluid mechanics Vol. 868
• Main Authors: Maretvadakethope, Smitha, Keaveny, Eric E., Hwang, Yongyun
• Format: Journal Article
• Language: English
• Published: Cambridge, UK Cambridge University Press 10.06.2019
• Subjects: Algae; Cells; Channel flow; Coastal ecology; Computational fluid dynamics; Continuum modeling; Experiments; Flow stability; Gravitational instability; Gravity; Instability; JFM Rapids; Microorganisms; Ocean surface; Oceans; Phytoplankton; Plankton; Stability analysis; Swimming; Thin films; Turbulence; Vorticity; bioconvection
• ISSN: 0022-1120; 1469-7645
• DOI: 10.1017/jfm.2019.227

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.