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Gyrotactic bioconvection at pycnoclines

Published online by Cambridge University Press:  26 September 2013

A. Karimi  and
A. M. Ardekani
A. Karimi*
Affiliation:
Department of Aerospace and Mechanical Engineering, University of Notre Dame, Notre Dame, IN 46556, USA
A. M. Ardekani
Affiliation:
Department of Aerospace and Mechanical Engineering, University of Notre Dame, Notre Dame, IN 46556, USA
*
†Email address for correspondence: [email protected]
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Abstract

Bioconvection is an important phenomenon in aquatic environments, affecting the spatial distribution of motile micro-organisms and enhancing mixing within the fluid. However, stratification arising from thermal or solutal gradients can play a pivotal role in suppressing the bioconvective flows, leading to the aggregation of micro-organisms and growth of their patchiness. We investigate the combined effects by considering gyrotactic motility where the up-swimming cells are directed by the balance of the viscous and gravitational torques. To study this system, we employ a continuum model consisting of Navier–Stokes equations with the Boussinesq approximation coupled with two conservation equations for the concentration of cells and stratification agent. We present a linear stability analysis to determine the onset of bioconvection for different flow parameters. Also, using large-scale numerical simulations, we explore different regimes of the flow by varying the corresponding boundary conditions and dimensionless variables such as Rayleigh number and Lewis number ($\mathit{Le}$) and we show that the cell distribution can be characterized using the ratio of the buoyancy forces as the determinant parameter when $\mathit{Le}\lt 1$ and the boundaries are insulated. But, in thermally stratified fluids corresponding to $\mathit{Le}\gt 1$, temperature gradients are demonstrated to have little impact on the bioconvective plumes provided that the walls are thermally insulated. In addition, we analyse the dynamical behaviour of the system in the case of persistent pycnoclines corresponding to constant salinity boundary conditions and we discuss the associated inhibition threshold of bioconvection in the light of the stability of linearized solutions.

JFM classification

Biological Fluid Dynamics: Bioconvection Convection: Buoyancy-driven instability Geophysical and Geological Flows: Stratified flows
Type
Papers
Information
Journal of Fluid Mechanics , Volume 733 , 25 October 2013 , pp. 245 - 267
Copyright
©2013 Cambridge University Press 

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Karimi and A. M. Ardekani supplementary movies

Plume dynamics represented as the time evolution of isosurfaces of cell concentration. The background fluid is homogenous and the domain aspect ratios are Γh=Γv=1.

Download Karimi and A. M. Ardekani supplementary movies(Video)
Video 1.4 MB

Karimi and A. M. Ardekani supplementary movies

Temporal evolution of isosurfaces of cell concentration and vertical distribution of salinity. The domain aspect ratios are Γh=1 and Γv=5 with parameters Le=0.03 and Rs =104.

Download Karimi and A. M. Ardekani supplementary movies(Video)
Video 4.3 MB