AbstractBioconvection 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.
Remarks on the stability of the Navier–Stokes equations supplemented with stress boundary conditions
