Bioconvection in a stratified environment: Experiments and theory

Abstract

Bioconvection is a fascinating phenomenon of fluid mechanics that is driven by the swimming motion of micro-organisms. Typically the velocity and spatial scale of the fluid motions are much larger than those associated with the swimming speed and size of an individual cell, resulting in rapid transport of cells and the formation of complex spatial patterns in cell concentration. Motile microalgae are ubiquitous in aquatic systems, and understanding how they are spatially distributed at a wide range of length and time scales is an important ecological task. In the natural environment, bioconvection is a little studied but potentially important mechanism influencing the vertical distribution, and therefore the growth and productivity, of motile microalgae at centimeter to meter scales. However, in order to make predictions about when and where bioconvection might occur, we need to understand how other physical factors, such as salinity stratification, will affect swimming behavior, fluid flow, and the resultant spatial distribution of cells. In this paper, we present laboratory experiments that demonstrate the importance of swimming in generating large scale, persistent spatial structure in stratified water. In the first experiment, cells in a weakly stratified fluid environment first aggregate at the surface, and then form a bioconvective plume that descends to the bottom of the tank over a distance of 20cm, equivalent to 104 cell body lengths. In the second experiment, addition of a low-salinity surface layer enables cells, initially well mixed due to bioconvection, to form a dense surface aggregation. Motivated by these experiments, we present a linear stability analysis for the onset of bioconvection in a stable linear salinity gradient. The concentration of cells is modeled by a continuous distribution and swimming is modeled as a constant upwards component combined with a diffusive component. We consider a deep chamber, where at equilibrium cells are concentrated in a thin boundary region. The ratio of chamber depth to boundary region depth is d⪢1. Using matched asymptotic analysis, we obtain the critical value of the cell Rayleigh number, Rcrit, for which the forcing due to a perturbation in cell concentration in the upper region drives flow. The effect of the salinity stratification depends on the salt Rayleigh number, Rs. If Rs1∕6=o(d), the salinity gradient suppresses the vertical extent of the perturbation to the flow and salinity to a region of nondimensional depth O(Rs−1∕6). The critical cell Rayleigh number is unaffected by the salinity gradient and is given at leading order by Rcrit=2d3δ, where δ is the ratio of horizontal to vertical cell self-diffusion. If Rs1∕6=O(d), the salinity gradient confines perturbations in the flow and salinity to the thin boundary region, and Rcrit is specified as an algebraic function of Rs. The experiments are then discussed in light of the derived theory.