Squirming in density-stratified fluids

Abstract

In this work, we study the axisymmetric motion of a prototypical swimming organism, a spherical squirmer, in a linearly density-stratified fluid. We assume the inertia is negligible, the stratification is weak, and the swimmer is oriented either vertically upward or downward. The swimmer acts as a settling particle or a neutrally buoyant organism depending on the relative magnitude of its density and the ambient fluid density. While the stratification reduces the speed of a settling particle, it increases (respectively, reduces) the speed of a neutrally buoyant puller (respectively, pusher). The stratification only affects the flow far from the swimmer and this far-field flow due to a settling particle (respectively, neutrally buoyant organism) at low advection of density is same as the flow due to a point-force (respectively, force-dipole) placed in a stratified fluid. The swimmer mixes the surrounding fluid. The mixing caused by a settling particle scales as the ratio of the particle size to the stratification length scale but the mixing due to a neutrally buoyant organism scales as the ratio of the buoyancy to the viscous forces. The latter mixing estimate is much larger than the previous estimate based on the force-dipole model of an organism but still negligible compared to the oceanic mixing. These results are useful to understand the stratification effects on the motility of the organism and the induced mixing.