Elongation enhances migration through hydrodynamic shear

Many species of plankton migrate through the water column to avoid predation and acquire resources available only at depth. These vertical migrations, however, can be thwarted by flow which is ubiquitous in the ocean and acts to reorient the motility of swimming plankton in different directions. The torques exerted on an organism by hydrodynamic shear are a strong function of its shape—while spherical organisms only experience the overturning effect of vorticity, more elongated organisms experience additional torques that tend to align them in the direction of principal strain. Recent simulations of directed migration through turbulence indicate that organisms with larger aspect ratios are capable of faster vertical migration, however, the underlying physical processes are not well understood. Here, we use simple models of flow to study how elongation affects the capacity of a swimmer to vertically migrate through shear. We explore how the orientation of a migrating swimmer in simple shear depends both on its aspect ratio and nondimensional stability, highlighting where a unique stable upward equilibrium is globally attracting, and where particles can undergo periodic orbits. In addition, we identify that stable up and down equilbria can coexist when there is a nonzero vertical component of vorticity. We go on to investigate how elongation affects the transport and spatial distribution of a migrating swimmer in an inhomogeneous Kolmogorov shear flow. Our results show that a swimmer's shape can profoundly affect its mean-field behavior in flow and tendency to aggregate in regions of high shear. These findings reveal how flow can select for the elongated morphologies commonly found in marine plankton and may also provide insights to rationally design microrobots to navigate ambient flows.