Reaching for the surface: Spheroidal microswimmers in surface gravity waves

Microswimmers (planktonic microorganisms or artificial active particles) immersed in a fluid interact with the ambient flow, altering their trajectories. In surface gravity waves, a common goal for microswimmers is vertical migration (e.g., to reach the free surface or to dive to deeper depths). By modelling microswimmers as spheroidal bodies with an intrinsic swimming velocity that supplements advection and reorientation by the flow, we investigate how shape and swimming affect vertical transport of microswimmers in waves. We find that it is possible for microswimmers to be initially swimming downwards, but to recover and head back to the surface, and vice versa. This is because the coupling between swimming and flow-induced reorientations introduces a shape dependency in the vertical transport. From a wave-averaged analysis of microswimmer trajectories, we show that each trajectory is bounded by critical planes in the position-orientation phase space that depend only on the shape. We also give explicit solutions to these trajectories and determine the fraction of microswimmers that begin within the water column and eventually reach the surface. For microswimmers that are initially randomly oriented, the fraction that reach the surface increases monotonically as the starting depth decreases, as expected, but also varies with shape and swimming speed. In the limit of small swimming speed, the fraction of highly prolate microswimmers reaching the surface is 0.5, suggesting that these swimmers would be able to choose direction of vertical transport with small changes in swimming behaviour.