Prolate microswimmer in surface gravity waves

Planktonic microorganisms immersed in a fluid interact with the ambient flow, altering their trajectories. In surface gravity waves, a common goal for microswimmers is vertical migration. By modeling phytoplankton as spheroidal bodies with a certain swimming velocity, we investigate how the combination of swimmer's dynamical characteristics and fluid velocity gradients affect the motion. We investigate the case of prolate, negative buoyant swimmers. We consider also the case of gyrotactic swimmers. We find that it is possible for microswimmers to be trapped at a finite depth below the sea level. This phenomenon is due to the coupling between swimming, gyrotaxis and flow-induced reorientations. The trajectories obtained by numerical simulations, indicate that the dynamics consist of fast oscillations at the surface wavelength superposed with a slower trend at a longer timescale. This suggests using a multiple time-scale expansion to remove the fast oscillations. The presence of stable fixed points for the slow dynamics allows the trapping behaviour.