Migration of gyrotactic micro-organisms in surface gravity waves

Many micro-organisms such as phytoplankton commonly inhabit the upper layers of aquatic environments, where surface waves are prevalent. In this study, we investigate the migration of gyrotactic micro-organisms in surface gravity waves using two complementary approaches: a wave-averaged simplified continuum theory specific to spherical micro-swimmers, which combines Lagrangian Stokes drift with generalized Taylor dispersion theory, and a wave-resolved random walk simulation. We begin with a parametric analysis of gyrotaxis and swimming on dispersion. While both methods show that stronger gyrotaxis enhances gravitactic focusing near the surface, the random walk simulation additionally reveals a regime in which gyrotactic swimmers exhibit a mean vertical position below that of passive solute particles. The migration of non-spherical micro-swimmers is analyzed using the random walk simulation. Rod- and disc-like micro-swimmers display distinct transport behaviors due to their shape-induced orientation preferences, which either enhance or inhibit vertical focusing. Incorporating non-linear wave effects shows that all swimmer types experience increased drift velocities, but only disc-like swimmers exhibit significantly amplified longitudinal dispersion. Finally, the addition of a background current weakens gravitactic focusing in spherical swimmers, while inducing opposite responses in rod- and disc-like ones. Our findings highlight the crucial role of swimmers' taxes and morphology and wave–swimmer interactions in shaping vertical distributions and dispersion characteristics, offering insight into the prevalence of elongated forms among motile phytoplankton.