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The motion of microswimmers in complex flows is ruled by the interplaybetween swimmer propulsion and the dynamics induced by the fluid velocityfield. Here we study the motion of a chiral microswimmer whose propulsion isprovided by the spinning of a helical tail with respect to its body in a simpleshear flow. Thanks to an efficient computational strategy that allowed us tosimulate thousands of different trajectories, we show that the tail shapedramatically affects the swimmer's motion. In the shear dominated regime, theswimmers carrying an elliptical helical tail show several differentJeffery-like (tumbling) trajectories depending on their initial configuration.As the propulsion torque increases, a progressive regularization of the motionis observed until, in the propulsion dominated regime, the swimmers converge tothe same final trajectory independently on the initial configuration. Overall,our results show that elliptical helix swimmer presents a much richer varietyof trajectories with respect to the usually studied circular helix tails.

Base flow decomposition for complex moving objects in linear hydrodynamics: application to helix-shaped flagellated microswimmers