Phytoplankton patchiness, namely the heterogeneous distribution of microalgae over multiple spatial scales, dramatically impacts marine ecology. A spectacular example of such heterogeneity occurs in thin phytoplankton layers (TPLs), where large numbers of photosynthetic microorganisms are found within a small depth interval. Some species of motile phytoplankton can form TPLs by gyrotactic trapping due to the interplay of their particular swimming style (directed motion biased against gravity) and the transport by a flow with shear along the direction of gravity. Here we consider gyrotactic swimmers in numerical simulations of the Kolmogorov shear flow, both in laminar and turbulent regimes. In the laminar case, we show that the swimmer motion is integrable and the formation of TPLs can be fully characterized by means of dynamical systems tools. We then study the effects of rotational Brownian motion or turbulent fluctuations (appearing when the Reynolds number is large enough) on TPLs. In both cases we show that TPLs become transient, and we characterize their persistence.

We study the effect of surface gravity waves on the motion of inertial particles in an incompressible fluid. We perform analytical calculations based on perturbation expansions which allow us to predict the dynamics of inertial particles in the deep-water regime. We find that the presence of inertia leads to a non-negligible correction to the well-known horizontal Stokes drift velocity. Moreover, we find that the vertical sedimentation velocity is also affected by a drift induced by waves. The latter result may have some relevant consequences on the rate of sedimentation of particles of finite size. We underline that the vertical drift would also be observed in the (hypothetical) absence of the gravitational force. Kinematic numerical simulations are performed and the results are found to be in excellent agreement with the analytical predictions, even for values of the parameters beyond the perturbative limit.

A suspension of gyrotactic microalgae Chlamydomonas augustae swimming in a cylindrical water vessel in solid-body rotation is studied. Our experiments show that swimming algae form an aggregate around the axis of rotation, whose intensity increases with the rotation speed. We explain this phenomenon by the centripetal orientation of the swimming direction towards the axis of rotation. This centripetal focusing is contrasted by diffusive fluxes due to stochastic reorientation of the cells. The competition of the two effects lead to a stationary distribution, which we analytically derive from a refined mathematical model of gyrotactic swimmers. The temporal evolution of the cell distribution, obtained via numerical simulations of the stochastic model, is in quantitative agreement with the experimental measurements in the range of parameters explored.

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We study the effect of surface gravity waves on the motion of inertial particles in an incompressible fluid. We perform analytical calculations based on perturbation expansion which allows us to predict the dynamics of inertial particles in deep water regime. We find that the presence of inertia leads to a non-negligible correction to the well-known horizontal Stokes drift velocity. Moreover, we find that the vertical sedimentation velocity is also affected by a drift induced by waves. The latter result may have some relevant consequences on the rate of sedimentation of particles of finite size. We underline that the vertical drift would also be observed in the (hypothetical) absence of the gravitational force. Kinematic numerical simulations are performed and the results are found to be in excellent agreement with the analytical predictions, even for values of parameters beyond the perturbative limit.