  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.
