Patchiness plays a fundamental role in phytoplankton ecology by dictating the rate at which individual cells encounter each other and their predators. The distribution of motile phytoplankton species is often considerably more patchy than that of non-motile species at submetre length scales, yet the mechanism generating this patchiness has remained unknown. Here we show that strong patchiness at small scales occurs when motile phytoplankton are exposed to turbulent flow. We demonstrate experimentally that Heterosigma akashiwo forms striking patches within individual vortices and prove with a mathematical model that this patchiness results from the coupling between motility and shear. When implemented within a direct numerical simulation of turbulence, the model reveals that cell motility can prevail over turbulent dispersion to create strong fractal patchiness, where local phytoplankton concentrations are increased more than 10-fold. This 'unmixing' mechanism likely enhances ecological interactions in the plankton and offers mechanistic insights into how turbulence intensity impacts ecosystem productivity.

We apply the iterated edge-state tracking algorithm to study the boundary between laminar and turbulent dynamics in plane Couette flow at Re= 400. Perturbations that are not strong enough to become fully turbulent or weak enough to relaminarize tend toward a hyperbolic coherent structure in state space, termed the edge state, which seems to be unique up to obvious continuous shift symmetries. The results reported here show that in cases where a fixed point has only one unstable direction, such as for the lower-branch solution in plane Couette flow, the iterated edge tracking algorithm converges to this state. They also show that the choice of initial state is not critical and that essentially arbitrary initial conditions can be used to find the edge state. DOI: 10.1103/PhysRevE.78.037301 PACS number͑s͒: 47.10.Fg, 47.27.Cn, 47.27.ed Plane Couette flow and pipe flow belong to the class of shear flows where turbulence occurs despite the persistent linear stability of the laminar profile ͓1͔. Triggering turbulence then requires the crossing of two thresholds, one in Reynolds number and one in perturbation amplitude. Guidance on the minimum Reynolds number is offered by the appearance of exact coherent states: once they are present, an entanglement of their stable and unstable manifolds can provide the necessary state space elements for chaotic, turbulent dynamics ͓2-14͔. Since the exact coherent states appear in saddle-node bifurcations, it is natural to associate the upper branch ͑characterized by a higher kinetic energy or a higher drag͒ with the turbulent dynamics and the lower branch with the threshold in perturbation amplitude ͓8,15-18͔. In plane Couette flow this scenario seems to be borne out: at the point of bifurcation, at a Reynolds number of about 127.7, the upper branch state is stable and the lower one has only one unstable direction ͓6,8,18͔. At slightly higher Reynolds numbers, the upper branch undergoes secondary bifurcations which could lead to the complex state space structure usually associated with turbulent dynamics. For the lower branch, on the other hand, there are no indications of further bifurcations. If it continues to have a single unstable direction only, its stable manifold can divide the state space such that initial conditions from one side decay more or less directly to the laminar profile, whereas those from the other side show some turbulent dynamics. Such a description of the transition along the lines of the phenomenology of saddle-node bifurcations has been advanced by Toh and Itano ͓15͔ for plane Poiseuille flow, by Wang et al. ͓18͔ and Viswanath ͓19,20͔ for plane Couette flow, and Kerswell and Tutty for pipe flow ͓21͔.Empirically, one may study the boundary between laminar and turbulent dynamics by following the time evolution of flow fields and thereby assigning a lifetime-i.e., the time it takes for a particular initial condition to decay toward the laminar profile ͓22-25͔. Increasing the amplitude of the perturbation one notes changes between regions with smooth variati...

The motility of microorganisms is often biased by gradients in physical and chemical properties of their environment, with myriad implications on their ecology. Here we show that fluid acceleration reorients gyrotactic plankton, triggering small-scale clustering. We experimentally demonstrate this phenomenon by studying the distribution of the phytoplankton Chlamydomonas augustae within a rotating tank and find it to be in good agreement with a new, generalized model of gyrotaxis. When this model is implemented in a direct numerical simulation of turbulent flow, we find that fluid acceleration generates multifractal plankton clustering, with faster and more stable cells producing stronger clustering. By producing accumulations in high-vorticity regions, this process is fundamentally different from clustering by gravitational acceleration, expanding the range of mechanisms by which turbulent flows can impact the spatial distribution of active suspensions.

Preferential concentration of inertial particles in turbulent flow is studied by high resolution direct numerical simulations of two-dimensional turbulence. The formation of network-like regions of high particle density, characterized by a length scale which depends on the Stokes number of inertial particles, is observed. At smaller scales, the size of empty regions appears to be distributed according to a universal scaling law.

We study the statistics of single-particle Lagrangian velocity in a shell model of turbulence. We show that the small-scale velocity fluctuations are intermittent, with scaling exponents connected to the Eulerian structure function scaling exponents. The observed reduced scaling range is interpreted as a manifestation of the intermediate dissipative range, as it disappears in a Gaussian model of turbulence. DOI: 10.1103/PhysRevE.66.066307 PACS number͑s͒: 47.27.Gs, 47.27.Qb In recent years there has been a great improvement in the laboratory experimental investigation of turbulence from a Lagrangian point of view ͓1-4͔. In the Lagrangian approach, the flow is described by the ͑Lagrangian͒ velocity v(x 0 ,t) of a fluid particle initially at position x(0)ϭx 0 . This is the natural description for studying transport and mixing of neutrally advected substances in turbulent flows.One of the simplest statistical quantities one can be interested in is single-particle velocity increments ␦v(t)ϭv(t)Ϫv (0) ͑where, assuming statistical homogeneity, we have dropped the dependence on x 0 ) for which dimensional analysis in fully developed turbulence predicts ͓5,6͔ ͑1͒where is the mean energy dissipation and C 0 is a numerical constant. The remarkable coincidence that the variance of ␦v(t) grows linearly with time is the physical basis on which stochastic models of particle dispersion are based. It is important to recall that the ''diffusive'' nature of Eq. ͑1͒ is purely incidental: it is a direct consequence of Kolmogorov scaling in the inertial range of turbulence and is not directly related to a diffusive process. Let us recall briefly the argument leading to the scaling in Eq. ͑1͒. We can think of the velocity v(t) advecting the Lagrangian trajectory as the superposition of the different velocity contributions coming from turbulent eddies ͑which also move with the same velocity of the Lagrangian trajectory͒. After a time t the components associated with the smaller ͑and faster͒ eddies, below a certain scale ᐉ, are decorrelated and thus at the leading order one has ␦v(t)Ӎ␦v(ᐉ). Within Kolmogorov scaling, the velocity fluctuation at scale ᐉ is given by ␦v(ᐉ), where V represents the typical velocity at the largest scale L. The correlation time of ␦v(ᐉ) scales as (ᐉ)ϳ 0 (ᐉ/L) 2/3 and thus one obtains the scaling in Eq. ͑1͒ with ϭV 2 / 0 . This argument shows that the linear scaling in Eq. ͑1͒ is the result of the combination of the Kolmogorov scaling for velocity fluctuations and eddy turnover time in physical space, as seen by a Lagrangian tracer. From a numerical point of view, the observation of Eq. ͑1͒ is more delicate than standard Eulerian structure functions, as it requires the correct resolution of the sweeping effect on the Lagrangian trajectories. Of course, this can be done in direct numerical simulations ͑but at moderate Reynolds numbers͒ ͓7͔ and, as we will see, in a Lagrangian version of the shell model of turbulence.Equation ͑1͒ can be generalized to higher-order moments with the introduction of a set of tem...

We use the intrinsic geometrical characteristics of space curves, i.e. curvature and torsion, to describe the paths of particles passively advected in a turbulent flow. We find that curvature increases with the Reynolds number and that the maxima in vorticity and curvature times local velocity are linearly correlated. Fluctuations around the maximal values in runs at a fixed Reynolds number are only weakly correlated, and the distributions are fairly wide, so that it is not possible to conclude that a tightly wound spiral has to correspond to a region of high vorticity.

Motile cilia are highly conserved structures in the evolution of organisms, generating the transport of fluid by periodic beating, through remarkably organized behavior in space and time. It is not known how these spatiotemporal patterns emerge and what sets their properties. Individual cilia are nonequilibrium systems with many degrees of freedom. However, their description can be represented by simpler effective force laws that drive oscillations, and paralleled with nonlinear phase oscillators studied in physics. Here a synthetic model of two phase oscillators, where colloidal particles are driven by optical traps, proves the role of the average force profile in establishing the type and strength of synchronization. We find that highly curved potentials are required for synchronization in the presence of noise. The applicability of this approach to biological data is also illustrated by successfully mapping the behavior of cilia in the alga Chlamydomonas onto the coarse-grained model.

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.