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Recent years have been characterized by an increasing interest in and awareness of the role of multi-scale interactions in shaping the ecology of wide aquatic environments as the ocean and small-scale active suspensions as biofilms. These interactions range from micro-scale physical-biological coupling characterising the life of individual organisms to the large-scale population dynamics whose impact can be felt at the level of the global climate.

Penetrating such new and intriguing research field demands a multidisciplinary approach accounting for the coupling of physics, chemistry, and biology from the microscale to the macroscale, thus the necessity of the proposed workshop which aims at setting up a new common ground for scientists with different backgrounds.

In particular, the remarkable evolution of large scale computations has in recent years created a new and revolutionary way of performing research in this field. The computational approach has, together with theoretical analysis and traditional experimental research, become an independent and extremely useful tool to gain new knowledge also in this field, traditionally characterised by experiments and field observations. The aim of the workshop is therefore to bring closer the three different tools of research and propose new ways to combine theory, laboratory experiments based on novel micro-fluidic devices, field observations and numerical modelling. The latter concerns both the locomotion of individual micro-organisms and the transport in turbulent flow.

Aquatic microorganisms affect large-scale processes in the ocean, including the cycling of many elements and the generation of climatically relevant gases, yet they live at the microscale. The microbial environment of swimming organisms can be large with respect to the cell size but still remains very small relative to most oceanographic processes. Therefore, the interactions between microorganisms and aquatic environment involves a huge range of scales which cannot be all resolved simultaneously.

In experiments, these difficulties are overcome by limiting the range of scales resolved, and this is a possible solution also in simulations (e.g. a tiny volume of fluid is simulated around the cell). Another promising approach makes use of simplified models for one component of the “active fluid” with an effective description which allows to reproduce accurately some features, in the same spirit of other successful methods in fluid dynamics such as Large Eddy Simulations.

Still, the simulation of microorganism motion in a (turbulent) flow is numerically challenging, especially at large densities when the feedback of cell motion on the fluid has to be taken into account. Indeed suspensions of swimming microorganism can affect the rheological properties of the flow field and can generate complex flow fields very similar to turbulent flows though the Reynolds number is negligibly small as recently found in swarming bacteria.

The numerical modeling of these phenomena is extremely difficult and requires the development of refined models. For example, recent investigations on bacterial turbulence have shown that the derivation of an effective equation from microscopic ingredients can lead to contradictions with respect to the observed phenomenology.

The novelty of the proposed workshop is to bring together the most active scientists working in the field, from fluid dynamicists to mathematicians, from marine biologists to computational scientists, with the objective of setting the state of the art in numerical and experimental approaches to “active fluids” and recognizing the most important criticalities.
The ambition of the workshop is, by recognizing the most important criticalities of the present approaches, to push the development of new conceptual and numerical models for this challenging problem.

The study of motile (self-propelled) microorganisms has been an active field of research in physics and fluid dynamics since many years. Given the typical microbial sizes and swimming velocities the Reynolds number associated with microbial locomotion is usually very small and the flow dominated by viscosity [Purcell(1977)]. During the last sixty years much has been understood about locomotory mechanisms of individual microorganisms [Lauga(2009)] and also how motility changes in response to chemical stimuli (chemotaxis) [Berg(2003)]. However, most of past research mainly focused on microbial locomotion in still fluids, and chemotaxis of model microorganisms such as the bacteria E. Coli. These studies led to fundamental advances in the understanding of propulsion and chemotaxis. The recognition that in natural aquatic environments such as oceans, rivers or lakes, the majority of microorganisms (bacteria, phytoplankton, micro-zooplankton and fish larvae) are motile [Fenchel(2001)] widened the spectrum of interests to microbial motility and tactic response in moving liquids, where turbulence of moderate intensity is generated by winds, tides etc. While recent advances in experimental techniques clarified the complex interplay between collective motion of microorganisms (e.g. in bacterial swarming) and the self-generated flow fields [Cisneros(2007), Wensink(2012)], high-performance numerical simulations have become a reliable research tool to model large scale interactions [Taylor(2012), Stocker(2012)].

Understanding microbial motility in unsteady aquatic environments is of utmost importance due to the effects that such microorganisms have on crucial climate-triggering processes such as the global carbon and nitrogen cycles [Falkowski(1994), Azam(1998)], Furthermore, the interplay among motility, fluid motion and predation strategies is crucial for understanding aquatic food webs and ecology [Seymour(2009)] and developing a quantitative modeling of planktonic microorganism ecology [Kiorboe(2008)].

Remarkably, the behavior of microorganisms living in unsteady flows is typically different from those which evolved in steady fluids. For example, studies on marine bacteria [Mitchell(2006)] revealed the existence of swimming strategies different from the standard run-and-tumble mechanism typical of E. coli [Berg(2003)]. Swimming is clearly influenced by flow shear forces that reorient organisms, depending on their detailed morphology [Pedley(1987),Pedley(1992)]. Turbulence stirs an mixes chemoeffectors, altering the gradients and thus affecting the microorganism behavior [Taylor(2012)]. Moreover, hydrodynamic interactions between swimmers also may play an important role in determining swimming strategies which reflect also in their chemotactic abilities [Locsei(2009)].

It should also be observed that the interplay between swimming and flow depends sensitively on the propulsion mechanism. The main distinction is between pullers, such as biflagellates, and pushers such as most of bacteria. Attraction or repulsion between neighbour swimmers may depend on the swimming mode [Cisneros(2007), Ishikawa(2009)].

Combination of self-propulsion and fluid motion can give rise to clustering of motile microorganisms which can explain their observed patchy distribution over many scales [Durham(2009),Durham(2013)]. For example, several species of microalgae are characterized can swim by beating two flagella anchored on the cell axis of symmetry oppositely to their center of mass which stays behind the center of buoyancy. In a still fluid, such "bottom heavy" algae swim upwards (a phenomenon dubbed gravitaxis or geotaxis). However, in the presence of a uniform shear, the viscous torque exerted by the fluid changes the swimming direction (gyrotaxis) [Pedley(1987),(1992)]. At a critical shear intensity, the balance between gravitational and shear torque breaks up, and the algae are trapped and swirl close to the velocity inversion region. This mechanism has been proposed as an explanation of the occurrence of high concentration of phytoplankton in thin layers close to coastal regions [Durham(2009)].

The flow generated by the microorganisms develops large scale structures with typical velocities larger that the swimming speed of the single swimmer [Sokolov(2007), Cisneros(2007)]. Such a phenomenon has been dubbed “bacterial turbulence” [Wolgemuth(2008)]. Diffusivity of substances is strongly enhanced by the presence of bacterial turbulence, similar to the case of high Reynolds number flows

[Wu(2000)]. In discrete (Lagrangian) models of a microbial colony, each swimmer is modeled by the superposition of few point-like forces, reproducing some qualitative features of coherent motions found in experiments [Hernandez-Ortiz(2005)]. A different approach in term of slender-body theory was also successfully employed [Saintillan(2007)]. Regarding continuous (Eulerian) models, the effect of dilute suspensions (relevant for bioconvection) can be accounted for with a Boussinesq term in the Navier-Stokes equations [Pedley(1992)]. In the case of bacterial turbulence, one needs to model the effect of swimming in the momentum equation of the fluid [Simha(2002)] or to resort to more phenomenological modeling [Dunkel(2013)]. Another possibility is to develop a kinetic approach in which the microbial colony is modeled by means of a set of fields representing the local coarse grained orientation and velocity of the swimmers [Saintillan(2008)], or two-phase models [Wolgemuth(2008)]. Moreover, these models are rather similar to those employed in soft matter for active gels or liquid crystals allowing for the use of consolidated techniques there developed [see, e.g., Simha(2002)]. It is also interesting to note that depending on the swimming mode (pusher or puller) these continuum models predict very different instabilities, coherent motions and rheology [Hatwalne(2004), Baskaran(2009)].

In summary, there are not yet large-scale computations of active suspensions in real configurations despite the fact that recent efforts have provided different complex models. There is therefore a need for improvements and design of new more efficient algorithms. Moreover, the behavior of populations in turbulent environment is not well explored although the fluid mechanics community has developed numerical tools for the large-scale simulations of these flows, including approximations such as the large eddy simulation. In this case, the challenge comes from the coupling with the biology, i.e. the correct simulation of the individual and population behavior.