Turbulence drives microscale patches of motile phytoplankton

Selection of photosynthetic traits by turbulent mixing governs formation of cyanobacterial blooms in shallow eutrophic lakes

Prediction of the complex cyanobacteria-environment interactions is vital for understanding harmful bloom formation. Most previous studies on these interactions considered specific properties of cyanobacterial cells as representative for the entire population (e.g. growth rate, mortality, and photosynthetic capacity (Pmax)), and assumed that they remained spatiotemporally unchanged. Although, at the population level, the alteration of such traits can be driven by intraspecific competition, little is known about how traits and their plasticity change in response to environmental conditions and affect the bloom formation. Here we test the hypothesis that intraspecific variations in Pmax of cyanobacteria (Microcystis spp.) play an important role in its population dynamics. We coupled a one-dimensional hydrodynamic model with a trait-based phytoplankton model to simulate the effects of physical drivers (turbulence and turbidity) on the Pmax of Microcystis populations for a range of dynamic conditions typical for shallow eutrophic lakes. Our results revealed that turbulence acts as a directional selective driver for changes in Pmax. Depending on the intensity of daily-periodic turbulence, representing wind-driven mixing, a shift in population-averaged phenotypes occurred toward either low Pmax, allowing the population to capture additional light in the upper layers, or high Pmax, enhancing the efficiency of light utilization. Moreover, we observed that a high intraspecific diversity in Pmax accelerated the formation of surface scum by up to more than four times compared to a lower diversity. This study offers insights into mechanisms by which cyanobacteria populations respond to turbulence and underscores the significance of intraspecific variations in cyanobacterial bloom formation.

HIGHLIGHTS

Perspectives on Principles of Cellular Behavior from the Biophysics of Protists

Cells are the fundamental unit of biological organization. Although it may be easy to think of them as little more than the simple building blocks of complex organisms such as animals, single cells are capable of behaviors of remarkable apparent sophistication. This is abundantly clear when considering the diversity of form and function among the microbial eukaryotes, the protists. How might we navigate this diversity in the search for general principles of cellular behavior? Here, we review cases in which the intensive study of protists from the perspective of cellular biophysics has driven insight into broad biological questions of morphogenesis, navigation and motility, and decision making. We argue that applying such approaches to questions of evolutionary cell biology presents rich, emerging opportunities. Integrating and expanding biophysical studies across protist diversity, exploiting the unique characteristics of each organism, will enrich our understanding of general underlying principles.

Methods and Measures for Investigating Microscale Motility

Motility is an essential factor for an organism's survival and diversification. With the advent of novel single-cell technologies, analytical frameworks, and theoretical methods, we can begin to probe the complex lives of microscopic motile organisms and answer the intertwining biological and physical questions of how these diverse lifeforms navigate their surroundings. Herein, we summarize the main mechanisms of microscale motility and give an overview of different experimental, analytical, and mathematical methods used to study them across different scales encompassing the molecular-, individual-, to population-level. We identify transferable techniques, pressing challenges, and future directions in the field. This review can serve as a starting point for researchers who are interested in exploring and quantifying the movements of organisms in the microscale world.

Unveiling the impact of the light-source and steric factors on [2+2] heterocycloaddition reactions

Information gained from in-depth mechanistic investigations can be used to control the selectivity of reactions, leading to the expansion of the generality of synthetic processes and the discovery of new reactivity. Here, we investigate the mechanism of light-driven [2+2] heterocycloadditions (Paternò-Büchi reactions) between indoles and ketones to develop insight into these processes. Using ground-state UV-Vis absorption and transient absorption spectroscopy (TAS), together with DFT calculations, we found that the reactions can proceed via an exciplex or electron-donor-acceptor (EDA) complex, which are key intermediates in determining the stereoselectivity of the reactions. We used this discovery to control the diastereoselectivity of the reactions, gaining access to previously inaccessible diastereoisomeric variants. When moving from 370 to 456 nm irradiation, the EDA complex is increasingly favoured, and the diastereomeric ratio (d.r.) of the product moves from >99:<1 to 47:53. In contrast, switching from methyl to ⁱpropyl substitution favours the exciplex intermediate, reversing the d.r. from 89:11 to 16:84. Our study shows how light and steric parameters can be rationally used to control the diastereoselectivity of photoreactions, creating mechanistic pathways to previously inaccessible stereochemical variants.

Impact of direct physical association and motility on fitness of a synthetic interkingdom microbial community

Mutualistic exchange of metabolites can play an important role in microbial communities. Under natural environmental conditions, such exchange may be compromised by the dispersal of metabolites and by the presence of non-cooperating microorganisms. Spatial proximity between members during sessile growth on solid surfaces has been shown to promote stabilization of cross-feeding communities against these challenges. Nonetheless, many natural cross-feeding communities are not sessile but rather pelagic and exist in turbulent aquatic environments, where partner proximity is often achieved via direct cell-cell adhesion, and cooperation occurs between physically associated cells. Partner association in aquatic environments could be further enhanced by motility of individual planktonic microorganisms. In this work, we establish a model bipartite cross-feeding community between bacteria and yeast auxotrophs to investigate the impact of direct adhesion between prokaryotic and eukaryotic partners and of bacterial motility in a stirred mutualistic co-culture. We demonstrate that adhesion can provide fitness benefit to the bacterial partner, likely by enabling local metabolite exchange within co-aggregates, and that it counteracts invasion of the community by a non-cooperating cheater strain. In a turbulent environment and at low cell densities, fitness of the bacterial partner and its competitiveness against a non-cooperating strain are further increased by motility that likely facilitates partner encounters and adhesion. These results suggest that, despite their potential fitness costs, direct adhesion between partners and its enhancement by motility may play key roles as stabilization factors for metabolic communities in turbulent aquatic environments.

Confinement, chaotic transport, and trapping of active swimmers in time-periodic flows

Microorganisms encounter complex unsteady flows, including algal blooms in marine settings, microbial infections in airways, and bioreactors for vaccine and biofuel production. Here, we study the transport of active swimmers in two-dimensional time-periodic flows using Langevin simulations and experiments with swimming bacteria. We find that long-term swimmer transport is controlled by two parameters, the pathlength of the unsteady flow and the normalized swimmer speed. The pathlength nonmonotonically controls swimmer dispersion dynamics, giving rise to three distinct dispersion regimes. Weak flows hinder swimmer transport by confining cells toward flow manifolds. As pathlength increases, chaotic transport along flow manifolds initiates, maximizing the number of unique flow cells traveled. Last, strong flows trap swimmers at the vortex core, suppressing dispersal. Experiments with Vibrio cholerae showed qualitative agreement with model dispersion patterns. Our results reveal that nontrivial chaotic transport can arise in simple unsteady flows and suggest a potentially optimal dispersal strategy for microswimmers in nature.

Investigating microscale patchiness of motile microbes under turbulence in a simulated convective mixed layer

Microbes play a primary role in aquatic ecosystems and biogeochemical cycles. Spatial patchiness is a critical factor underlying these activities, influencing biological productivity, nutrient cycling and dynamics across trophic levels. Incorporating spatial dynamics into microbial models is a long-standing challenge, particularly where small-scale turbulence is involved. Here, we combine a fully 3D direct numerical simulation of convective mixed layer turbulence, with an individual-based microbial model to test the key hypothesis that the coupling of gyrotactic motility and turbulence drives intense microscale patchiness. The fluid model simulates turbulent convection caused by heat loss through the fluid surface, for example during the night, during autumnal or winter cooling or during a cold-air outbreak. We find that under such conditions, turbulence-driven patchiness is depth-structured and requires high motility: Near the fluid surface, intense convective turbulence overpowers motility, homogenising motile and non-motile microbes approximately equally. At greater depth, in conditions analogous to a thermocline, highly motile microbes can be over twice as patch-concentrated as non-motile microbes, and can substantially amplify their swimming velocity by efficiently exploiting fast-moving packets of fluid. Our results substantiate the predictions of earlier studies, and demonstrate that turbulence-driven patchiness is not a ubiquitous consequence of motility but rather a delicate balance of motility and turbulent intensity.

Evolution of toxins as a public good in phytoplankton

Toxic phytoplankton blooms have increased in many waterbodies worldwide with well-known negative impacts on human health, fisheries and ecosystems. However, why and how phytoplankton evolved toxin production is still a puzzling question, given that the producer that pays the costs often shares the benefit with other competing algae and thus provides toxins as a 'public good' (e.g. damaging a common competitor or predator). Furthermore, blooming phytoplankton species often show a high intraspecific variation in toxicity and we lack an understanding of what drives the dynamics of coexisting toxic and non-toxic genotypes. Here, by using an individual-based two-dimensional model, we show that small-scale patchiness of phytoplankton strains caused by demography can explain toxin evolution in phytoplankton with low motility and the maintenance of genetic diversity within their blooms. This patchiness vanishes for phytoplankton with high diffusive motility, suggesting different evolutionary pathways for different phytoplankton groups. In conclusion, our study reveals that small-scale spatial heterogeneity, generated by cell division and counteracted by diffusive cell motility and turbulence, can crucially affect toxin evolution and eco-evolutionary dynamics in toxic phytoplankton species. This contributes to a better understanding of conditions favouring toxin production and the evolution of public goods in asexually reproducing organisms in general.

Dissipation-range fluid turbulence and thermal noise

We revisit the issue of whether thermal fluctuations are relevant for incompressible fluid turbulence and estimate the scale at which they become important. As anticipated by Betchov in a prescient series of works more than six decades ago, this scale is about equal to the Kolmogorov length, even though that is several orders of magnitude above the mean free path. This result implies that the deterministic version of the incompressible Navier-Stokes equation is inadequate to describe the dissipation range of turbulence in molecular fluids. Within this range, the fluctuating hydrodynamics equation of Landau and Lifschitz is more appropriate. In particular, our analysis implies that both the exponentially decaying energy spectrum and the far-dissipation-range intermittency predicted by Kraichnan for deterministic Navier-Stokes will be generally replaced by Gaussian thermal equipartition at scales just below the Kolmogorov length. Stochastic shell model simulations at high Reynolds numbers verify our theoretical predictions and reveal furthermore that inertial-range intermittency can propagate deep into the dissipation range, leading to large fluctuations in the equipartition length scale. We explain the failure of previous scaling arguments for the validity of deterministic Navier-Stokes equations at any Reynolds number and we provide a mathematical interpretation and physical justification of the fluctuating Navier-Stokes equation as an "effective field theory" valid below some high-wave-number cutoff Λ, rather than as a continuum stochastic partial differential equation. At Reynolds number around a million, comparable to that in Earth's atmospheric boundary layer, the strongest turbulent excitations observed in our simulation penetrate down to a length scale of about eight microns, still two orders of magnitude greater than the mean free path of air. However, for longer observation times or for higher Reynolds numbers, more extreme turbulent events could lead to a local breakdown of fluctuating hydrodynamics.

Clustering of fast gyrotactic particles in low-Reynolds-number flow

Systems of particles in turbulent flows exhibit clustering where particles form patches in certain regions of space. Previous studies have shown that motile particles accumulate inside the vortices and in downwelling regions, while light and heavy non-motile particles accumulate inside and outside the vortices, respectively. While strong clustering is generated in regions of high vorticity, clustering of motile particles is still observed in fluid flows where vortices are short-lived. In this study, we investigate the clustering of fast swimming particles in a low-Reynolds-number turbulent flow and characterize the probability distributions of particle speed and acceleration and their influence on particle clustering. We simulate gyrotactic swimming particles in a cubic system with homogeneous and isotropic turbulent flow. Here, the swimming velocity explored is relatively faster than what has been explored in other reports. The fluid flow is produced by conducting a direct numerical simulation of the Navier-Stokes equation. In contrast with the previous results, our results show that swimming particles can accumulate outside the vortices, and clustering is dictated by the swimming number and is invariant with the stability number. We have also found that highly clustered particles are sufficiently characterized by their acceleration, where the increase in the acceleration frequency distribution of the most clustered particles suggests a direct influence of acceleration on clustering. Furthermore, the acceleration of the most clustered particles resides in acceleration values where a cross-over in the acceleration PDFs are observed, an indicator that particle acceleration generates clustering. Our findings on motile particles clustering can be applied to understanding the behavior of faster natural or artificial swimmers.

Gyrotactic cluster formation of bottom-heavy squirmers

Squirmers that are bottom-heavy experience a torque that aligns them along the vertical so that they swim upwards. In a suspension of many squirmers, they also interact hydrodynamically via flow fields that are initiated by their swimming motion and by gravity. Swimming under the combined action of flow field vorticity and gravitational torque is called gyrotaxis. Using the method of multi-particle collision dynamics, we perform hydrodynamic simulations of a many-squirmer system floating above the bottom surface. Due to gyrotaxis they exhibit pronounced cluster formation with increasing gravitational torque. The clusters are more volatile at low values but compactify to smaller clusters at larger torques. The mean distance between clusters is mainly controlled by the gravitational torque and not the global density. Furthermore, we observe that neutral squirmers form clusters more easily, whereas pullers require larger gravitational torques due to their additional force-dipole flow fields. We do not observe clustering for pusher squirmers. Adding a rotlet dipole to the squirmer flow field induces swirling clusters. At high gravitational strengths, the hydrodynamic interactions with the no-slip boundary create an additional vertical alignment for neutral squirmers, which also supports cluster formation.

Experimental investigation of preferential concentration in zooplankton swimming in turbulence

Turbulence can cause particles to accumulate within specific regions of the flow. One mechanism responsible for this phenomenon, called preferential concentration, consists in particle-fluid interactions yielding inhomogeneous spatial distribution of particles into clusters or depleted regions due to density difference or finite-size effects. In the case of living particles such as plankton, clustering may also originate from their motility or from their behavioral response to turbulent forcing. Preferential concentration of plankton has attracted much attention, because it is a key determinant of encounter rates and therefore relevant for a wide range of ecological processes. However, most studies have focused on microscopic cells, and consequently the case of larger organisms remains poorly studied. Here, we use high-performance particle tracking and three-dimensional Voronoï analysis to test for the emergence of clustering in the spatial distribution of calanoid copepods, the most important metazoans in the oceans in terms of biomass. We found that neither inertia nor motility resulted in significant departure from a random Poisson process over a range of turbulence intensity from very strong to moderate. However, we observed weak clustering in calm water, which may originate from hydrodynamic and olfactory interactions between organisms. Our results improve our understanding of fluid-particle interactions in the zooplankton and have important implications for the modeling of their encounter rates in turbulence.

Responding to the signal and the noise: behavior of planktonic gastropod larvae in turbulence

Swimming organisms may actively adjust their behavior in response to the flow around them. Ocean flows are typically turbulent, and characterized by chaotic velocity fluctuations. While some studies have observed planktonic larvae altering their behavior in response to turbulence, it is not always clear whether a plankter is responding to an individual turbulent fluctuation or to the time-averaged flow. To distinguish between these two paradigms, we conducted laboratory experiments with larvae in turbulence. We observed veliger larvae of the gastropod Crepidula fornicata in a jet-stirred turbulence tank while simultaneously measuring two-components of the fluid and larval velocity. Larvae were studied at two different stages of development, early-stage and late-stage, and their behavior was analyzed in response to different characteristics of turbulence: acceleration, dissipation, and vorticity. Our analysis considered both the effects of the time-averaged flow and the instantaneous flow around the larvae. Overall, we found that both stages of larvae increased their upward swimming speeds in response to increasing turbulence. However, we found that the early-stage larvae tended to respond to the time-averaged flow whereas the late-stage larvae tended to respond to the instantaneous flow around them. These observations indicate that larvae can integrate flow information over time and that their behavioral responses to turbulence can depend on both their present and past flow environments.

Unknown Extracellular and Bioactive Metabolites of the Genus Alexandrium: A Review of Overlooked Toxins

Various species of Alexandrium can produce a number of bioactive compounds, e.g., paralytic shellfish toxins (PSTs), spirolides, gymnodimines, goniodomins, and also uncharacterised bioactive extracellular compounds (BECs). The latter metabolites are released into the environment and affect a large range of organisms (from protists to fishes and mammalian cell lines). These compounds mediate allelochemical interactions, have anti-grazing and anti-parasitic activities, and have a potentially strong structuring role for the dynamic of Alexandrium blooms. In many studies evaluating the effects of Alexandrium on marine organisms, only the classical toxins were reported and the involvement of BECs was not considered. A lack of information on the presence/absence of BECs in experimental strains is likely the cause of contrasting results in the literature that render impossible a distinction between PSTs and BECs effects. We review the knowledge on Alexandrium BEC, (i.e., producing species, target cells, physiological effects, detection methods and molecular candidates). Overall, we highlight the need to identify the nature of Alexandrium BECs and urge further research on the chemical interactions according to their ecological importance in the planktonic chemical warfare and due to their potential collateral damage to a wide range of organisms.

Bacteria hinder large-scale transport and enhance small-scale mixing in time-periodic flows

Understanding mixing and transport of passive scalars in active fluids is important to many natural (e.g., algal blooms) and industrial (e.g., biofuel, vaccine production) processes. Here, we study the mixing of a passive scalar (dye) in dilute suspensions of swimming Escherichia coli in experiments using a two-dimensional (2D) time-periodic flow and in a simple simulation. Results show that the presence of bacteria hinders large-scale transport and reduces overall mixing rate. Stretching fields, calculated from experimentally measured velocity fields, show that bacterial activity attenuates fluid stretching and lowers flow chaoticity. Simulations suggest that this attenuation may be attributed to a transient accumulation of bacteria along regions of high stretching. Spatial power spectra and correlation functions of dye-concentration fields show that the transport of scalar variance across scales is also hindered by bacterial activity, resulting in an increase in average size and lifetime of structures. On the other hand, at small scales, activity seems to enhance local mixing. One piece of evidence is that the probability distribution of the spatial concentration gradients is nearly symmetric with a vanishing skewness. Overall, our results show that the coupling between activity and flow can lead to nontrivial effects on mixing and transport.

Differences in Specific Mass Density Between Dinoflagellate Life Stages and Relevance to Accumulation by Hydrodynamic Processes

One previously unstudied aspect of differences between sexual and asexual life stages in large-scale transport and accumulation is density (mass per unit volume) of cells in each life stage. The specific density was determined for Scrippsiella lachrymosa cells in medium with and without nitrogen (N) enrichment through density-gradient centrifugation. Growth medium without N addition is often called "encystment medium" when used for the purpose of resting cyst formation in cyst-forming dinoflagellates; mating gametes are usually seen after 2-3 days. Significant differences in specific density were found after 2 days in encystment medium simultaneously with the observation of typical gamete swimming behavior and mating. The specific density of cells in encystment medium was 1.06 g · cm^-3 ; whereas, the specific density of cells in growth medium was 1.11 g · cm^-3 . Cells in encystment medium were found to have significantly increased lipid content, reduced chlorophyll content, and reduced internal complexity. The findings may explain differential transport of less dense and chemotactically aggregating gametes into surface blooms in contrast to denser vegetative cells that perform daily vertical migration and do not aggregate. Passive accumulation of non-migrating gametes into layers in stagnant water also can be explained, as well as sinking of zygotes when the storage of highly dense starch increases. Resting cysts had a density of over 1.14 g · cm^-3 and would sink to become part of the silt fraction of the sediment. We suggest that differences in behavior and buoyancy between sexual and asexual life stages cause differences in cell accumulation, and therefore large-scale, environmental transport could be directly dependent upon life-cycle transitions.

Change in rheotactic behavior patterns of dinoflagellates in response to different microfluidic environments

Plankton live in dynamic fluid environments. Their ability to change in response to different hydrodynamic cues is critical to their energy allocation and resource uptake. This study used a microfluidic device to evaluate the rheotactic behaviors of a model dinoflagellate species, Karlodinium veneficum, in different flow conditions. Although dinoflagellates experienced forced alignment in strong shear (i.e. “trapping”), fluid straining did not play a decisive role in their rheotactic movements. Moderate hydrodynamic magnitude (20 < |u_f| < 40 µm s⁻¹) was found to induce an orientation heading towards an oncoming current (positive rheotaxis), as dinoflagellates switched to cross-flow swimming when flow speed exceeded 50 µm s⁻¹. Near the sidewalls of the main channel, the steric mechanism enabled dinoflagellates to adapt upstream orientation through vertical migration. Under oscillatory flow, however, positive rheotaxis dominated with occasional diversion. The varying flow facilitated upstream exploration with directional controlling, through which dinoflagellates exhibited avoidance of both large-amplitude perturbance and very stagnant zones. In the mixed layer where water is not steady, these rheotactic responses could lead to spatial heterogeneity of dinoflagellates. The outcome of this study helps clarify the interaction between swimming behaviors of dinoflagellates and the hydrodynamic environment they reside in.

Effects of Stem Density and Reynolds Number on Fine Sediment Interception by Emergent Vegetation

Suspended sediment collected by vegetation in marshes and wetlands contributes to vertical accretion, which can buffer against rising sea levels. Effective capture efficiency (ECE), a parameter quantifying the fraction of incoming suspended particles directly captured by underwater vegetation surfaces, plays a key role in determining the significance of direct interception in morphodynamic models. The ways in which physical characteristics of collectors and transitionally turbulent flows affect ECE are not yet thoroughly understood. We conducted a set of 12 experiments at three flow velocities and three stem densities (plus equivalent zero-collector control experiments), plus four experiments where biofilm was allowed to accumulate. We determined that ECE decreases with increasing collector Reynolds number (study range: 66 to 200; p < 0.05 for two of three treatments) and increasing collector density (solid volume fraction: 0.22% to 1.17%; p < 0.05 for two of three treatments). Adding biofilm increased ECE in all cases, by a multiplicative factor ranging from 1.53 to 7.15 at different collector densities and biofilm growth durations. In some cases, the impact of biofilm on ECE far outweighed that of collector Reynolds number and density. By combining our data with those of one similar study, we present a preliminary model quantitatively assessing the effect of collector density on ECE.

Bistability in oxidative stress response determines the migration behavior of phytoplankton in turbulence

Turbulence has long been known to drive phytoplankton fitness and species succession: motile species dominate in calmer environments and non-motile species in turbulent conditions. Yet a mechanistic understanding of the effect of turbulence on phytoplankton migratory behavior and physiology is lacking. By combining a method to generate turbulent cues, quantification of stress accumulation and physiology, and a mathematical model of stress dynamics, we show that motile phytoplankton use their mechanical stability to sense the intensity of turbulent cues and integrate these cues in time via stress signaling to trigger switches in migratory behavior. The stress-mediated warning strategy we discovered provides a paradigm for how phytoplankton cope with turbulence, thereby potentially governing which species will be successful in a changing ocean.

Turbulence is an important determinant of phytoplankton physiology, often leading to cell stress and damage. Turbulence affects phytoplankton migration both by transporting cells and by triggering switches in migratory behavior, whereby vertically migrating cells can actively invert their direction of migration upon exposure to turbulent cues. However, a mechanistic link between single-cell physiology and vertical migration of phytoplankton in turbulence is currently missing. Here, by combining physiological and behavioral experiments with a mathematical model of stress accumulation and dissipation, we show that the mechanism responsible for the switch in the direction of migration in the marine raphidophyte Heterosigma akashiwo is the integration of reactive oxygen species (ROS) signaling generated by turbulent cues. Within timescales as short as tens of seconds, the emergent downward-migrating subpopulation exhibited a twofold increase in ROS, an indicator of stress, 15% lower photosynthetic efficiency, and 35% lower growth rate over multiple generations compared to the upward-migrating subpopulation. The origin of the behavioral split as a result of a bistable oxidative stress response is corroborated by the observation that exposure of cells to exogenous stressors (H₂O₂, UV-A radiation, or high irradiance), in lieu of turbulence, caused comparable ROS accumulation and an equivalent split into the two subpopulations. By providing a mechanistic link between the single-cell mechanics of swimming and physiology on the one side and the emergent population-scale migratory response and impact on fitness on the other, the ROS-mediated early warning response we discovered contributes to our understanding of phytoplankton community composition in future ocean conditions.

Fractal structures arising from interfacial instabilities in bio-oil atomization

The intriguing multi-scale fractal patterns ubiquitously observed in nature similarly emerge as fascinating structures in two-phase fluid flows of bio-oil breakup and atomization processes. High-resolution microscopy of the two-phase flows under 15 flow conditions (cases of different flow rates of the liquid and co-flowing air streams as well as different degrees of liquid preheating) reveal that the geometrical complexities evolve under the competing/combined action of the instability mechanisms such as Kelvin-Helmholtz, Rayleigh-Taylor and Rayleigh-Plateau leading into the transition from break-up to atomization. A thorough analysis of the higher order moments of statistics evaluated based on the probability density functions from 15,000 fractal dimension samples suggest that a single-value analysis is not sufficient to describe the complex reshaping mechanisms in two-phase flows. Consistently positive skewness of the statistics reveal the role of abrupt two-phase mechanisms such as liquid column rupture, ligament disintegration, liquid sheet bursting and droplet distortions in a hierarchical geometrical entanglement. Further, large kurtosis values at increased flow inertia are found associated with turbulence-induced intermittent geometrical reshaping. Interestingly, the proposed power-law correlation reveals that the global droplet size obtained from laser-diffraction measurements declines as the two-phase geometrical complexity increases.

Capturing Velocity Gradients and Particle Rotation Rates in Turbulence

Turbulent fluid flows exhibit a complex small-scale structure with frequently occurring extreme velocity gradients. Particles probing such swirling and straining regions respond with an intricate shape-dependent orientational dynamics, which sensitively depends on the particle history. Here, we systematically develop a reduced-order model for the small-scale dynamics of turbulence, which captures the velocity gradient statistics along particle paths. An analysis of the resulting stochastic dynamical system allows pinpointing the emergence of non-Gaussian statistics and nontrivial temporal correlations of vorticity and strain, as previously reported from experiments and simulations. Based on these insights, we use our model to predict the orientational statistics of anisotropic particles in turbulence, enabling a host of modeling applications for complex particulate flows.

Small-scale distribution of microbes and biogeochemistry in the Great Barrier Reef

Microbial communities distribute heterogeneously at small-scales (mm-cm) due to physical, chemical and biological processes. To understand microbial processes and functions it is necessary to appreciate microbes and matter at small scales, however, few studies have determined microbial, viral, and biogeochemical distribution over space and time at these scales. In this study, the small-scale spatial and temporal distribution of microbes (bacteria and chlorophyll a), viruses, dissolved inorganic nutrients and dissolved organic carbon were determined at five locations (spatial) along the Great Barrier Reef (Australia), and over 4 consecutive days (temporal) at a coastal location. Our results show that: (1) the parameters show high small-scale heterogeneity; (2) none of the parameters measured explained the bacterial abundance distributions at these scales spatially or temporally; (3) chemical (ammonium, nitrate/nitrite, phosphate, dissolved organic carbon, and total dissolved nitrogen) and biological (chl a, and bacterial and viral abundances) measurements did not reveal significant relationships at the small scale; and (4) statistically significant differences were found between sites/days for all parameter measured but without a clear pattern.

On the fate of sinking diatoms: the transport of active buoyancy-regulating cells in the ocean

Diatoms are one of the most abundant, diverse and ecologically relevant phytoplanktonic group, contributing enormously to global biogeochemical processes like the carbon and silica cycles. This large success has been partly attributed to the mechanical and optical properties of the silica shell (the frustule) that envelops their body. But since they lack motility it is difficult to conceive how they cope with the fast-fluctuating environment they live in and where distributions of resources are very heterogeneous and dynamical. This pinpoints an important but yet poorly understood feature of diatoms physiology: buoyancy regulation that helps them controlling their sinking speed and position in the water column. While buoyancy regulation by light and nutrients availability has been well studied, the effect of hydromechanical stress via fluid shear has been rather overlooked when considering diatoms dynamics. Here, we aim to start filling this gap by first presenting direct experimental evidences for buoyancy control in response to hydro-mechanical stress and then review recent theoretical models where simple couplings between local shear and buoyancy control always result in heterogeneous cell distributions, specific accumulation regions within complex flows and increased sedimentation times to the depths, features of direct ecological relevance. We conclude by suggesting future experiments aiming to unveil such coupling and therefore gain better understanding on the fate of these fascinating microorganisms in their natural habitat. This article is part of the theme issue 'Stokes at 200 (part 2)'.

Preferential Concentration of Free-Falling Heavy Particles in Turbulence

We present a sweep-stick mechanism for heavy particles transported by a turbulent flow under the action of gravity. Direct numerical simulations show that these particles preferentially explore regions of the flow with close to zero Lagrangian acceleration. However, the actual Lagrangian acceleration of the fluid elements where particles accumulate is not zero, and has a dependence on the Stokes number, the gravity acceleration, and the settling velocity of the particles.

Diffusion properties of self-propelled particles in cellular flows

We study the dynamics of a self-propelled particle advected by a steady laminar flow. The persistent motion of the self-propelled particle is described by an active Ornstein-Uhlenbeck process. We focus on the diffusivity properties of the particle as a function of persistence time and free-diffusion coefficient, revealing non-monotonic behaviors, with the occurrence of a minimum and a steep growth in the regime of large persistence time. In the latter limit, we obtain an analytical prediction for the scaling of the diffusion coefficient with the parameters of the active force. Our study sheds light on the effect of a flow-field on the diffusion of active particles, such as living microorganisms and motile phytoplankton in fluids.

Understanding how the collective behaviour of phytoflagellates is affected by light attenuation and diel vertical migration using individual-based modelling

In this article, we investigate the question of the impact of the diel vertical migration (DVM) and the light attenuation by the cells on both spatial pattern and population dynamics of phytoflagellates. For these purposes, we performed a simulation study by using a spatially explicit individual-based model (IBM). The designed IBM includes 2 global mechanisms: cellular motion which is modelled through a stochastic differential equation and demographic process that is density and light intensity dependent. We showed that under no-DVM, for competitive environment, increasing the light absorption helps the creation of a strong oscillatory behaviour, that breeds aggregation-break up rhythm, which is beneficial. However, when we pass to DVM regime, it will be more advantageous for the cells to reduce their light absorption. In regards of DVM effect, we showed that it has other benefits, apart from the acquisition of resources, such as enhancing the attraction mechanism that promotes cooperation and also helping the creation of spatial voids that permit the penetration of the light. Also, we showed that the DVM reduces the predation rate, so we prove quantitatively that the DVM reduces, in general, the grazing losses. Also, we found that the DVM strategy depends on the impact of the competition and cooperation between the cells on the division and death rates. So, probably for the motile species, the local competition is not high in order to let the cells gain advantages from the DVM regarding their survivability that is explained by an annual cyclic behaviour under seasonal environment.

Machine learning strategies for path-planning microswimmers in turbulent flows

We develop an adversarial-reinforcement learning scheme for microswimmers in statistically homogeneous and isotropic turbulent fluid flows, in both two and three dimensions. We show that this scheme allows microswimmers to find nontrivial paths, which enable them to reach a target on average in less time than a naïve microswimmer, which tries, at any instant of time and at a given position in space, to swim in the direction of the target. We use pseudospectral direct numerical simulations of the two- and three-dimensional (incompressible) Navier-Stokes equations to obtain the turbulent flows. We then introduce passive microswimmers that try to swim along a given direction in these flows; the microswimmers do not affect the flow, but they are advected by it. Two nondimensional control parameters play important roles in our learning scheme: (a) the ratio V[over ̃]_{s} of the microswimmer's bare velocity V_{s} and the root-mean-square (rms) velocity u_{rms} of the turbulent fluid and (b) the product B[over ̃] of the microswimmer-response time B and the rms vorticity ω_{rms} of the fluid. We show that the average time required for the microswimmers to reach the target, by using our adversarial-reinforcement learning scheme, eventually reduces below the average time taken by microswimmers that follow the naïve strategy.

Effects of small-scale turbulence on two species of Dinophysis

Dinoflagellate species of Dinophysis, in particular D. acuminata and D. acuta, produce lipophilic toxins that pose a threat to human health when concentrated in shellfish and jeopardize shellfish exploitations in western Europe. In northwestern Iberia, D. acuminata has a long growing season, from spring to early autumn, and populations develop as soon as shallow stratification forms when the upwelling season begins. In contrast, D. acuta blooms in late summer, when the depth of the pycnocline is maximal and upwelling pulses are moderate. In situ observations on the hydrodynamic regimes during the two windows of opportunity for Dinophysis species led us to hypothesize that D. acuta should be more sensitive to turbulence than D. acuminata. To test this hypothesis, we studied the response of D. acuminata and D. acuta to three realistic turbulence levels low (LT), ε ≈ 10^-6 m² s^-3; medium (MT), ε ≈ 10^-5  m² s^-3 and high (HT), ε ≈ 10^-4 m² s^-3generated by Turbogen, a highly reproducible, computer-controlled system. Cells of both species exposed to LT and MT grew at rates similar to the controls. Marked differences were found in the response to HT: D. acuminata grew slowly after an initial lag phase, whereas D. acuta cell numbers declined. Results from this study support the hypothesis that turbulence may play a role in shaping the spatio-temporal distribution of individual species of Dinophysis. We also hypothesize that, in addition to cell disturbance affecting division, sustained high shear generated by microturbulence may cause a decline in Dinophysis numbers due to decreased densities of ciliate prey.

Turbulence induces clustering and segregation of non-motile, buoyancy-regulating phytoplankton

Turbulence plays a major role in shaping marine community structure as it affects organism dispersal and guides fundamental ecological interactions. Below oceanographic mesoscale dynamics, turbulence also impinges on subtle physical-biological coupling at the single cell level, setting a sea of chemical gradients and determining microbial interactions with profound effects on scales much larger than the organisms themselves. It has been only recently that we have started to disentangle details of this coupling for swimming microorganisms. However, for non-motile species, which comprise some of the most abundant phytoplankton groups on Earth, a similar level of mechanistic understanding is still missing. Here, we explore by means of extensive numerical simulations the interplay between buoyancy regulation in non-motile phytoplankton and cellular responses to turbulent mechanical cues. Using a minimal mechano-response model, we show how such a mechanism would contribute to spatial heterogeneity and affect vertical fluxes and trigger community segregation.

Chain formation can enhance the vertical migration of phytoplankton through turbulence

Many species of motile phytoplankton can actively form long multicellular chains by remaining attached to one another after cell division. While chains swim more rapidly than single cells of the same species, chain formation also markedly reduces phytoplankton's ability to maintain their bearing. This suggests that turbulence, which acts to randomize swimming direction, could sharply attenuate a chain's ability to migrate between well-lit surface waters during the day and deeper nutrient-rich waters at night. Here, we use numerical models to investigate how chain formation affects the migration of phytoplankton through a turbulent water column. Unexpectedly, we find that the elongated shape of chains helps them travel through weak to moderate turbulence much more effectively than single cells, and isolate the physical processes that confer chains this ability. Our findings provide a new mechanistic understanding of how turbulence can select for phytoplankton with elongated morphologies and may help explain why turbulence triggers chain formation.

Alignment of Nonspherical Active Particles in Chaotic Flows

We study the orientation statistics of spheroidal, axisymmetric microswimmers, with shapes ranging from disks to rods, swimming in chaotic, moderately turbulent flows. Numerical simulations show that rodlike active particles preferentially align with the flow velocity. To explain the underlying mechanism, we solve a statistical model via the perturbation theory. We show that such an alignment is caused by correlations of fluid velocity and its gradients along particle paths combined with fore-aft symmetry breaking due to both swimming and particle nonsphericity. Remarkably, the discovered alignment is found to be a robust kinematical effect, independent of the underlying flow evolution. We discuss its possible relevance for aquatic ecology.

Physical flow effects can dictate plankton population dynamics

Oceanic flows do not necessarily mix planktonic species. Differences in individual organisms’ physical and hydrodynamic properties can cause changes in drift normal to the mean flow, leading to segregation between species. This physically driven heterogeneity may have important consequences at the scale of population dynamics. Here, we describe how one form of physical forcing, circulating flows with different inertia effects between phytoplankton and zooplankton, can dramatically alter excitable plankton bloom dynamics. This may impact our understanding of the initiation and development of harmful algal blooms (HABs), which have significant negative ecological and socio-economic consequences. We study this system in detail, providing spatio-temporal dynamics for particular scenarios and summarizing large-scale behaviour via spatially averaged bifurcation diagrams. The key message is that, across a large range of parameter values, fluid flow can induce plankton blooms and mean-field population dynamics that are distinct from those predicted for well-mixed systems. The implications for oceanic population dynamic studies are manifest: we argue that the formation of HABs will depend strongly on the physical and biological state of the ecosystem, and that local increases in zooplankton heterogeneity are likely to precede phytoplankton blooms.

Not Just Going with the Flow: The Effects of Fluid Flow on Bacteria and Plankton

Microorganisms often live in habitats characterized by fluid flow, from lakes and oceans to soil and the human body. Bacteria and plankton experience a broad range of flows, from the chaotic motion characteristic of turbulence to smooth flows at boundaries and in confined environments. Flow creates forces and torques that affect the movement, behavior, and spatial distribution of microorganisms and shapes the chemical landscape on which they rely for nutrient acquisition and communication. Methodological advances and closer interactions between physicists and biologists have begun to reveal the importance of flow-microorganism interactions and the adaptations of microorganisms to flow. Here we review selected examples of such interactions from bacteria, phytoplankton, larvae, and zooplankton. We hope that this article will serve as a blueprint for a more in-depth consideration of the effects of flow in the biology of microorganisms and that this discussion will stimulate further multidisciplinary effort in understanding this important component of microorganism habitats.

Bacterial scattering in microfluidic crystal flows reveals giant active Taylor-Aris dispersion

The natural habitats of planktonic and swimming microorganisms, from algae in the oceans to bacteria living in soil or intestines, are characterized by highly heterogeneous fluid flows. The complex interplay of flow-field topology, self-propulsion, and porous microstructure is essential to a wide range of biophysical and ecological processes, including marine oxygen production, remineralization of organic matter, and biofilm formation. Although much progress has been made in the understanding of microbial hydrodynamics and surface interactions over the last decade, the dispersion of active suspensions in complex flow environments still poses unsolved fundamental questions that preclude predictive models for microbial transport and spreading under realistic conditions. Here, we combine experiments and simulations to identify the key physical mechanisms and scaling laws governing the dispersal of swimming bacteria in idealized porous media flows. By tracing the scattering dynamics of swimming bacteria in microfluidic crystal lattices, we show that hydrodynamic gradients hinder transverse bacterial dispersion, thereby enhancing stream-wise dispersion [Formula: see text]-fold beyond canonical Taylor-Aris dispersion of passive Brownian particles. Our analysis further reveals that hydrodynamic cell reorientation and Lagrangian flow structure induce filamentous density patterns that depend upon the incident angle of the flow and disorder of the medium, in striking analogy to classical light-scattering experiments.

Enhanced transport of nutrients powered by microscale flows of the self-spinning dinoflagellate Symbiodinium sp

The metabolism of a living organism (e.g. bacteria, algae, zooplankton) requires a continuous uptake of nutrients from the surrounding environment. However, within local spatial scales, nutrients are quickly used up under dense concentrations of organisms. Here, we report that self-spinning dinoflagellates Symbiodinium sp. (clade E) generate a microscale flow that mitigates competition and enhances the uptake of nutrients from the surrounding environment. Our experimental and theoretical results reveal that this incessant active behavior enhances transport by approximately 80-fold when compared with Brownian motion in living fluids. We found that the tracer ensemble probability density function for displacement is time-dependent, but consists of a Gaussian core and robust exponential tails (so-called non-Gaussian diffusion). This can be explained by interactions of far-field Brownian motions and a near-field entrainment effect along with microscale flows. The contribution of exponential tails sharply increases with algal density, and saturates at a critical density, implying a trade-off between aggregated benefit and negative competition for the spatially self-organized cells. Our work thus shows that active motion and migration of aquatic algae play key roles in diffusive transport and should be included in theoretical and numerical models of physical and biogeochemical ecosystems.

Generation of large pollution patches via collisions of sticky floating parcels driven by wind and surface currents

We study the evolution of large systems of sticky patches of pollution that float on the sea surface and are moved around by realistic wind and simulated surface currents. The study area is the Gulf of Finland in the eastern Baltic Sea that hosts extremely heavy cargo and tanker traffic. It is assumed that patches merge at collision. Collisions are enhanced by wind impact that depends on the patch size. We implement a space partitioning algorithm for fast simulations of large systems of >8000 patches and perform a series of simulations with different initial size and location of the patches. The resulting empirical distribution of the number of patches of different size is governed universally by a stretched-exponential power law f(x) = A exp (-x^b). This indicates that the evolution of large systems of pollution patches on the sea surface exhibits classic self-organization and scale invariance properties. This may be the key effect explaining how the patchiness of waste in marine environment is formed under the impact of different drivers.

Gyrotactic phytoplankton in laminar and turbulent flows: A dynamical systems approach

Gyrotactic algae are bottom heavy, motile cells whose swimming direction is determined by a balance between a buoyancy torque directing them upwards and fluid velocity gradients. Gyrotaxis has, in recent years, become a paradigmatic model for phytoplankton motility in flows. The essential attractiveness of this peculiar form of motility is the availability of a mechanistic description which, despite its simplicity, revealed predictive, rich in phenomenology, easily complemented to include the effects of shape, feedback on the fluid and stochasticity (e.g., in cell orientation). In this review we consider recent theoretical, numerical and experimental results to discuss how, depending on flow properties, gyrotaxis can produce inhomogeneous phytoplankton distributions on a wide range of scales, from millimeters to kilometers, in both laminar and turbulent flows. In particular, we focus on the phenomenon of gyrotactic trapping in nonlinear shear flows and in fractal clustering in turbulent flows. We shall demonstrate the usefulness of ideas and tools borrowed from dynamical systems theory in explaining and interpreting these phenomena.

Preferential Sampling of Elastic Chains in Turbulent Flows

A string of tracers interacting elastically in a turbulent flow is shown to have a dramatically different behavior when compared to the noninteracting case. In particular, such an elastic chain shows strong preferential sampling of the turbulent flow unlike the usual tracer limit: An elastic chain is trapped in the vortical regions. The degree of preferential sampling and its dependence on the elasticity of the chain is quantified via the Okubo-Weiss parameter. The effect of modifying the deformability of the chain via the number of links that form it is also examined.

Micro food web networks on suspended sediment

The genesis of suspended aggregates in aquatic ecosystems is not only a result of hydrodynamic mineral interactions but also a complex microbial food web network. A microbiological-physical model (BFLOC2) is introduced here to predict aggregate geometry and settling velocity under simultaneous effects of hydrodynamic and biological processes. While minerals can contribute to aggregate dynamics through collision, aggregation, and breakup, living microorganisms can colonize and establish food web interactions that involve growth and grazing, and modify the aggregate structure. The BFLOC2 model describes the aggregate dynamics resulting from interactions between minerals and three types of microorganisms, namely bacteria, flagellates, and ciliates. BFLOC2 was first calibrated against the size and capacity (fractal) dimension of aggregates formed in a pure mineral system at different mineral concentrations and fluid shear rates, and then against the abundance of aggregate-attached cells in a pure microbial environment. BFLOC2 model and calibrated parameters were then tested against biomineral aggregate size, capacity dimension, and biomass fraction formed in biomineral flocculation experiments at four nutrient concentrations. Modelling of biomineral aggregate dynamics over a wide range of environmental conditions showed that maximum aggregate size, biomass fraction, and settling velocity could occur at different optimal environmental conditions. Unlike mineral aggregates, which have maximum size when shear rate tends to zero, a relative maximum size of biomineral aggregates can be reached at intermediate shear rates as a result of microbiological processes. The settling velocity was ultimately controlled by aggregate size, capacity dimension, and biomass fraction. Microorganism dynamics including cell motility and food web network interactions significantly controlled aggregate-attached cell abundance and aggregate dynamics.

A 3D Individual-Based Model to Study Effects of Chemotaxis, Competition and Diffusion on the Motile-Phytoplankton Aggregation

In this paper, we develop a 3D-individual-based model (IBM) to understand effect of various small-scale mechanisms in phytoplankton cells, on the cellular aggregation process. These mechanisms are: spatial interactions between cells due to their chemosensory abilities (chemotaxis), a molecular diffusion and a demographical process. The latter is considered as a branching process with a density-dependent death rate to take into account the local competition on resources. We implement the IBM and simulate various scenarios under real parameter values for phytoplankton cells. To quantify the effects of the different processes quoted above on the spatial and temporal distribution of phytoplankton, we used two spatial statistics: the Clark-Evans index and the group belonging percentage. Our simulation study highlights the role of the branching process with a weak-to-medium competition in reinforcing the aggregating structure that forms from attraction mechanisms (under suitable conditions for diffusion and attraction forces), and shows by contrast that aggregations cannot form when competition is high.

Emergence of phytoplankton patchiness at small scales in mild turbulence

Phytoplankton often encounter turbulence in their habitat. As most toxic phytoplankton species are motile, resolving the interplay of motility and turbulence has fundamental repercussions on our understanding of their own ecology and of the entire ecosystems they inhabit. The spatial distribution of motile phytoplankton cells exhibits patchiness at distances of decimeter to millimeter scales for numerous species with different motility strategies. The explanation of this general phenomenon remains challenging. Furthermore, hydrodynamic cell-cell interactions, which grow more relevant as the density in the patches increases, have been so far ignored. Here, we combine particle simulations and continuum theory to study the emergence of patchiness in motile microorganisms in three dimensions. By addressing the combined effects of motility, cell-cell interaction, and turbulent flow conditions, we uncover a general mechanism: The coupling of cell-cell interactions to the turbulent dynamics favors the formation of dense patches. Identification of the important length and time scales, independent from the motility mode, allows us to elucidate a general physical mechanism underpinning the emergence of patchiness. Our results shed light on the dynamical characteristics necessary for the formation of patchiness and complement current efforts to unravel planktonic ecological interactions.

Anomalous mobility of a driven active particle in a steady laminar flow

We study, via extensive numerical simulations, the force-velocity curve of an active particle advected by a steady laminar flow, in the nonlinear response regime. Our model for an active particle relies on a colored noise term that mimics its persistent motion over a time scale [Formula: see text]. We find that the active particle dynamics shows non-trivial effects, such as negative differential and absolute mobility (NDM and ANM, respectively). We explore the space of the model parameters and compare the observed behaviors with those obtained for a passive particle ([Formula: see text]) advected by the same laminar flow. Our results show that the phenomena of NDM and ANM are quite robust with respect to the details of the considered noise: in particular for finite [Formula: see text] a more complex force-velocity relation can be observed.

Can Rates of Ocean Primary Production and Biological Carbon Export Be Related Through Their Probability Distributions?

We describe the basis of a theory for interpreting measurements of two key biogeochemical fluxes-primary production by phytoplankton (p, μg C · L^-1 · day^-1) and biological carbon export from the surface ocean by sinking particles (f, mg C · m^-2 · day^-1)-in terms of their probability distributions. Given that p and f are mechanistically linked but variable and effectively measured on different scales, we hypothesize that a quantitative relationship emerges between collections of the two measurements. Motivated by the many subprocesses driving production and export, we take as a null model that large-scale distributions of p and f are lognormal. We then show that compilations of p and f measurements are consistent with this hypothesis. The compilation of p measurements is extensive enough to subregion by biome, basin, depth, or season; these subsets are also well described by lognormals, whose log-moments sort predictably. Informed by the lognormality of both p and f we infer a statistical scaling relationship between the two quantities and derive a linear relationship between the log-moments of their distributions. We find agreement between two independent estimates of the slope and intercept of this line and show that the distribution of f measurements is consistent with predictions made from the moments of the p distribution. These results illustrate the utility of a distributional approach to biogeochemical fluxes. We close by describing potential uses and challenges for the further development of such an approach.

Evidence for ubiquitous preferential particle orientation in representative oceanic shear flows

In situ measurements were undertaken to characterize particle fields in undisturbed oceanic environments. Simultaneous, co-located depth profiles of particle fields and flow characteristics were recorded using a submersible holographic imaging system and an acoustic Doppler velocimeter, under different flow conditions and varying particle concentration loads, typical of those found in coastal oceans and lakes. Nearly one million particles with major axis lengths ranging from ∼14 μm to 11.6 mm, representing diverse shapes, sizes, and aspect ratios were characterized as part of this study. The particle field consisted of marine snow, detrital matter, and phytoplankton, including colonial diatoms, which sometimes formed "thin layers" of high particle abundance. Clear evidence of preferential alignment of particles was seen at all sampling stations, where the orientation probability density function (PDF) peaked at near horizontal angles and coincided with regions of low velocity shear and weak turbulent dissipation rates. Furthermore, PDF values increased with increasing particle aspect ratios, in excellent agreement with models of spheroidal particle motion in simple shear flows. To the best of our knowledge, although preferential particle orientation in the ocean has been reported in two prior cases, our findings represent the first comprehensive field study examining this phenomenon. Evidence of nonrandom particle alignment in aquatic systems has significant consequences to aquatic optics theory and remote sensing, where perfectly random particle orientation and thus isotropic symmetry in optical parameters is assumed. Ecologically, chain-forming phytoplankton may have evolved to form large aspect ratio chains as a strategy to optimize light harvesting.

Statistical Model for the Orientation of Nonspherical Particles Settling in Turbulence

The orientation of small anisotropic particles settling in a turbulent fluid determines some essential properties of the suspension. We show that the orientation distribution of small heavy spheroids settling through turbulence can be accurately predicted by a simple Gaussian statistical model that takes into account particle inertia and provides a quantitative understanding of the orientation distribution on the problem parameters when fluid inertia is negligible. Our results open the way to a parametrization of the distribution of ice crystals in clouds, and potentially lead to an improved understanding of radiation reflection or particle aggregation through collisions in clouds.