Immiscible Rayleigh-Taylor turbulence: Implications for bacterial degradation in oil spills.

An unstable density stratification between two fluids mixes spontaneously under the effect of gravity, a phenomenon known as Rayleigh-Taylor (RT) turbulence. If the two fluids are immiscible, for example, oil and water, surface tension prevents intermixing at the molecular level. However, turbulence fragments one fluid into the other, generating an emulsion in which the typical droplet size decreases over time as a result of the competition between the rising kinetic energy and the surface energy density. Even though the first phenomenological theory describing this emulsification process was derived many years ago, it has remained elusive to experimental verification, hampering our ability to predict the fate of oil in applications such as deep-water spills. Here, we provide the first experimental and numerical verification of the immiscible RT turbulence theory, unveiling a unique turbulent state that originates at the oil-water interface due to the interaction of multiple capillary waves. We show that a single, non-dimensional, and time-independent parameter controls the range of validity of the theory. Our findings have wide-ranging implications for the understanding of the mixing of immiscible fluids. This includes in particular oil spills, where our work enables the prediction of the oil-water interface dynamics that ultimately determine the rate of oil biodegradation by marine bacteria.

Steering self-organisation through confinement.

Self-organisation is the spontaneous emergence of spatio-temporal structures and patterns from the interaction of smaller individual units. Examples are found across many scales in very different systems and scientific disciplines, from physics, materials science and robotics to biology, geophysics and astronomy. Recent research has highlighted how self-organisation can be both mediated and controlled by confinement. Confinement is an action over a system that limits its units' translational and rotational degrees of freedom, thus also influencing the system's phase space probability density; it can function as either a catalyst or inhibitor of self-organisation. Confinement can then become a means to actively steer the emergence or suppression of collective phenomena in space and time. Here, to provide a common framework and perspective for future research, we examine the role of confinement in the self-organisation of soft-matter systems and identify overarching scientific challenges that need to be addressed to harness its full scientific and technological potential in soft matter and related fields. By drawing analogies with other disciplines, this framework will accelerate a common deeper understanding of self-organisation and trigger the development of innovative strategies to steer it using confinement, with impact on, e.g., the design of smarter materials, tissue engineering for biomedicine and in guiding active matter.

Dimensional effects in Rayleigh-Taylor mixing.

We study the effects of dimensional confinement on the evolution of incompressible Rayleigh-Taylor mixing both in a bulk flow and in porous media by means of numerical simulations of the transport equations. In both cases, the confinement to two-dimensional flow accelerates the mixing process and increases the speed of the mixing layer. Dimensional confinement also produces stronger correlations between the density and the velocity fields affecting the efficiency of the mass transfer, quantified by the dependence of the Nusselt number on the Rayleigh number. This article is part of the theme issue 'Scaling the turbulence edifice (part 2)'.

Conformal invariance of weakly compressible two-dimensional turbulence.

We study conformal invariance of vorticity clusters in weakly compressible two-dimensional turbulence at low Mach numbers. On the basis of very high resolution direct numerical simulation we demonstrate the scaling invariance of the inverse cascade with scaling close to Kolmogorov prediction. In this range of scales, the statistics of zero-vorticity isolines are found to be compatible with those of critical percolation, thus generalizing the results obtained in incompressible Navier-Stokes turbulence.

Condensate formation and multiscale dynamics in two-dimensional active suspensions.

The collective effects of microswimmers in active suspensions result in active turbulence, a spatiotemporally chaotic dynamics at mesoscale, which is characterized by the presence of vortices and jets at scales much larger than the characteristic size of the individual active constituents. To describe this dynamics, Navier-Stokes-based one-fluid models driven by small-scale forces have been proposed. Here, we provide a justification of such models for the case of dense suspensions in two dimensions (2D). We subsequently carry out an in-depth numerical study of the properties of one-fluid models as a function of the active driving in view of possible transition scenarios from active turbulence to large-scale pattern, referred to as condensate, formation induced by the classical inverse energy cascade in Newtonian 2D turbulence. Using a one-fluid model it was recently shown [M. Linkmann et al., Phys. Rev. Lett 122, 214503 (2019)10.1103/PhysRevLett.122.214503] that two-dimensional active suspensions support two nonequilibrium steady states, one with a condensate and one without, which are separated by a subcritical transition. Here, we report further details on this transition such as hysteresis and discuss a low-dimensional model that describes the main features of the transition through nonlocal-in-scale coupling between the small-scale driving and the condensate.

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.

Phase Transition to Large Scale Coherent Structures in Two-Dimensional Active Matter Turbulence.

The collective motion of microswimmers in suspensions induce patterns of vortices on scales that are much larger than the characteristic size of a microswimmer, attaining a state called bacterial turbulence. Hydrodynamic turbulence acts on even larger scales and is dominated by inertial transport of energy. Using an established modification of the Navier-Stokes equation that accounts for the small-scale forcing of hydrodynamic flow by microswimmers, we study the properties of a dense suspension of microswimmers in two dimensions, where the conservation of enstrophy can drive an inverse cascade through which energy is accumulated on the largest scales. We find that the dynamical and statistical properties of the flow show a sharp transition to the formation of vortices at the largest length scale. The results show that 2D bacterial and hydrodynamic turbulence are separated by a subcritical phase transition.

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.

Time irreversibility in reversible shell models of turbulence.

Turbulent flows governed by the Navier-Stokes equations (NSE) generate an out-of-equilibrium time irreversible energy cascade from large to small scales. In the NSE, the energy transfer is due to the nonlinear terms that are formally symmetric under time reversal. As for the dissipative term: first, it explicitly breaks time reversibility; second, it produces a small-scale sink for the energy transfer that remains effective even in the limit of vanishing viscosity. As a result, it is not clear how to disentangle the time irreversibility originating from the non-equilibrium energy cascade from the explicit time-reversal symmetry breaking due to the viscous term. To this aim, in this paper we investigate the properties of the energy transfer in turbulent shell models by using a reversible viscous mechanism, avoiding any explicit breaking of the [Formula: see text] symmetry. We probe time irreversibility by studying the statistics of Lagrangian power, which is found to be asymmetric under time reversal also in the time-reversible model. This suggests that the turbulent dynamics converges to a strange attractor where time reversibility is spontaneously broken and whose properties are robust for what concerns purely inertial degrees of freedoms, as verified by the anomalous scaling behavior of the velocity structure functions.

Statistical conservation law in two- and three-dimensional turbulent flows.

Particles in turbulence live complicated lives. It is nonetheless sometimes possible to find order in this complexity. It was proposed in Falkovich et al. [Phys. Rev. Lett. 110, 214502 (2013)] that pairs of Lagrangian tracers at small scales, in an incompressible isotropic turbulent flow, have a statistical conservation law. More specifically, in a d-dimensional flow the distance R(t) between two neutrally buoyant particles, raised to the power -d and averaged over velocity realizations, remains at all times equal to the initial, fixed, separation raised to the same power. In this work we present evidence from direct numerical simulations of two- and three-dimensional turbulence for this conservation. In both cases the conservation is lost when particles exit the linear flow regime. In two dimensions we show that, as an extension of the conservation law, an Evans-Cohen-Morriss or Gallavotti-Cohen type fluctuation relation exists. We also analyze data from a 3D laboratory experiment [Liberzon et al., Physica D 241, 208 (2012)], finding that although it probes small scales they are not in the smooth regime. Thus instead of 〈R-3〉, we look for a similar, power-law-in-separation conservation law. We show that the existence of an initially slowly varying function of this form can be predicted but that it does not turn into a conservation law. We suggest that the conservation of 〈R-d〉, demonstrated here, can be used as a check of isotropy, incompressibility, and flow dimensionality in numerical and laboratory experiments that focus on small scales.

Flight-crash events in turbulence.

The statistical properties of turbulence differ in an essential way from those of systems in or near thermal equilibrium because of the flux of energy between vastly different scales at which energy is supplied and at which it is dissipated. We elucidate this difference by studying experimentally and numerically the fluctuations of the energy of a small fluid particle moving in a turbulent fluid. We demonstrate how the fundamental property of detailed balance is broken, so that the probabilities of forward and backward transitions are not equal for turbulence. In physical terms, we found that in a large set of flow configurations, fluid elements decelerate faster than accelerate, a feature known all too well from driving in dense traffic. The statistical signature of rare "flight-crash" events, associated with fast particle deceleration, provides a way to quantify irreversibility in a turbulent flow. Namely, we find that the third moment of the power fluctuations along a trajectory, nondimensionalized by the energy flux, displays a remarkable power law as a function of the Reynolds number, both in two and in three spatial dimensions. This establishes a relation between the irreversibility of the system and the range of active scales. We speculate that the breakdown of the detailed balance characterized here is a general feature of other systems very far from equilibrium, displaying a wide range of spatial scales.

Turbulent fluid acceleration generates clusters of gyrotactic microorganisms.

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.

Universal profile of the vortex condensate in two-dimensional turbulence.

An inverse turbulent cascade in a restricted two-dimensional periodic domain creates a condensate-a pair of coherent system-size vortices. We perform extensive numerical simulations of this system and carry out theoretical analysis based on momentum and energy exchanges between the turbulence and the vortices. We show that the vortices have a universal internal structure independent of the type of small-scale dissipation, small-scale forcing, and boundary conditions. The theory predicts not only the vortex inner region profile, but also the amplitude, which both perfectly agree with the numerical data.

Turbulence drives microscale patches of motile phytoplankton.

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.

Unraveling the influence of endothelial cell density on VEGF-A signaling.

Vascular endothelial growth factor-A (VEGF) is the master determinant for the activation of the angiogenic program leading to the formation of new blood vessels to sustain solid tumor growth and metastasis. VEGF specific binding to VEGF receptor-2 (VEGFR-2) triggers different signaling pathways, including phospholipase C-γ (PLC-γ) and Akt cascades, crucial for endothelial proliferation, permeability, and survival. By combining biologic experiments, theoretical insights, and mathematical modeling, we found that: (1) cell density influences VEGFR-2 protein level, as receptor number is 2-fold higher in long-confluent than in sparse cells; (2) cell density affects VEGFR-2 activation by reducing its affinity for VEGF in long-confluent cells; (3) despite reduced ligand-receptor affinity, high VEGF concentrations provide long-confluent cells with a larger amount of active receptors; (4) PLC-γ and Akt are not directly sensitive to cell density but simply transduce downstream the upstream difference in VEGFR-2 protein level and activation; and (5) the mathematical model correctly predicts the existence of at least one protein tyrosine phosphatase directly targeting PLC-γ and counteracting the receptor-mediated signal. Our data-based mathematical model quantitatively describes VEGF signaling in quiescent and angiogenic endothelium and is suitable to identify new molecular determinants and therapeutic targets.

Drag reduction in the turbulent Kolmogorov flow.

We investigate the phenomenon of drag reduction in a viscoelastic fluid model of dilute polymer solutions. By means of direct numerical simulations of the three-dimensional turbulent Kolmogorov flow we show that drag reduction takes place above a critical Reynolds number Re(c). An explicit expression for the dependence of Re(c) on polymer elasticity and diffusivity is derived. The values of the drag coefficient obtained for different fluid parameters collapse onto a universal curve when plotted as a function of the rescaled Reynolds number Re/ Re(c). The analysis of the momentum budget allows us to gain some insight on the physics of drag reduction, and suggests the existence of a Re-independent value of the drag cofficient--lower than the Newtonian one--for large Reynolds numbers.

Lagrangian tracers on a surface flow: the role of time correlations.

Finite time correlations of the velocity in a surface flow are found to be important for the formation of clusters of Lagrangian tracers. The degree of clustering characterized by the Lyapunov spectrum of the flow is numerically shown to be in qualitative agreement with the predictions for the white-in-time compressible Kraichnan flow, but to deviate quantitatively. For intermediate values of compressibility the clustering is surprisingly weakened by time correlations.

Two-dimensional turbulence of dilute polymer solutions.

We investigate theoretically and numerically the effect of polymer additives on two-dimensional turbulence by means of a viscoelastic model. We provide compelling evidence that, at vanishingly small concentrations, such that the polymers are passively transported, the probability distribution of polymer elongation has a power law tail: Its slope is related to the statistics of finite-time Lyapunov exponents of the flow, in quantitative agreement with theoretical predictions. We show that at finite concentrations and sufficiently large elasticity the polymers react on the flow with manifold consequences: Velocity fluctuations are drastically depleted, as observed in soap film experiments; the velocity statistics becomes strongly intermittent; the distribution of finite-time Lyapunov exponents shifts to lower values, signaling the reduction of Lagrangian chaos.

Diffusive transport and self-consistent dynamics in coupled maps.

The study of diffusion in Hamiltonian systems has been a problem of interest for a number of years. In this paper we explore the influence of self-consistency on the diffusion properties of systems described by coupled symplectic maps. Self-consistency, i.e., the backinfluence of the transported quantity on the velocity field of the driving flow, despite of its critical importance, is usually overlooked in the description of realistic systems, for example, in plasma physics. We propose a class of self-consistent models consisting of an ensemble of maps globally coupled through a mean field. Depending on the kind of coupling, two different general types of self-consistent maps are considered: maps coupled to the field only through the phase, and fully coupled maps, i.e., through the phase and the amplitude of the external field. The analogies and differences of the diffusion properties of these two kinds of maps are discussed in detail.