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It has been long known that the addition of linear friction on two-dimensional Navier-Stokes (NS) turbulence, often referred to as Ekman-Navier-Stokes (ENS) turbulence, induces strong intermittent fluctuations on small-scale vorticity. Such fluctuations are strong enough to be measurable at low-order statistics such as the energy or enstrophy spectrum. Simple heuristics lead to corrections in the spectrum which are proportional to the linear friction coefficient. In this work, we study the spectral correction by the implementation of a GPU-accelerated high-resolution numerical simulation of ENS covering a large range of Reynolds numbers. Among our findings, we highlight the importance of non-locality when comparing the expected results to the measured ones.

We study the temporal fluctuations of the flux of surface potential energy in Surface Quasi-Geostrophic (SQG) turbulence. By means of high-resolution, direct numerical simulations of the SQG model in the regime of forced and dissipated cascade of temperature variance, we show that the instantaneous imbalance in the energy budget originates a subleading correction to the spectrum of the turbulent cascade. Using a multiple-scale approach combined with a dimensional closure we derive a theoretical prediction for the power-law behavior of the corrections, which holds for a class of turbulent transport equations known as {\alpha}-turbulence. Further, we develop and apply a method to disentangle the equilibrium and non-equilibrium contribution in the instantaneous spectra, which can be generalized to other turbulent systems.

We study the statistics of free-surface turbulence at large Reynolds numbers produced by direct numerical simulations in a fluid layer at different thickness with fixed characteristic forcing scale. We observe the production of a transient inverse cascade, with a duration which depends on the thickness of the layer, followed by a transition to three-dimensional turbulence initially produced close to the bottom, no-slip boundary. By switching off the forcing, we study the decaying turbulent regime and we find that it cannot be described by an exponential law. Our results show that boundary conditions play a fundamental role in the nature of turbulence produced in thin layers and give limits on the conditions to produce a two-dimensional phenomenology., Comment: 9 pages, 8 figures

We study, by means of extensive direct numerical simulations, the turbulent flow produced by a two-dimensional cellular forcing in a cubic box with periodic boundary conditions. In spite of the strong anisotropy of the forcing, we find that turbulence recovers almost complete isotropy at small scales. Nonetheless, the signature of the forcing remains in the mean flow (averaged over time and over the homogeneous direction) and this allows to introduce a friction factor, whose dependence on the Reynolds number is investigated. We further find that the flow is characterized by large temporal fluctuations of the total energy, as a consequence of the exchange between the forced mean flow at large scales and turbulent fluctuations at small scales. Such temporal fluctuations produce a correction to the energy spectrum that can be explained by a simple dimensional argument., Comment: 11 pages, 9 figures

We report the numerical evidence of a new state of active turbulence in confined domains. By means of extensive numerical simulations of the Toner-Tu-Swift-Hohenberg model for dense bacterial suspensions in circular geometry, we discover the formation a stable, ordered state in which the angular momentum symmetry is broken. This is achieved by self-organization of a turbulent-like flow into a single, giant vortex of the size of the domain. The giant vortex is surrounded by an annular region close to the boundary, characterized by small-scale, radial vorticity streaks. The average radial velocity profile of the vortex is found to be in agreement with a simple analytical prediction. We also provide an estimate of the temporal and spatial scales of a suitable experimental setup comparable with our numerical findings., Comment: 5 pages, 4 figures

Many aquatic microorganisms are able to swim. In natural environments they typically do so in the presence of flows. In recent years it has been shown that the interplay of swimming and flows can give rise to interesting and biologically relevant phenomena, such as accumulation of microorganisms in specific flow regions and local alignment with the flow properties. Here, we consider a mechanical model for elongated microswimmers in a Kolmogorov flow, a prototypic shear flow, both in steady and in turbulent conditions. By means of direct numerical simulations, supported by analytical calculation in a simplified stochastic setting, we find that the alignment of the swimming direction with the local velocity is a general phenomenon. We also explore how the accumulation of microorganisms, typically observed in steady flows, is modified by the presence of unsteady fluctuations., Comment: 17 pages, 6 figures

We report of a series of laboratory experiments and numerical simulations of freely-decaying rotating turbulent flows confined in domains with variable height. We show that the vertical confinement has important effects on the formation of large-scale columnar vortices, the hallmark of rotating turbulence, and in particular delays the development of the cyclone-anticyclone asymmetry. We compare the experimental and numerical results face-to-face, showing the robustness of the results., Comment: 12 pages, 10 figures

Particles suspended in a fluid exert feedback forces that can significantly impact the flow, altering the turbulent drag and velocity fluctuations. We study flow modulation induced by particles heavier than the carrier fluid in the framework of an Eulerian two-way coupled model, where particles are represented by a continuum density transported by a compressible velocity field, exchanging momentum with the fluid phase. We implement the model in direct numerical simulations of the turbulent Kolmogorov flow, a simplified setting allowing for studying the momentum balance and the turbulent drag in the absence of boundaries. We show that the amplitude of the mean flow and the turbulence intensity are reduced by increasing particle mass loading with the consequent enhancement of the friction coefficient. Surprisingly, turbulence suppression is stronger for particles of smaller inertia. We understand such a result by mapping the equations for dusty flow, in the limit of vanishing inertia, to a Newtonian flow with an effective forcing reduced by the increase in fluid density due to the presence of particles. We also discuss the negative feedback produced by turbophoresis which mitigates the effects of particles, especially with larger inertia, on the turbulent flow., Comment: 20 pages, 7 figures

Pushing two fluids with different density one against the other causes the development of the Rayleigh-Taylor instability at their interface, which further evolves in a complex mixing layer. In porous media, this process is influenced by the viscous resistance experienced while flowing through the pores, which is described by the Darcy's law. Here, we investigate the mixing properties of the Darcy-Rayleigh-Taylor system in the limit of large P\'eclet number by means of direct numerical simulations in three and two dimensions. In the mixing zone, the balance between gravity and viscous forces results in a non-self-similar growth of elongated plumes, whose length increases linearly in time while their width follows a diffusive growth. The mass-transfer Nusselt number is found to increase linearly with the Darcy-Rayleigh number supporting a universal scaling in porous convection at high Ra numbers. Finally, we find that the mixing process displays important quantitative differences between two and three dimensions., Comment: 7 pages, 3 figures

We investigate the effects of turbulent fluctuations on the Lagrangian statistics of absorption of a scalar field by tracer particles, as a model for nutrient uptake by suspended non-motile microorganisms. By means of extensive direct numerical simulations of an Eulerian-Lagrangian model we quantify, in terms of the Sherwood number, the increase of the scalar uptake induced by turbulence and its dependence on the Peclet and Reynolds numbers. Numerical results are compared with classical predictions for a stationary shear flow extended here to take into account the presence of a restoring scalar flux. We find that mean field predictions agree with numerical simulations at low Peclet numbers but are unable to describe the large fluctuations of local scalar uptake observed for large Peclet numbers. We also study the role of velocity fluctuations in the local uptake by looking at the temporal correlation between local shear and uptake rate and we find that the latter follows fluid velocity fluctuations with a delay given by Kolmogorov time scale. The relevance of our results for aquatic microorganisms is also discussed., Comment: 20 pages, 7 figures

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 rod-like active particles preferentially align with the flow velocity. To explain the underlying mechanism we solve a statistical model via perturbation theory. We show that such 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., Comment: 5 pages, 3 figures, Supplements in Ancillary directory, accepted in Physical Review Letters

Rayleigh--Taylor fluid turbulence through a bed of rigid, finite-size, spheres is investigated by means of high-resolution Direct Numerical Simulations (DNS), fully coupling the fluid and the solid phase via a state-of-the art Immersed Boundary Method (IBM). The porous character of the medium reveals a totally different physics for the mixing process when compared to the well-known phenomenology of classical RT mixing. For sufficiently small porosity, the growth-rate of the mixing layer is linear in time (instead of quadratical) and the velocity fluctuations tend to saturate to a constant value (instead of linearly growing). We propose an effective continuum model to fully explain these results where porosity originated by the finite-size spheres is parameterized by a friction coefficient., Comment: 5 pages, 6 figures

The dynamics of Rayleigh-Taylor turbulence convection in presence of an alternating, time periodic acceleration is studied by means of extensive direct numerical simulations of the Boussinesq equations. Within this framework, we discover a new mechanism of relaminarization of turbulence: The alternating acceleration, which initially produces a growing turbulent mixing layer, at longer times suppresses turbulent fluctuation and drives the system toward an asymptotic stationary configuration. Dimensional arguments and linear stability theory are used to predict the width of the mixing layer in the asymptotic state as a function of the period of the acceleration. Our results provide an example of simple control and suppression of turbulent convection with potential applications in different fields., Comment: 5 pages, 5 figures

We present a technique for measuring the two-dimensional surface water wave elevation both in space and time based on the low-cost Microsoft Kinect sensor. We discuss the capabilities of the system and a method for its calibration. We illustrate the application of the Kinect to an experiment in a small wave tank. A detailed comparison with standard capacitive wave gauges is also performed. Spectral analysis of a random-forced wave field is used to obtain the dispersion relation of water waves, demonstrating the potentialities of the setup for the investigation of the statistical properties of surface waves.

We study the chaoticity and the predictability of a turbulent flow on the basis of high-resolution direct numerical simulations at different Reynolds numbers. We find that the Lyapunov exponent of turbulence, which measures the exponential separation of two initially close solution of the Navier-Stokes equations, grows with the Reynolds number of the flow, with an anomalous scaling exponent, larger than the one obtained on dimensional grounds. For large perturbations, the error is transferred to larger, slower scales where it grows algebraically generating an "inverse cascade" of perturbations in the inertial range. In this regime our simulations confirm the classical predictions based on closure models of turbulence. We show how to link chaoticity and predictability of a turbulent flow in terms of a finite size extension of the Lyapunov exponent., Comment: 5 pages, 5 figures

We present an efficient point-particle approach to simulate reaction-diffusion processes of spherical absorbing particles in the diffusion-limited regime, as simple models of cellular uptake. The exact solution for a single absorber is used to calibrate the method, linking the numerical parameters to the physical particle radius and uptake rate. We study configurations of multiple absorbers of increasing complexity to examine the performance of the method, by comparing our simulations with available exact analytical or numerical results. We demonstrate the potentiality of the method in resolving the complex diffusive interactions, here quantified by the Sherwood number, measuring the uptake rate in terms of that of isolated absorbers. We implement the method in a pseudo-spectral solver that can be generalized to include fluid motion and fluid-particle interactions. As a test case of the presence of a flow, we consider the uptake rate by a particle in a linear shear flow. Overall, our method represents a powerful and flexible computational tool that can be employed to investigate many complex situations in biology, chemistry and related sciences., Comment: 13 pages, 13 figures

The turbulent Rayleigh--Taylor system in a rotating reference frame is investigated by direct numerical simulations within the Oberbeck-Boussinesq approximation. On the basis of theoretical arguments, supported by our simulations, we show that the Rossby number decreases in time, and therefore the Coriolis force becomes more important as the system evolves and produces many effects on Rayleigh--Taylor turbulence. We find that rotation reduces the intensity of turbulent velocity fluctuations and therefore the growth rate of the temperature mixing layer. Moreover, in presence of rotation the conversion of potential energy into turbulent kinetic energy is found to be less effective and the efficiency of the heat transfer is reduced. Finally, during the evolution of the mixing layer we observe the development of a cyclone-anticyclone asymmetry.

We study the time irreversibility of the direct cascade in two-dimensional turbulence by looking at the time derivative of the square vorticity along Lagrangian trajectories, a quantity which we call metenstrophy. By means of extensive numerical simulations we measure the time irreversibility from the asymmetry of the PDF of the metenstrophy and we find that it increases with the Reynolds number of the cascade, similarly to what found in three-dimensional turbulence. A detailed analysis of the different contributions to the enstrophy budget reveals a remarkable difference with respect to what observed for the direct cascade, in particular the role of the statistics of the forcing to determine the degree of irreversibility., Comment: 6 pages, 7 figures

A suspension of gyrotactic microalgae Chlamydomonas augustae swimming in a cylindrical water vessel in solid-body rotation is studied. Our experiments show that swimming algae form an aggregate around the axis of rotation, whose intensity increases with the rotation speed. We explain this phenomenon by the centripetal orientation of the swimming direction towards the axis of rotation. This centripetal focusing is contrasted by diffusive fluxes due to stochastic reorientation of the cells. The competition of the two effects lead to a stationary distribution, which we analytically derive from a refined mathematical model of gyrotactic swimmers. The temporal evolution of the cell distribution, obtained via numerical simulations of the stochastic model, is in quantitative agreement with the experimental measurements in the range of parameters explored., Comment: 16 pages, 5 figures

We study the motion of small inertial particles in stratified turbulence. We derive a simplified model, valid within the Boussinesq approximation, for the dynamics of small particles in presence of a mean linear density profile. By means of extensive direct numerical simulations, we investigate the statistical distribution of particles as a function of the two dimensionless parameters of the problem. We find that vertical confinement of particles is mainly ruled by the degree of stratification, with a weak dependency on the particle properties. Conversely, small scale fractal clustering, typical of inertial particles in turbulence, depends on the particle relaxation time and is almost independent on the flow stratification. The implications of our findings for the formation of thin phytoplankton layers are discussed., Comment: 5 pages, 6 figures

Numerical simulations of a thin layer of turbulent flow in stably stratified conditions within the Boussinesq approximation have been performed. The statistics of energy transfer among scales have been investigated for different values of control parameters: thickness of the layer and density stratification. It is shown that in a thin layer with a quasi-two-dimensional phenomenology, stratification provides a new channel for the energy transfer towards small scales and reduces the inverse cascade. The role of vortex stretching and enstrophy flux in the transfer of kinetic energy into potential energy at small scales is discussed., Comment: 15 pages, 8 figures

The Kolmogorov flow provides an ideal instance of a virtual channel flow: It has no boundaries, but nevertheless it possesses well defined mean flow in each half-wavelength. We exploit this remarkable feature for the purpose of investigating the interplay between the mean flow and the turbulent drag of the bulk flow. By means of a set of direct numerical simulations at increasing Reynolds number we show the dependence of the bulk turbulent drag on the amplitude of the mean flow. Further, we present a detailed analysis of the scale-by-scale energy balance, which describes how kinetic energy is redistributed among different regions of the flow while being transported toward small dissipative scales. Our results allow us to obtain an accurate prediction for the spatial energy transport at large scales., Comment: 7 pages, 8 figures

We study the effect of surface gravity waves on the motion of inertial particles in an incompressible fluid. Using the multiple-scale technique, we perform an analytical calculation which allows us to predict the dynamics of such particles; results are shown for both the infinite- and finite-depth regimes. Numerical simulations based on the velocity field resulting from the second-order Stokes theory for the surface elevation have been performed, and an excellent agreement with the analytical predictions is observed. Such an agreement seems to hold even beyond the formal applicability of the theory. We find that the presence of inertia leads to a non-negligible correction to the well-known horizontal Stokes drift; moreover, we find that the vertical velocity is also affected by a drift. The latter result may have some relevant consequences on the rate of sedimentation of particles of finite size. We underline that such a drift would also be observed in the (hypothetical) absence of the gravitational force., Comment: 9 pages, 4 figures

We study the clustering properties of inertial particles in a turbulent viscoelastic fluid. The investigation is carried out by means of direct numerical simulations of turbulence in the Oldroyd-B model. The effects of polymers on the small scale properties of homogeneous turbulence are considered in relation with their consequences on clustering of particles, both lighter and heavier than the carrying fluid. We show that, depending on particle and flow parameters, polymers can either increase or decrease clustering.

A signature of El Nino-Southern Oscillation is found in the historical dataset of the Alaskan Tanana river breakups where the average ice breaking day is found to anticipate of about 3.4 days when conditioned over El Nino years. This results represents a statistically significant example of ENSO teleconnection on regions remote from tropical Pacific., Comment: 4 pages, 2 figures; never able to publish

The role of polymers additives on the turbulent convective flow of a Rayleigh--Taylor system is investigated by means of direct numerical simulations (DNS) of Oldroyd-B viscoelastic model. The dynamics of polymers elongation follow adiabatically the self-similar evolution of the turbulent mixing layer, and shows the appearance of a strong feedback on the flow which originate a cut off for polymer elongations. The viscoelastic effects on the mixing properties of the flow are twofold. Mixing is appreciably enhanced at large scales (the mixing layer growth-rate is larger than that of the purely Newtonian case) and depleted at small scales (thermal plumes are more coherent with respect to the Newtonian case). The observed speed up of the thermal plumes, together with an increase of the correlations between temperature field and vertical velocity, contributes to a significant {\it enhancement of heat transport}. Our findings are consistent with a scenario of {\it drag reduction} between falling and rising plumes induced by polymers, and provide further evidence of the occurrence of drag reduction in absence of boundary layers. A weakly non-linear model proposed by Fermi for the growth of the mixing layer is reported in the Appendix., Comment: 19 pages, 12 figures

We investigate the statistical properties of Rayleigh-Taylor turbulence in a convective cell of high aspect ratio, in which one transverse side is much smaller that the others. We show that the scale of confinement determines the Bolgiano scale of the system, which in the late stage of the evolution is characterized by the Kolmogorov-Obukhov and the Bolgiano-Obukhov phenomenology at small and large scales, respectively. The coexistence of these regimes is associated to a three to two-dimensional transition of the system which occurs when the width of the turbulent mixing layer becomes larger that the scale of confinement., Comment: 4 pages, 5 figures

We investigate the dynamics of the two-dimensional periodic Kolmogorov flow of a viscoelastic fluid, described by the Oldroyd-B model, by means of direct numerical simulations. Above a critical Weissenberg number the flow displays a transition from stationary to randomly fluctuating states, via periodic ones. The increasing complexity of the flow in both time and space at progressively higher values of elasticity accompanies the establishment of mixing features. The peculiar dynamical behavior observed in the simulations is found to be related to the appearance of filamental propagating patterns, which develop even in the limit of very small inertial non-linearities, thanks to the feedback of elastic forces on the flow., Comment: 10 pages, 14 figures

Three-dimensional miscible Rayleigh--Taylor (RT) turbulence at small Atwood number and at Prandtl number one is investigated by means of high resolution direct numerical simulations of the Boussinesq equations. RT turbulence is a paradigmatic time-dependent turbulent system in which the integral scale grows in time following the evolution of the mixing region. In order to fully characterize the statistical properties of the flow, both temporal and spatial behavior of relevant statistical indicators have been analyzed. Scaling of both global quantities ({\it e.g.}, Rayleigh, Nusselt and Reynolds numbers) and scale dependent observables built in terms of velocity and temperature fluctuations are considered. We extend the mean-field analysis for velocity and temperature fluctuations to take into account intermittency, both in time and space domains. We show that the resulting scaling exponents are compatible with those of classical Navier--Stokes turbulence advecting a passive scalar at comparable Reynolds number. Our results support the scenario of universality of turbulence with respect to both the injection mechanism and the geometry of the flow.

Statistical features of homogeneous, isotropic, two-dimensional turbulence is discussed on the basis of a set of direct numerical simulations up to the unprecedented resolution $32768^2$. By forcing the system at intermediate scales, narrow but clear inertial ranges develop both for the inverse and for direct cascades where the two Kolmogorov laws for structure functions are, for the first time, simultaneously observed. The inverse cascade spectrum is found to be consistent with Kolmogorov-Kraichnan prediction and is robust with respect the presence of an enstrophy flux. The direct cascade is found to be more sensible to finite size effects: the exponent of the spectrum has a correction with respect theoretical prediction which vanishes by increasing the resolution.

We study the effects of polymer additives on turbulence generated by the ubiquitous Rayleigh-Taylor instability. Numerical simulations of complete viscoelastic models provide clear evidence that the heat transport is enhanced up to 50% with respect to the Newtonian case. This phenomenon is accompanied by a speed up of the mixing layer growth. We give a phenomenological interpretation of these results based on small-scale turbulent reduction induced by polymers., Comment: 4 pages, 5 figures

The complex evolution of turbulent mixing in Rayleigh-Taylor convection is studied in terms of eddy diffusiviy models for the mean temperature profile. It is found that a non-linear model, derived within the general framework of Prandtl mixing theory, reproduces accurately the evolution of turbulent profiles obtained from numerical simulations. Our model allows to give very precise predictions for the turbulent heat flux and for the Nusselt number in the ultimate state regime of thermal convection., Comment: 4 pages, 4 figure, PRL in press

The effects of polymer additives on Rayleigh--Taylor (RT) instability of immiscible fluids is investigated using the Oldroyd-B viscoelastic model. Analytic results obtained exploiting the phase-field approach show that in polymer solution the growth rate of the instability speeds up with elasticity (but remains slower than in the pure solvent case). Numerical simulations of the viscoelastic binary fluid model confirm this picture.

The Rayleigh--Taylor (RT) turbulence is investigated by means of high resolution numerical simulations. The main question addressed here is on whether RT phenomenology can be considered as a manifestation of universality of Navier--Stokes equations with respect to forcing mechanisms. At a theoretical level the situation is far from being firmly established and, indeed, contrasting predictions have been formulated. Our first aim here is to clarify the above controversy through a deep analysis of scaling behavior of relevant statistical observables. The effects of intermittency on the mean field scaling predictions is also discussed., Comment: 4 pages, 5 figures

Mixing of a passive scalar in the peripheral region close to a wall is investigated by means of accurate direct numerical simulations of both a three-dimensional Couette channel flow at low Reynolds numbers and a two-dimensional synthetic flow. In both cases, the resulting phenomenology can be understood in terms of the theory recently developed by Lebedev and Turitsyn [Phys. Rev. E 69, 036301, 2004]. Our results prove the robustness of the identified mechanisms responsible for the persistency of scalar concentration close to the wall with important consequences in completely different fields ranging from microfluidic applications to environmental dispersion modeling., Comment: 4 pages, 5 figures

We study the double cascade of energy and wave action in a local model of superfluid vortex filaments. The model is obtained from a truncated expansion of the 2D Local Induction Approximation and it is shown to support six-wave interactions. We argue that, because of the uncertainty in the vortex core profile, this model has the same status of validity as the traditionally used Biot-Savart model with cutoff, but it has advantage of being much simpler. Our minimal model leads to a wave kinetic equation for which we predict existence of two distinct power-law scaling in the spectrum, corresponding to a direct cascade of energy and an inverse one of wave action. Direct numerical simulations confirm the theoretical predictions in the weak turbulence regime., Comment: 7 pages, 2 figures

The paper {\it On the multifractal nature of fully developed turbulence and chaotic systems}, by R. Benzi {\it et al.} published in this journal in 1984 (vol {\bf 17}, page 3521) has been a starting point of many investigations on the different faces of selfsimilarity and intermittency in turbulent phenomena. Since then, the multifractal model has become a useful tool for the study of small scale turbulence, in particular for detailed predictions of different Eulerian and Lagrangian statistical properties. In the occasion of the 50-th birthday of our unforgettable friend and colleague Giovanni Paladin (1958-1996), we review here the basic concepts and some applications of the multifractal model for turbulence.

We investigate the effect of polymer additives on a two-dimensional Kolmogorov flow at very low Reynolds numbers by direct numerical simulations of the Oldroyd-B viscoelastic model. We find that above the elastic instability threshold the flow develops the elastic turbulence regime recently observed in experiments. We observe that both the turbulent drag and the Lyapunov exponent increase with Weissenberg, indicating the presence of a disordered, turbulent-like mixing flow. The energy spectrum develops a power-law scaling range with an exponent close to the experimental and theoretical expectations.

We show that rocky shorelines with fractal dimension 4/3 are conformally invariant curves by measuring the statistics of their winding angles from global high-resolution data. Such coastlines are thus statistically equivalent to the outer boundary of the random walk and of percolation clusters. A simple model of coastal erosion gives an explanation for these results. Conformal invariance allows also to predict the highly intermittent spatial distribution of the flux of pollutant diffusing ashore.

High resolution direct numerical simulations of two-dimensional turbulence in stationary conditions are presented. The development of an energy-enstrophy double cascade is studied and found to be compatible with the classical Kraichnan theory in the limit of extended inertial ranges. The analysis of the joint distribution of energy and enstrophy fluxes in physical space reveals a small value of cross correlation. This result supports many experimental and numerical studies where only one cascade is generated., Comment: 4 pages, 6 figures

Single-particle dispersion in the Bolgiano--Obukhov regime of two-dimensional turbulent convection is investigated. Unlike dispersion in a flow displaying the classical K41 phenomenology, here, the leading contribution to the Lagrangian velocity fluctuations is given by the largest eddies. This implies a linear behavior in time for a typical velocity fluctuation in the time interval $t$. The contribution to the Lagrangian velocity fluctuations of local eddies (i.e. with a characteristic time of order $t$), whose space/time scalings are ruled by the Bolgiano--Obukhov theory, is thus not detectable by standard Lagrangian statistical observables. To disentangle contributions arising from the large eddies from those of local eddies, a strategy based on exit-time statistics has successfully been exploited. Lagrangian velocity increments in Bolgiano convection thus provide a physically relevant example of signal with \emph{more than smooth} fluctuations., Comment: 4 pages, 5 figures

We offer a new example of conformal invariance far from equilibrium -- the inverse cascade of Surface Quasi-Geostrophic (SQG) turbulence. We show that temperature isolines are statistically equivalent to curves that can be mapped into a one-dimensional Brownian walk (called Schramm-Loewner Evolution or SLE$_\kappa$). The diffusivity is close to $\kappa=4$, that is iso-temperature curves belong to the same universality class as domain walls in the O(2) spin model. Several statistics of temperature clusters and isolines are measured and shown to be consistent with the theoretical expectations for such a spin system at criticality. We also show that the direct cascade in two-dimensional Navier-Stokes turbulence is not conformal invariant. The emerging picture is that conformal invariance may be expected for inverse turbulent cascades of strongly interacting systems., Comment: 4 pages, 6 figures

The small scale statistics of homogeneous isotropic turbulence of dilute polymer solutions is investigated by means of direct numerical simulations of a simplified viscoelastic fluid model. It is found that polymers only partially suppress the turbulent cascade below the Lumley scale, leaving a remnant energy flux even for large elasticity. As a consequence, fluid acceleration in viscoelastic flows is reduced with respect to Newtonian turbulence, whereas its rescaled probability density is left unchanged. At large scales the velocity field is found to be unaffected by the presence of polymers., Comment: 7 pages, 4 figures

Simplicity of fundamental physical laws manifests itself in fundamental symmetries. While systems with an infinity of strongly interacting degrees of freedom (in particle physics and critical phenomena) are hard to describe, they often demonstrate symmetries, in particular scale invariance. In two dimensions (2d) locality often promotes scale invariance to a wider class of conformal transformations which allow for nonuniform re-scaling. Conformal invariance allows a thorough classification of universality classes of critical phenomena in 2d. Is there conformal invariance in 2d turbulence, a paradigmatic example of strongly-interacting non-equilibrium system? Here, using numerical experiment, we show that some features of 2d inverse turbulent cascade display conformal invariance. We observe that the statistics of vorticity clusters is remarkably close to that of critical percolation, one of the simplest universality classes of critical phenomena. These results represent a new step in the unification of 2d physics within the framework of conformal symmetry., Comment: 10 pages, 5 figures, 1 table

The weakly nonlinear regime of a viscoelastic Navier--Stokes fluid is investigated. For the purely hydrodynamic case, it is known that large-scale perturbations tend to the minima of a Ginzburg-Landau free-energy functional with a double-well (fourth-order) potential. The dynamics of the relaxation process is ruled by a one-dimensional Cahn--Hilliard equation that dictates the hyperbolic tangent profiles of kink-antikink structures and their mutual interactions. For the viscoelastic case, we found that the dynamics still admits a formulation in terms of a Ginzburg--Landau free-energy functional. For sufficiently small elasticities, the phenomenology is very similar to the purely hydrodynamic case: the free-energy functional is still a fourth-order potential and slightly perturbed kink-antikink structures hold. For sufficiently large elasticities, a critical point sets in: the fourth-order term changes sign and the next-order nonlinearity must be taken into account. Despite the double-well structure of the potential, the one-dimensional nature of the problem makes the dynamics sensitive to the details of the potential. We analysed the interactions among these generalized kink-antikink structures, demonstrating their role in a new, elastic instability. Finally, consequences for the problem of polymer drag reduction are presented., Comment: 26 pages, 17 figures, submitted to The Journal of Fluid Mechanics

We present the results of Direct Numerical Simulations (DNS) of turbulent flows seeded with millions of passive inertial particles. The maximum Taylor's Reynolds number is around 200. We consider particles much heavier than the carrier flow in the limit when the Stokes drag force dominates their dynamical evolution. We discuss both the transient and the stationary regimes. In the transient regime, we study the growt of inhomogeneities in the particle spatial distribution driven by the preferential concentration out of intense vortex filaments. In the stationary regime, we study the acceleration fluctuations as a function of the Stokes number in the range [0.16:3.3]. We also compare our results with those of pure fluid tracers (St=0) and we find a critical behavior of inertia for small Stokes values. Starting from the pure monodisperse statistics we also characterize polydisperse suspensions with a given mean Stokes., Comment: 13 pages, 10 figures, 2 tables

We study the anomalous scaling of the mass density measure of Lagrangian tracers in a compressible flow realized on the free surface on top of a three dimensional flow. The full two dimensional probability distribution of local stretching rates is measured. The intermittency exponents which quantify the fluctuations of the mass measure of tracers at small scales are calculated from the large deviation form of stretching rate fluctuations. The results indicate the existence of a critical exponent $n_c \simeq 0.86$ above which exponents saturate, in agreement with what has been predicted by an analytically solvable model. Direct evaluation of the multi-fractal dimensions by reconstructing the coarse-grained particle density supports the results for low order moments., Comment: 7 pages, 4 figures, submitted to EPL

We present the results of direct numerical simulations of heavy particle transport in homogeneous, isotropic, fully developed turbulence, up to resolution $512^3$ ($R_\lambda\approx 185$). Following the trajectories of up to 120 million particles with Stokes numbers, $St$, in the range from 0.16 to 3.5 we are able to characterize in full detail the statistics of particle acceleration. We show that: ({\it i}) The root-mean-squared acceleration $a_{\rm rms}$ sharply falls off from the fluid tracer value already at quite small Stokes numbers; ({\it ii}) At a given $St$ the normalised acceleration $a_{\rm rms}/(\epsilon^3/\nu)^{1/4}$ increases with $R_\lambda$ consistently with the trend observed for fluid tracers; ({\it iii}) The tails of the probability density function of the normalised acceleration $a/a_{\rm rms}$ decrease with $St$. Two concurrent mechanisms lead to the above results: preferential concentration of particles, very effective at small $St$, and filtering induced by the particle response time, that takes over at larger $St$., Comment: 10 pages, 3 figs, 2 tables. A section with new results has been added. Revised version accepted for pubblication on Journal of Fluid Mechanics

Phase separation between two fluids in two-dimensions is investigated by means of Direct Numerical Simulations of coupled Navier-Stokes and Cahn-Hilliard equations. We study the phase ordering process in the presence of an external stirring acting on the velocity field. For both active and passive mixtures we find that, for a sufficiently strong stirring, coarsening is arrested in a stationary dynamical state characterized by a continuous rupture and formation of finite domains. Coarsening arrest is shown to be independent of the chaotic or regular nature of the flow., Comment: 4 pages, 5 figures; discussion on the dependence of the arrest scale on the shear rate has been added; figures have been modified accordingly