Flocking turbulence of microswimmers in confined domains.

We extensively study the Toner-Tu-Swift-Hohenberg model of motile active matter by means of direct numerical simulations in a two-dimensional confined domain. By exploring the space of parameters of the model we investigate the emergence of a new state of active turbulence which occurs when the aligning interactions and the self-propulsion of the swimmers are strong. This regime of flocking turbulence is characterized by a population of few strong vortices, each surrounded by an island of coherent flocking motion. The energy spectrum of flocking turbulence displays a power-law scaling with an exponent which depends weakly on the model parameters. By increasing the confinement we observe that the system, after a long transient characterized by power-law-distributed transition times, switches to the ordered state of a single giant vortex.

Giant vortex dynamics in confined bacterial turbulence.

We report the numerical evidence of a new state of bacterial 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.

Incompressible Rayleigh-Taylor mixing in circular and spherical geometries.

We present a numerical investigation of the turbulent evolution of the mixing layer developing from the Rayleigh-Taylor instability for miscible incompressible fluids in circular (in two dimensions) and in spherical (in three dimensions) geometries in the Boussinesq approximation. We show that the main difference caused by the convergent geometry with respect to the planar case is that the center of the mixing layer drifts toward the center of the domain during the evolution of the mixing layer. A similar effect is observed for the radial profile of the density flux. We derive a simple geometrical relation for this inward drift based on mass conservation. In the late stage of the evolution we observe also the appearance of an inward-outward asymmetry in the radial profiles.

Suppression of Rayleigh-Taylor turbulence by time-periodic acceleration.

The dynamics of Rayleigh-Taylor turbulence convection in the 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 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.

Chaos and Predictability of Homogeneous-Isotropic Turbulence.

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 solutions 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.

Irreversibility of the two-dimensional enstrophy cascade.

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 called metenstrophy. By means of extensive direct numerical simulations we measure the time irreversibility from the asymmetry of the probability density function of the metenstrophy and we find that it increases with the Reynolds number of the cascade, similarly to what is found in three-dimensional turbulence. A detailed analysis of the different contributions to the enstrophy budget reveals a remarkable difference with respect to what is observed for the energy cascade, in particular the role of the statistics of the forcing to determine the degree of irreversibility.

Turbulent channel without boundaries: the periodic Kolmogorov flow.

The Kolmogorov flow provides an ideal instance of a virtual channel flow: It has no boundaries, but 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.

Dimensional transition in rotating turbulence.

In this work we investigate, by means of direct numerical hyperviscous simulations, how rotation affects the bidimensionalization of a turbulent flow. We study a thin layer of fluid, forced by a two-dimensional forcing, within the framework of the "split cascade" in which the injected energy flows both to small scales (generating the direct cascade) and to large scale (to form the inverse cascade). It is shown that rotation reinforces the inverse cascade at the expense of the direct one, thus promoting bidimensionalization of the flow. This is achieved by a suppression of the enstrophy production at large scales. Nonetheless, we find that, in the range of rotation rates investigated, increasing the vertical size of the computational domain causes a reduction of the flux of the inverse cascade. Our results suggest that, even in rotating flows, the inverse cascade may eventually disappear when the vertical scale is sufficiently large with respect to the forcing scale. We also study how the split cascade and confinement influence the breaking of symmetry induced by rotation.

Anomalous diffusion in confined turbulent convection.

Turbulent convection in quasi-one-dimensional geometry is studied by means of high-resolution direct numerical simulations within the framework of Rayleigh-Taylor turbulence. Geometrical confinement has dramatic effects on the dynamics of the turbulent flow, inducing a transition from superdiffusive to subdiffusive evolution of the mixing layer and arresting the growth of kinetic energy. A nonlinear diffusion model is shown to reproduce accurately the above phenomenology. The model is used to predict, without free parameters, the spatiotemporal evolution of the heat flux profile and the dependence of the Nusselt number on the Rayleigh number.

Control of particle clustering in turbulence by polymer additives.

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.

Effects of polymer additives on Rayleigh-Taylor turbulence.

The role of polymer additives on the turbulent convective flow of a Rayleigh-Taylor system is investigated by means of direct numerical simulations of Oldroyd-B viscoelastic model. The dynamics of polymer elongations follows adiabatically the self-similar evolution of the turbulent mixing layer and shows the appearance of a strong feedback on the flow which originates a cutoff 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 enhancement of heat transport. Our findings are consistent with a scenario of drag reduction induced by polymers. A weakly nonlinear model proposed by Fermi for the growth of the mixing layer is reported in the Appendix.

Shell model for quasi-two-dimensional turbulence.

We discuss the possibility to introduce geometrical constraints in shell models of turbulence in order to mimic the turbulent dynamics that takes place in fluid layers with large aspect ratio. By using a scale-dependent set of coupling parameters, we are able to resolve both scales larger and smaller than a geometrical dimension of the flow. The proposed model is able to resolve with high accuracy the split energy cascade phenomenon recently observed in such flows, and allows us to investigate in detail the scaling properties of turbulent convection confined in narrow convective cells.

Evidence for the double cascade scenario in two-dimensional turbulence.

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 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.

Polymer heat transport enhancement in thermal convection: the case of Rayleigh-Taylor turbulence.

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.

Nonlinear diffusion model for Rayleigh-Taylor mixing.

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

Kolmogorov scaling and intermittency in Rayleigh-Taylor turbulence.

Turbulence induced by Rayleigh-Taylor instability is a ubiquitous phenomenon with applications ranging from atmospheric physics and geophysics to supernova explosions and plasma confinement fusion. Despite its fundamental character, a phenomenological theory has been proposed only recently and several predictions are untested. In this Rapid Communication we confirm spatiotemporal predictions of the theory by means of direct numerical simulations at high resolution and we extend the phenomenology to take into account intermittency effects. We show that scaling exponents are indistinguishable from those of Navier-Stokes turbulence at comparable Reynolds number, a result in support of the universality of turbulence with respect to the forcing mechanism. We also show that the time dependence of Rayleigh, Reynolds, and Nusselt numbers realizes the Kraichnan scaling regime associated with the ultimate state of thermal convection.

Two-dimensional elastic turbulence.

We report numerical evidence of elastic turbulence phenomenology in a two-dimensional periodic Kolmogorov flow. By direct numerical simulations of the Oldroyd-B viscoelastic model at very small Reynolds numbers, we find that above the elastic instability threshold the flow develops an elastic turbulent regime. We observe that both the turbulent drag and the Lyapunov exponent increase with the Weissenberg number, indicating the presence of a disordered, turbulentlike mixing flow. The energy spectrum develops a power-law scaling range with an exponent close to the experimental and theoretical expectations.

Inertial particles driven by a telegraph noise.

We present a model for the Lagrangian dynamics of inertial particles in a compressible flow, where fluid velocity gradients are modeled by a telegraph noise. The model allows for an analytic investigation of the role of time correlation of the flow in the aggregation-disorder transition of inertial particles. The dependence on the Stokes number St and the Kubo number Ku of the Lyapunov exponent of particle trajectories reveals the presence of a region in parameter space (St, Ku), where the leading Lyapunov exponent changes sign, thus signaling the transition. The asymptotics of short- and long-correlated flows are discussed, as well as the fluid-tracer limit.

Heavy particle concentration in turbulence at dissipative and inertial scales.

Spatial distributions of heavy particles suspended in an incompressible isotropic and homogeneous turbulent flow are investigated by means of high resolution direct numerical simulations. In the dissipative range, it is shown that particles form fractal clusters with properties independent of the Reynolds number. Clustering is there optimal when the particle response time is of the order of the Kolmogorov time scale tau(eta). In the inertial range, the particle distribution is no longer scale invariant. It is, however, shown that deviations from uniformity depend on a rescaled contraction rate, which is different from the local Stokes number given by dimensional analysis. Particle distribution is characterized by voids spanning all scales of the turbulent flow; their signature in the coarse-grained mass probability distribution is an algebraic behavior at small densities.

Multiple-scale analysis and renormalization for preasymptotic scalar transport.

Preasymptotic transport of a scalar quantity passively advected by a velocity field formed by a large-scale component superimposed on a small-scale fluctuation is investigated both analytically and by means of numerical simulations. Exploiting the multiple-scale expansion one arrives at a Fokker-Planck equation which describes the preasymptotic scalar dynamics. This equation is associated with a Langevin equation involving a multiplicative noise and an effective (compressible) drift. For the general case, no explicit expression for either the affective drift on the effective diffusivity (actually a tensorial field) can be obtained. We discuss an approximation under which an explicit expression for the diffusivity (and thus for the drift) can be obtained. Its expression permits us to highlight the important fact that the diffusivity explicitly depends on the large-scale advecting velocity. Finally, the robustness of the aforementioned approximation is checked numerically by means of direct numerical simulations.