Turbulence Unsteadiness Drives Extreme Clustering.

We show that the unsteadiness of turbulence has a drastic effect on turbulence parameters and in particle cluster formation. To this end we use direct numerical simulations of particle laden flows with a steady forcing that generates an unsteady large-scale flow. Particle clustering correlates with the instantaneous Taylor-based flow Reynolds number, and anticorrelates with its instantaneous turbulent energy dissipation constant. A dimensional argument for these correlations is presented. In natural flows, unsteadiness can result in extreme particle clustering, which is stronger than the clustering expected from averaged inertial turbulence effects.

Extraction of invariant manifolds and application to turbulence with a passive scalar.

The reduction of dimensionality of physical systems, especially in fluid dynamics, leads in many situations to nonlinear ordinary differential equations which have global invariant manifolds with algebraic expressions containing relevant physical information on the original system. We present a method to identify such manifolds, and we apply it to a reduced model for the Lagrangian evolution of field gradients in homogeneous and isotropic turbulence with a passive scalar.

Broken Mirror Symmetry of Tracer's Trajectories in Turbulence.

Topological properties of physical systems play a crucial role in our understanding of nature, yet their experimental determination remains elusive. We show that the mean helicity, a dynamical invariant in ideal flows, quantitatively affects trajectories of fluid elements: the linking number of Lagrangian trajectories depends on the mean helicity. Thus, a global topological invariant and a topological number of fluid trajectories become related, and we provide an empirical expression linking them. The relation shows the existence of long-term memory in the trajectories: the links can be made of the trajectory up to a given time, with particles positions in the past. This property also allows experimental measurements of mean helicity.

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.

Lessons from being challenged by COVID-19.

We present results of different approaches to model the evolution of the COVID-19 epidemic in Argentina, with a special focus on the megacity conformed by the city of Buenos Aires and its metropolitan area, including a total of 41 districts with over 13 million inhabitants. We first highlight the relevance of interpreting the early stage of the epidemic in light of incoming infectious travelers from abroad. Next, we critically evaluate certain proposed solutions to contain the epidemic based on instantaneous modifications of the reproductive number. Finally, we build increasingly complex and realistic models, ranging from simple homogeneous models used to estimate local reproduction numbers, to fully coupled inhomogeneous (deterministic or stochastic) models incorporating mobility estimates from cell phone location data. The models are capable of producing forecasts highly consistent with the official number of cases with minimal parameter fitting and fine-tuning. We discuss the strengths and limitations of the proposed models, focusing on the validity of different necessary first approximations, and caution future modeling efforts to exercise great care in the interpretation of long-term forecasts, and in the adoption of non-pharmaceutical interventions backed by numerical simulations.

Passive scalars: Mixing, diffusion, and intermittency in helical and nonhelical rotating turbulence.

We use direct numerical simulations to compute structure functions, scaling exponents, probability density functions, and effective transport coefficients of passive scalars in turbulent rotating helical and nonhelical flows. We show that helicity affects the inertial range scaling of the velocity and of the passive scalar when rotation is present, with a spectral law consistent with ∼k_{⊥}^{-1.4} for the passive scalar variance spectrum. This scaling law is consistent with a phenomenological argument [P. Rodriguez Imazio and P. D. Mininni, Phys. Rev. E 83, 066309 (2011)PLEEE81539-375510.1103/PhysRevE.83.066309] for rotating nonhelical flows, which follows directly from Kolmogorov-Obukhov scaling and states that if energy follows a E(k)∼k^{-n} law, then the passive scalar variance follows a law V(k)∼k^{-n_{θ}} with n_{θ}=(5-n)/2. With the second-order scaling exponent obtained from this law, and using the Kraichnan model, we obtain anomalous scaling exponents for the passive scalar that are in good agreement with the numerical results. Multifractal intermittency models are also considered. Intermittency of the passive scalar is stronger than in the nonhelical rotating case, a result that is also confirmed by stronger non-Gaussian tails in the probability density functions of field increments. Finally, Fick's law is used to compute the effective diffusion coefficients in the directions parallel and perpendicular to rotation. Calculations indicate that horizontal diffusion decreases in the presence of helicity in rotating flows, while vertical diffusion increases. A simple mean field argument explains this behavior in terms of the amplitude of velocity fluctuations.

von Kármán-Howarth equation for three-dimensional two-fluid plasmas.

We derive the von Kármán-Howarth equation for a full three-dimensional incompressible two-fluid plasma. In the long-time limit and for very large Reynolds numbers we obtain the equivalent of the hydrodynamic "four-fifths" law. This exact law predicts the scaling of the third-order two-point correlation functions, and puts a strong constraint on the plasma turbulent dynamics. Finally, we derive a simple expression for the 4/5 law in terms of third-order structure functions, which is appropriate for comparison with in situ measurements in the solar wind at different spatial ranges.

The spatio-temporal spectrum of turbulent flows.

Identification and extraction of vortical structures and of waves in a disorganised flow is a mayor challenge in the study of turbulence. We present a study of the spatio-temporal behavior of turbulent flows in the presence of different restitutive forces. We show how to compute and analyse the spatio-temporal spectrum from data stemming from numerical simulations and from laboratory experiments. Four cases are considered: homogeneous and isotropic turbulence, rotating turbulence, stratified turbulence, and water wave turbulence. For homogeneous and isotropic turbulence, the spectrum allows identification of sweeping by the large-scale flow. For rotating and for stratified turbulence, the spectrum allows identification of the waves, precise quantification of the energy in the waves and in the turbulent eddies, and identification of physical mechanisms such as Doppler shift and wave absorption in critical layers. Finally, in water wave turbulence the spectrum shows a transition from gravity-capillary waves to bound waves as the amplitude of the forcing is increased.

Stably stratified turbulence in the presence of large-scale forcing.

We perform two high-resolution direct numerical simulations of stratified turbulence for Reynolds number equal to Re≈25000 and Froude number, respectively, of Fr≈0.1 and Fr≈0.03. The flows are forced at large scale and discretized on an isotropic grid of 2048(3) points. Stratification makes the flow anisotropic and introduces two extra characteristic scales with respect to homogeneous isotropic turbulence: the buoyancy scale, L(B), and the Ozmidov scale, ℓ(oz). The former is related to the number of layers that the flow develops in the direction of gravity, and the latter is regarded as the scale at which isotropy is recovered. The values of L(B) and ℓ(oz) depend on the Froude number, and their absolute and relative amplitudes affect the repartition of energy among Fourier modes in ways that are not easy to predict. By contrasting the behavior of the two simulated flows we identify some surprising similarities: After an initial transient the two flows evolve towards comparable values of the kinetic and potential enstrophy and energy dissipation rate. This is the result of the Reynolds number being large enough in both flows for the Ozmidov scale to be resolved. When properly dimensionalized, the energy dissipation rate is compatible with atmospheric observations. Further similarities emerge at large scales: The same ratio between potential and total energy (≈0.1) is spontaneously selected by the flows, and slow modes grow monotonically in both regimes, causing a slow increase of the total energy in time. The axisymmetric total energy spectrum shows a wide variety of spectral slopes as a function of the angle between the imposed stratification and the wave vector. One-dimensional energy spectra computed in the direction parallel to gravity are flat from the forcing up to buoyancy scale. At intermediate scales a ∼k(-3) parallel spectrum develops for the Fr≈0.03 run, whereas for weaker stratification, the saturation spectrum does not have enough scales to develop and instead one observes a power law compatible with Kolmogorov scaling. Finally, the spectrum of helicity is flat until L(B), as observed in the nocturnal planetary boundary layer.

Absorption of waves by large-scale winds in stratified turbulence.

The atmosphere is a nonlinear stratified fluid in which internal gravity waves are present. These waves interact with the flow, resulting in wave turbulence that displays important differences with the turbulence observed in isotropic and homogeneous flows. We study numerically the role of these waves and their interaction with the large-scale flow, consisting of vertically sheared horizontal winds. We calculate their space- and time-resolved energy spectrum (a four-dimensional spectrum) and show that most of the energy is concentrated along a dispersion relation that is Doppler shifted by the horizontal winds. We also observe that when uniform winds are let to develop in each horizontal layer of the flow, waves whose phase velocity is equal to the horizontal wind speed have negligible energy. This indicates a nonlocal transfer of their energy to the mean flow. Both phenomena, the Doppler shift and the absorption of waves traveling with the wind speed, are not accounted for in current theories of stratified wave turbulence.

Magnetic field reversals and long-time memory in conducting flows.

Employing a simple ideal magnetohydrodynamic model in spherical geometry, we show that the presence of either rotation or finite magnetic helicity is sufficient to induce dynamical reversals of the magnetic dipole moment. The statistical character of the model is similar to that of terrestrial magnetic field reversals, with the similarity being stronger when rotation is present. The connection between long-time correlations, 1/f noise, and statistics of reversals is supported, consistent with earlier suggestions.

Large-scale anisotropy in stably stratified rotating flows.

We present results from direct numerical simulations of the Boussinesq equations in the presence of rotation and/or stratification, both in the vertical direction. The runs are forced isotropically and randomly at small scales and have spatial resolutions of up to 1024(3) grid points and Reynolds numbers of ≈1000. We first show that solutions with negative energy flux and inverse cascades develop in rotating turbulence, whether or not stratification is present. However, the purely stratified case is characterized instead by an early-time, highly anisotropic transfer to large scales with almost zero net isotropic energy flux. This is consistent with previous studies that observed the development of vertically sheared horizontal winds, although only at substantially later times. However, and unlike previous works, when sufficient scale separation is allowed between the forcing scale and the domain size, the kinetic energy displays a perpendicular (horizontal) spectrum with power-law behavior compatible with ∼k(⊥)(-5/3), including in the absence of rotation. In this latter purely stratified case, such a spectrum is the result of a direct cascade of the energy contained in the large-scale horizontal wind, as is evidenced by a strong positive flux of energy in the parallel direction at all scales including the largest resolved scales.

Wave turbulence in shallow water models.

We study wave turbulence in shallow water flows in numerical simulations using two different approximations: the shallow water model and the Boussinesq model with weak dispersion. The equations for both models were solved using periodic grids with up to 2048{2} points. In all simulations, the Froude number varies between 0.015 and 0.05, while the Reynolds number and level of dispersion are varied in a broader range to span different regimes. In all cases, most of the energy in the system remains in the waves, even after integrating the system for very long times. For shallow flows, nonlinear waves are nondispersive and the spectrum of potential energy is compatible with ∼k{-2} scaling. For deeper (Boussinesq) flows, the nonlinear dispersion relation as directly measured from the wave and frequency spectrum (calculated independently) shows signatures of dispersion, and the spectrum of potential energy is compatible with predictions of weak turbulence theory, ∼k{-4/3}. In this latter case, the nonlinear dispersion relation differs from the linear one and has two branches, which we explain with a simple qualitative argument. Finally, we study probability density functions of the surface height and find that in all cases the distributions are asymmetric. The probability density function can be approximated by a skewed normal distribution as well as by a Tayfun distribution.

Turbulence comes in bursts in stably stratified flows.

There is a clear distinction between simple laminar and complex turbulent fluids; however, in some cases, as for the nocturnal planetary boundary layer, a stable and well-ordered flow can develop intense and sporadic bursts of turbulent activity that disappear slowly in time. This phenomenon is ill understood and poorly modeled and yet it is central to our understanding of weather and climate dynamics. We present here data from direct numerical simulations of stratified turbulence on grids of 20483 points that display the somewhat paradoxical result of measurably stronger events for more stable flows, not only in the temperature and vertical velocity derivatives as commonplace in turbulence, but also in the amplitude of the fields themselves, contrary to what happens for homogenous isotropic turbulent flows. A flow visualization suggests that the extreme values take place in Kelvin-Helmoltz overturning events and fronts that develop in the field variables. These results are confirmed by the analysis of a simple model that we present. The model takes into consideration only the vertical velocity and temperature fluctuations and their vertical derivatives. It indicates that in stably stratified turbulence, the stronger bursts can occur when the flow is expected to be more stable. The bursts are generated by a rapid nonlinear amplification of energy stored in waves and are associated with energetic interchanges between vertical velocity and temperature (or density) fluctuations in a range of parameters corresponding to the well-known saturation regime of stratified turbulence.

Sign cancellation and scaling in the vertical component of velocity and vorticity in rotating turbulence.

We study sign changes and scaling laws in the Cartesian components of the velocity and vorticity of rotating turbulence, in the helicity, and in the components of vertically averaged fields. Data for the analysis are provided by high-resolution direct numerical simulations of rotating turbulence with different forcing functions, with up to 1536(3) grid points, with Reynolds numbers between ≈1100 and ≈5100, and with moderate Rossby numbers between ≈0.06 and ≈8. When rotation is negligible, all Cartesian components of the velocity show similar scaling, in agreement with the expected isotropy of the flow. However, in the presence of rotation, only the vertical components of the fields show clear scaling laws, with evidence of possible sign singularity in the limit of an infinite Reynolds number. Horizontal components of the velocity are smooth and do not display rapid fluctuations for arbitrarily small scales. The vertical velocity and vorticity, as well as the vertically averaged vertical velocity and vorticity, show the same scaling within error bars, in agreement with theories that predict that these quantities have the same dynamical equation for very strong rotation.

Helicity dynamics in stratified turbulence in the absence of forcing.

A numerical study of decaying stably stratified flows is performed. Relatively high stratification (Froude number ≈10(-2)-10(-1)) and moderate Reynolds (Re) numbers (Re≈ 3-6×10(3)) are considered and a particular emphasis is placed on the role of helicity (velocity-vorticity correlations), which is not an invariant of the nondissipative equations. The problem is tackled by integrating the Boussinesq equations in a periodic cubical domain using different initial conditions: a nonhelical Taylor-Green (TG) flow, a fully helical Beltrami [Arnold-Beltrami-Childress (ABC)] flow, and random flows with a tunable helicity. We show that for stratified ABC flows helicity undergoes a substantially slower decay than for unstratified ABC flows. This fact is likely associated to the combined effect of stratification and large-scale coherent structures. Indeed, when the latter are missing, as in random flows, helicity is rapidly destroyed by the onset of gravitational waves. A type of large-scale dissipative "cyclostrophic" balance can be invoked to explain this behavior. No production of helicity is observed, contrary to the case of rotating and stratified flows. When helicity survives in the system, it strongly affects the temporal energy decay and the energy distribution among Fourier modes. We discover in fact that the decay rate of energy for stratified helical flows is much slower than for stratified nonhelical flows and can be considered with a phenomenological model in a way similar to what is done for unstratified rotating flows. We also show that helicity, when strong, has a measurable effect on the Fourier spectra, in particular at scales larger than the buoyancy scale, for which it displays a rather flat scaling associated with vertical shear, as observed in the planetary boundary layer.

Effective diffusivity of passive scalars in rotating turbulence.

We use direct numerical simulations to compute turbulent transport coefficients for passive scalars in turbulent rotating flows. Effective diffusion coefficients in the directions parallel and perpendicular to the rotation axis are obtained by studying the diffusion of an imposed initial profile for the passive scalar, and calculated by measuring the scalar average concentration and average spatial flux as a function of time. The Rossby and Schmidt numbers are varied to quantify their effect on the effective diffusion. It is found that rotation reduces scalar diffusivity in the perpendicular direction. The perpendicular diffusion can be estimated from mixing length arguments using the characteristic velocities and lengths perpendicular to the rotation axis. Deviations are observed for small Schmidt numbers, for which turbulent transport decreases and molecular diffusion becomes more significant.

Ideal evolution of magnetohydrodynamic turbulence when imposing Taylor-Green symmetries.

We investigate the ideal and incompressible magnetohydrodynamic (MHD) equations in three space dimensions for the development of potentially singular structures. The methodology consists in implementing the fourfold symmetries of the Taylor-Green vortex generalized to MHD, leading to substantial computer time and memory savings at a given resolution; we also use a regridding method that allows for lower-resolution runs at early times, with no loss of spectral accuracy. One magnetic configuration is examined at an equivalent resolution of 6144(3) points and three different configurations on grids of 4096(3) points. At the highest resolution, two different current and vorticity sheet systems are found to collide, producing two successive accelerations in the development of small scales. At the latest time, a convergence of magnetic field lines to the location of maximum current is probably leading locally to a strong bending and directional variability of such lines. A novel analytical method, based on sharp analysis inequalities, is used to assess the validity of the finite-time singularity scenario. This method allows one to rule out spurious singularities by evaluating the rate at which the logarithmic decrement of the analyticity-strip method goes to zero. The result is that the finite-time singularity scenario cannot be ruled out, and the singularity time could be somewhere between t=2.33 and t=2.70. More robust conclusions will require higher resolution runs and grid-point interpolation measurements of maximum current and vorticity.

High Reynolds number magnetohydrodynamic turbulence using a Lagrangian model.

With the help of a model of magnetohydrodynamic (MHD) turbulence tested previously, we explore high Reynolds number regimes up to equivalent resolutions of 6000(3) grid points in the absence of forcing and with no imposed uniform magnetic field. For the given initial condition chosen here, with equal kinetic and magnetic energy, the flow ends up being dominated by the magnetic field, and the dynamics leads to an isotropic Iroshnikov-Kraichnan energy spectrum. However, the locally anisotropic magnetic field fluctuations perpendicular to the local mean field follow a Kolmogorov law. We find that the ratio of the eddy turnover time to the Alfvén time increases with wave number, contrary to the so-called critical balance hypothesis. Residual energy and helicity spectra are also considered; the role played by the conservation of magnetic helicity is studied, and scaling laws are found for the magnetic helicity and residual helicity spectra. We put these results in the context of the dynamics of a globally isotropic MHD flow that is locally anisotropic because of the influence of the strong large-scale magnetic field, leading to a partial equilibration between kinetic and magnetic modes for the energy and the helicity.

Anomalous scaling of passive scalars in rotating flows.

We present results of direct numerical simulations of passive scalar advection and diffusion in turbulent rotating flows. Scaling laws and the development of anisotropy are studied in spectral space, and in real space using an axisymmetric decomposition of velocity and passive scalar structure functions. The passive scalar is more anisotropic than the velocity field, and its power spectrum follows a spectral law consistent with ~ k[Please see text](-3/2). This scaling is explained with phenomenological arguments that consider the effect of rotation. Intermittency is characterized using scaling exponents and probability density functions of velocity and passive scalar increments. In the presence of rotation, intermittency in the velocity field decreases more noticeably than in the passive scalar. The scaling exponents show good agreement with Kraichnan's prediction for passive scalar intermittency in two dimensions, after correcting for the observed scaling of the second-order exponent.