Fluid dynamics of COVID-19 airborne infection suggests urgent data for a scientific design of social distancing.

The COVID-19 pandemic is largely caused by airborne transmission, a phenomenon that rapidly gained the attention of the scientific community. Social distancing is of paramount importance to limit the spread of the disease, but to design social distancing rules on a scientific basis the process of dispersal of virus-containing respiratory droplets must be understood. Here, we demonstrate that available knowledge is largely inadequate to make predictions on the reach of infectious droplets emitted during a cough and on their infectious potential. We follow the position and evaporation of thousands of respiratory droplets by massive state-of-the-art numerical simulations of the airflow caused by a typical cough. We find that different initial distributions of droplet size taken from literature and different ambient relative humidity lead to opposite conclusions: (1) most versus none of the viral content settles in the first 1-2 m; (2) viruses are carried entirely on dry nuclei versus on liquid droplets; (3) small droplets travel less than [Formula: see text] versus more than [Formula: see text]. We point to two key issues that need to be addressed urgently in order to provide a scientific foundation to social distancing rules: (I1) a careful characterisation of the initial distribution of droplet sizes; (I2) the infectious potential of viruses carried on dry nuclei versus liquid droplets.

Buoyancy-Driven Flow through a Bed of Solid Particles Produces a New Form of Rayleigh-Taylor Turbulence.

Rayleigh-Taylor (RT) fluid turbulence through a bed of rigid, finite-size spheres is investigated by means of high-resolution direct numerical simulations, fully coupling the fluid and the solid phase via a state-of-the-art immersed boundary method. 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 parametrized by a friction coefficient.

Passive appendages generate drift through symmetry breaking.

Plants and animals use plumes, barbs, tails, feathers, hairs and fins to aid locomotion. Many of these appendages are not actively controlled, instead they have to interact passively with the surrounding fluid to generate motion. Here, we use theory, experiments and numerical simulations to show that an object with a protrusion in a separated flow drifts sideways by exploiting a symmetry-breaking instability similar to the instability of an inverted pendulum. Our model explains why the straight position of an appendage in a fluid flow is unstable and how it stabilizes either to the left or right of the incoming flow direction. It is plausible that organisms with appendages in a separated flow use this newly discovered mechanism for locomotion; examples include the drift of plumed seeds without wind and the passive reorientation of motile animals.

Minimal model for zero-inertia instabilities in shear-dominated non-Newtonian flows.

The emergence of fluid instabilities in the relevant limit of vanishing fluid inertia (i.e., arbitrarily close to zero Reynolds number) has been investigated for the well-known Kolmogorov flow. The finite-time shear-induced order-disorder transition of the non-Newtonian microstructure and the corresponding viscosity change from lower to higher values are the crucial ingredients for the instabilities to emerge. The finite-time low-to-high viscosity change for increasing shear characterizes the rheopectic fluids. The instability does not emerge in shear-thinning or -thickening fluids where viscosity adjustment to local shear occurs instantaneously. The lack of instabilities arbitrarily close to zero Reynolds number is also observed for thixotropic fluids, in spite of the fact that the viscosity adjustment time to shear is finite as in rheopectic fluids. Renormalized perturbative expansions (multiple-scale expansions), energy-based arguments (on the linearized equations of motion), and numerical results (of suitable eigenvalue problems from the linear stability analysis) are the main tools leading to our conclusions. Our findings may have important consequences in all situations where purely hydrodynamic fluid instabilities or mixing are inhibited due to negligible inertia, as in microfluidic applications. To trigger mixing in these situations, suitable (not necessarily viscoelastic) non-Newtonian fluid solutions appear as a valid answer. Our results open interesting questions and challenges in the field of smart (fluid) materials.

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.

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.

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.

Influence of helicity on anomalous scaling of a passive scalar advected by the turbulent velocity field with finite correlation time: two-loop approximation.

The influence of helicity on the stability of scaling regimes, on the effective diffusivity, and on the anomalous scaling of structure functions of a passive scalar advected by a Gaussian solenoidal velocity field with finite correlation time is investigated by the field theoretic renormalization group and operator-product expansion within the two-loop approximation. The influence of helicity on the scaling regimes is discussed and shown in the plane of exponents epsilon-eta, where epsilon characterizes the energy spectrum of the velocity field in the inertial range E proportional to k(1-2epsilon), and eta is related to the correlation time at the wave number k, which is scaled as k(-2+eta). The restrictions given by nonzero helicity on the regions with stable fixed points that correspond to the scaling regimes are analyzed in detail. The dependence of the effective diffusivity on the helicity parameter is discussed. The anomalous exponents of the structure functions of the passive scalar field which define their anomalous scaling are calculated and it is shown that, although the separate composite operators which define them strongly depend on the helicity parameter, the resulting two-loop contributions to the critical dimensions of the structure functions are independent of helicity. Details of calculations are shown.

Anomalous scaling of passively advected magnetic field in the presence of strong anisotropy.

Inertial-range scaling behavior of high-order (up to order N=51 ) two-point correlation functions of a passively advected vector field has been analyzed in the framework of the rapid-change model with strong small-scale anisotropy with the aid of the renormalization group and the operator-product expansion. Exponents of the power-like asymptotic behavior of the correlation functions have been calculated in the one-loop approximation. These exponents are shown to depend on anisotropy parameters in such a way that a specific hierarchy related to the degree of anisotropy is observed. Deviations from power-law behavior like oscillations or logarithmic behavior in the corrections to correlation functions have not been found.

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.

Lorenz-like systems and classical dynamical equations with memory forcing: an alternate point of view for singling out the origin of chaos.

An alternate view for the emergence of chaos in Lorenz-like systems is presented in this paper. For such purpose, the Lorenz problem is reformulated in a classical mechanical form and it turns out to be equivalent to the problem of a damped and forced one-dimensional motion of a particle in a two-well potential, with a forcing term depending on the "memory" of the particle past motion. The dynamics of the original Lorenz system in the proposed particle phase space can then be rewritten in terms of a one-dimensional first-exit-time problem. The emergence of chaos turns out to be due to the discontinuous solutions of the transcendental equation ruling the time for the particle to cross the intermediate potential wall. The whole problem is tackled analytically deriving a piecewise linearized Lorenz-like system that preserves all the essential properties of the original model.

Passive scalar turbulence in high dimensions.

Exploiting a Lagrangian strategy we present a numerical study for both perturbative and nonperturbative regions of the Kraichnan advection model. The major result is the numerical assessment of the first-order 1/d expansion by Chertkov, Falkovich, Kolokolov, and Lebedev [Phys. Rev. E 52, 4924 (1995)] for the fourth-order scalar structure function in the limit of high dimension d's. In addition to the perturbative results, the behavior of the anomaly for the sixth-order structure functions versus the velocity scaling exponent, xi, is investigated and the resulting behavior is discussed.

Manifestation of anisotropy persistence in the hierarchies of magnetohydrodynamical scaling exponents

An example of a turbulent system where the failure of the hypothesis of small-scale isotropy restoration is detectable both in the "flattening" of the inertial-range scaling exponent hierarchy and in the behavior of odd-order dimensionless ratios, e.g., skewness and hyperskewness, is presented. Specifically, within the kinematic approximation in magnetohydrodynamical turbulence, we show that for compressible flows, the isotropic contribution to the scaling of magnetic correlation functions and the first anisotropic ones may become practically indistinguishable. Moreover, the skewness factor now diverges as the Peclet number goes to infinity, a further indication of small-scale anisotropy.

Persistence of small-scale anisotropies and anomalous scaling in a model of magnetohydrodynamics turbulence

The problem of anomalous scaling in magnetohydrodynamics turbulence is considered within the framework of the kinematic approximation, in the presence of a large-scale background magnetic field. The velocity field is Gaussian, delta-correlated in time, and scales with a positive exponent xi. Explicit inertial-range expressions for the magnetic correlation functions are obtained; they are represented by superpositions of power laws with nonuniversal amplitudes and universal (independent of the anisotropy and forcing) anomalous exponents. The complete set of anomalous exponents for the pair correlation function is found nonperturbatively, in any space dimension d, using the zero-mode technique. For higher-order correlation functions, the anomalous exponents are calculated to O(xi) using the renormalization group. The exponents exhibit a hierarchy related to the degree of anisotropy; the leading contributions to the even correlation functions are given by the exponents from the isotropic shell, in agreement with the idea of restored small-scale isotropy. Conversely, the small-scale anisotropy reveals itself in the odd correlation functions: the skewness factor is slowly decreasing going down to small scales and higher odd dimensionless ratios (hyperskewness, etc.) dramatically increase, thus diverging in the r-->0 limit.

Universality and saturation of intermittency in passive scalar turbulence

The statistical properties of a scalar field advected by the nonintermittent Navier-Stokes flow arising from a two-dimensional inverse energy cascade are investigated. The universality properties of the scalar field are probed by comparing the results obtained with two types of injection mechanisms. Scaling properties are shown to be universal, even though anisotropies injected at large scales persist down to the smallest scales and local isotropy is not fully restored. Scalar statistics is strongly intermittent and scaling exponents saturate to a constant for sufficiently high orders. This is observed also for the advection by a velocity field rapidly changing in time, pointing to the genericity of the phenomenon.

Passive scalar intermittency in compressible flow.

A compressible generalization of the Kraichnan model [Phys. Rev. Lett. 72, 1016 (1994)] of passive scalar advection is considered. The dynamical role of compressibility on the intermittency of the scalar statistics is investigated for the direct cascade regime. Simple physical arguments suggest that an enhanced intermittency should appear for increasing compressibility, due to the slowing down of Lagrangian trajectory separations. This is confirmed by a numerical study of the dependence of intermittency exponents on the degree of compressibility, by a Lagrangian method for calculating simultaneous N-point tracer correlations.

Anisotropic nonperturbative zero modes for passively advected magnetic fields.

An analytic assessment of the role of anisotropic corrections to the isotropic anomalous scaling exponents is given for the d-dimensional kinematic magnetohydrodynamics problem in the presence of a mean magnetic field. The velocity advecting the magnetic field changes very rapidly in time and scales with a positive exponent xi. Inertial-range anisotropic contributions to the scaling exponents, zeta(j), of second-order magnetic correlations are associated with zero modes and have been calculated nonperturbatively. For d=3, the limit xi-->0 yields zeta(j)=j-2+xi(2j(3)+j(2)-5j-4)/[2(4j(2)-1)], where j (j>or=2) is the order in the Legendre polynomial decomposition applied to correlation functions. Conjectures on the fact that anisotropic components cannot change the isotropic threshold to the dynamo effect are also made.