Periodic epidemic outbursts explained by local saturation of clusters.

Adding the notion of spatial locality to the susceptible-infected-recovered (or SIR) model, allows to capture local saturation of an epidemic. The resulting minimum model of an epidemic, consisting of five ordinary differential equations with constant model coefficients, reproduces slowly decaying periodic outbursts, as observed in the COVID-19 or Spanish flu epidemic. It is shown that if immunity decays, even slowly, the model yields a fully periodic dynamics.

Spontaneous generation and reversal of helicity in anisotropic turbulence.

Helicity plays an important role in spectacular geophysical phenomena such as hurricanes or the generation of the terrestrial magnetic field. The present investigation shows how helicity can be created in a statistically homogeneous but anisotropic flow, driven by buoyancy. If the flow is close enough to a two-dimensional limit, spontaneous symmetry breaking leads to the generation of mean helicity. In particular, we explain these observations by identifying a simple linear mechanism, the relevance of which is illustrated by simulations of unstably stratified turbulence in a conducting fluid on which a magnetic field is imposed. Finally it is shown that the self-organized state displays dynamical reversals of the sign of the mean helicity.

Modeling the role of clusters and diffusion in the evolution of COVID-19 infections during lock-down.

The dynamics of the spread of epidemics, such as the recent outbreak of the SARS-CoV-2 virus, is highly nonlinear and therefore difficult to predict. As time evolves in the present pandemic, it appears more and more clearly that a clustered dynamics is a key element of the description. This means that the disease rapidly evolves within spatially localized networks, that diffuse and eventually create new clusters. We improve upon the simplest possible compartmental model, the SIR model, by adding an additional compartment associated with the clustered individuals. This sophistication is compatible with more advanced compartmental models and allows, at the lowest level of complexity, to leverage the well-mixedness assumption. The so-obtained SBIR model takes into account the effect of inhomogeneity on epidemic spreading, and compares satisfactorily with results on the pandemic propagation in a number of European countries, during and immediately after lock-down. Especially, the decay exponent of the number of new cases after the first peak of the epidemic is captured without the need to vary the coefficients of the model with time. We show that this decay exponent is directly determined by the diffusion of the ensemble of clustered individuals and can be related to a global reproduction number, that overrides the classical, local reproduction number.

Linearly forced isotropic turbulence at low Reynolds numbers.

We investigate the forcing strength needed to sustain a flow using linear forcing. A critical Reynolds number R_{c} is determined, based on the longest wavelength allowed by the system, the forcing strength and the viscosity. A simple model is proposed for the dissipation rate, leading to a closed expression for the kinetic energy of the flow as a function of the Reynolds number. The dissipation model and the prediction for the kinetic energy are assessed using direct numerical simulations and two-point closure integrations. An analysis of the dissipation-rate equation and the triadic structure of the nonlinear transfer allows to refine the model in order to reproduce the low-Reynolds-number asymptotic behavior, where the kinetic energy is proportional to R-R_{c}.

Generation of Atmospheric Turbulence with Unprecedentedly Large Reynolds Number in a Wind Tunnel.

Generating laboratory flows resembling atmospheric turbulence is of prime importance to study the effect of wind fluctuations on objects such as buildings, vehicles, or wind turbines. A novel driving of an active grid following a stochastic process is used to generate velocity fluctuations with correlation lengths, and, thus, integral scales, much larger than the transverse dimension of the wind tunnel. The combined action of the active grid and a modulation of the fan speed allows one to generate a flow characterized by a four-decade inertial range and an integral scale Reynolds number of 2×10^{7}.

Efficiency of laminar and turbulent mixing in wall-bounded flows.

A turbulent flow mixes in general more rapidly a passive scalar than a laminar flow does. From an energetic point of view, for statistically homogeneous or periodic flows, the laminar regime is more efficient. However, the presence of walls may change this picture. We consider in this investigation mixing in two-dimensional laminar and turbulent wall-bounded flows using direct numerical simulation. We show that for sufficiently large Schmidt number, turbulent flows more efficiently mix a wall-bounded scalar field than a chaotic or laminar flow does. The mixing efficiency is shown to be a function of the Péclet number, and a phenomenological explanation yields a scaling law, consistent with the observations.

Power fluctuations in turbulence.

To generate or maintain a turbulent flow, one needs to introduce kinetic energy. This energy injection necessarily fluctuates and these power fluctuations act on all turbulent excited length scales. If the power is injected using forces proportional to the velocity, such as those common in shear flows, or with a force acting at the largest scales only, the spectrum of these fluctuations is shown to have a universal inertial range, proportional to the energy spectrum.

Structure of sheared and rotating turbulence: Multiscale statistics of Lagrangian and Eulerian accelerations and passive scalar dynamics.

The acceleration statistics of sheared and rotating homogeneous turbulence are studied using direct numerical simulation results. The statistical properties of Lagrangian and Eulerian accelerations are considered together with the influence of the rotation to shear ratio, as well as the scale dependence of their statistics. The probability density functions (pdfs) of both Lagrangian and Eulerian accelerations show a strong and similar dependence on the rotation to shear ratio. The variance and flatness of both accelerations are analyzed and the extreme values of the Eulerian acceleration are observed to be above those of the Lagrangian acceleration. For strong rotation it is observed that flatness yields values close to three, corresponding to Gaussian-like behavior, and for moderate and vanishing rotation the flatness increases. Furthermore, the Lagrangian and Eulerian accelerations are shown to be strongly correlated for strong rotation due to a reduced nonlinear term in this case. A wavelet-based scale-dependent analysis shows that the flatness of both Eulerian and Lagrangian accelerations increases as scale decreases, which provides evidence for intermittent behavior. For strong rotation the Eulerian acceleration is even more intermittent than the Lagrangian acceleration, while the opposite result is obtained for moderate rotation. Moreover, the dynamics of a passive scalar with gradient production in the direction of the mean velocity gradient is analyzed and the influence of the rotation to shear ratio is studied. Concerning the concentration of a passive scalar spread by the flow, the pdf of its Eulerian time rate of change presents higher extreme values than those of its Lagrangian time rate of change. This suggests that the Eulerian time rate of change of scalar concentration is mainly due to advection, while its Lagrangian counterpart is only due to gradient production and viscous dissipation.

Angular statistics of Lagrangian trajectories in turbulence.

The angle between subsequent particle displacement increments is evaluated as a function of the time lag in isotropic turbulence. It is shown that the evolution of this angle contains two well-defined power laws, reflecting the multiscale dynamics of high-Reynolds number turbulence. The probability density function of the directional change is shown to be self-similar and well approximated by an analytically derived model assuming Gaussianity and independence of the velocity and the Lagrangian acceleration.

Dependence of turbulent advection on the Lagrangian correlation time.

In turbulent scalar mixing, starting from random initial conditions, the root-mean-square advection term rapidly drops as the flow and the scalar field organize. We show first analytically, for the simplified case of a blob in shear flow with a finite correlation time, how the advection term is reduced compared to a randomly aligned scalar structure. This picture is then generalized to turbulent mixing. These examples show that the rapid depletion of advection depends on the lifetime of turbulent structures, compared to the local straining time scale. A turbulence closure is used to show that the Lagrangian correlation time indeed determines the deviation from Gaussian behavior. In particular it is shown that in the inertial range the depletion mechanism is self-similar, since a constant ratio is observed between the advection spectrum and its Gaussian equivalent. Finally, direct numerical simulation shows that in the limit of an infinite correlation time of the turbulent eddies, corresponding to a frozen velocity field, the mean-square advection tends to a zero fraction of its Gaussian estimate.

Intrinsic rotation of toroidally confined magnetohydrodynamics.

The spatiotemporal self-organization of viscoresistive magnetohydrodynamics in a toroidal geometry is studied. Curl-free toroidal magnetic and electric fields are imposed. It is observed in our simulations that a flow is generated, which evolves from dominantly poloidal to toroidal when the Lundquist numbers are increased. It is shown that this toroidal organization of the flow is consistent with the tendency of the velocity field to align with the magnetic field. Up-down asymmetry of the geometry causes the generation of a nonzero toroidal angular momentum.

Influence of initial mean helicity on homogeneous turbulent shear flow.

Helicity statistics are studied in homogeneous turbulent shear flow. Initial mean helicity is imposed on an isotropic turbulence field using a decomposition of the flow into complex-valued helical waves. The initial decay of the turbulent kinetic energy is weakened in the presence of strong mean helicity, consistent with an analytic analysis of the spectral tensor of velocity correlations. While exponential growth of the mean turbulent kinetic energy is obtained, the mean helicity decays. Probability distribution functions (PDFs) of helicity are skewed and show that the imposed mean helicity prevails throughout the simulations. A wavelet-based scale-dependent analysis shows a trend to two dimensionalization for large scales of motion and a preference for helical motion at small scales. The magnitude of the skewness of the PDFs decreases for smaller scales. Joint PDFs indicate a strong correlation of the signs of both, helicity and superhelicity, for all cases. This correlation supports the conjecture that superhelicity dissipates helicity.

Rapid generation of angular momentum in bounded magnetized plasma.

Direct numerical simulations of two-dimensional decaying MHD turbulence in bounded domains show the rapid generation of angular momentum in nonaxisymmetric geometries. It is found that magnetic fluctuations enhance this mechanism. On a larger time scale, the generation of a magnetic angular momentum, or angular field, is observed. For axisymmetric geometries, the generation of angular momentum is absent; nevertheless, a weak magnetic field can be observed. The derived evolution equations for both the angular momentum and angular field yield possible explanations for the observed behavior.

Extreme Lagrangian acceleration in confined turbulent flow.

A Lagrangian study of two-dimensional turbulence for two different geometries, a periodic and a confined circular geometry, is presented to investigate the influence of solid boundaries on the Lagrangian dynamics. It is found that the Lagrangian acceleration is even more intermittent in the confined domain than in the periodic domain. The flatness of the Lagrangian acceleration as a function of the radius shows that the influence of the wall on the Lagrangian dynamics becomes negligible in the center of the domain, and it also reveals that the wall is responsible for the increased intermittency. The transition in the Lagrangian statistics between this region, not directly influenced by the walls, and a critical radius which defines a Lagrangian boundary layer is shown to be very sharp with a sudden increase of the acceleration flatness from about 5 to about 20.

Small-scale intermittency in anisotropic turbulence.

Isotropic, rotating, and stratified turbulent flows are analyzed using a scale- and direction-dependent flatness. The anisotropy of the spatial fluctuations of the energy distribution can hereby be quantified for different length scales. This measure allows one to distinguish between longitudinal and transversal intermittency as well as between horizontal and vertical intermittency. The difference between longitudinal and transversal intermittency is argued to be related to the incompressiblity constraint. A large difference between horizontal and vertical intermittency for stratified turbulence can be explained by an energy depletion of the horizontal plane in Fourier space.