Folding Dynamics and Its Intermittency in Turbulence.

Fluid elements deform in turbulence by stretching and folding. In this Letter, by projecting the material deformation tensor onto the largest stretching direction, we depict the dynamics of folding through the evolution of the material curvature. Results from direct numerical simulation (DNS) show that the curvature growth exhibits two regimes: first, a linear stage dominated by folding fluid elements through a persistent velocity Hessian that then transition to an exponential-growth stage driven by the stretching of already strongly bent fluid elements. This transition leads to strong curvature intermittency at later stages, which can be explained by a proposed curvature-evolution model. The link between velocity Hessian to folding provides a new way to understand the crucial steps in energy cascade and mixing in turbulence beyond the classical linear description of stretching dynamics.

A mathematical framework for estimating risk of airborne transmission of COVID-19 with application to face mask use and social distancing.

A mathematical model for estimating the risk of airborne transmission of a respiratory infection such as COVID-19 is presented. The model employs basic concepts from fluid dynamics and incorporates the known scope of factors involved in the airborne transmission of such diseases. Simplicity in the mathematical form of the model is by design so that it can serve not only as a common basis for scientific inquiry across disciplinary boundaries but it can also be understandable by a broad audience outside science and academia. The caveats and limitations of the model are discussed in detail. The model is used to assess the protection from transmission afforded by face coverings made from a variety of fabrics. The reduction in the transmission risk associated with increased physical distance between the host and susceptible is also quantified by coupling the model with available and new large eddy simulation data on scalar dispersion in canonical flows. Finally, the effect of the level of physical activity (or exercise intensity) of the host and the susceptible in enhancing the transmission risk is also assessed.

High-Reynolds-number fractal signature of nascent turbulence during transition.

Transition from laminar to turbulent flow occurring over a smooth surface is a particularly important route to chaos in fluid dynamics. It often occurs via sporadic inception of spatially localized patches (spots) of turbulence that grow and merge downstream to become the fully turbulent boundary layer. A long-standing question has been whether these incipient spots already contain properties of high-Reynolds-number, developed turbulence. In this study, the question is posed for geometric scaling properties of the interface separating turbulence within the spots from the outer flow. For high-Reynolds-number turbulence, such interfaces are known to display fractal scaling laws with a dimension [Formula: see text], where the 1/3 excess exponent above 2 (smooth surfaces) follows from Kolmogorov scaling of velocity fluctuations. The data used in this study are from a direct numerical simulation, and the spot boundaries (interfaces) are determined by using an unsupervised machine-learning method that can identify such interfaces without setting arbitrary thresholds. Wide separation between small and large scales during transition is provided by the large range of spot volumes, enabling accurate measurements of the volume-area fractal scaling exponent. Measurements show a dimension of [Formula: see text] over almost 5 decades of spot volume, i.e., trends fully consistent with high-Reynolds-number turbulence. Additional observations pertaining to the dependence on height above the surface are also presented. Results provide evidence that turbulent spots exhibit high-Reynolds-number fractal-scaling properties already during early transitional and nonisotropic stages of the flow evolution.

Grand challenges in the science of wind energy.

Harvested by advanced technical systems honed over decades of research and development, wind energy has become a mainstream energy resource. However, continued innovation is needed to realize the potential of wind to serve the global demand for clean energy. Here, we outline three interdependent, cross-disciplinary grand challenges underpinning this research endeavor. The first is the need for a deeper understanding of the physics of atmospheric flow in the critical zone of plant operation. The second involves science and engineering of the largest dynamic, rotating machines in the world. The third encompasses optimization and control of fleets of wind plants working synergistically within the electricity grid. Addressing these challenges could enable wind power to provide as much as half of our global electricity needs and perhaps beyond.

Large-deviation statistics of vorticity stretching in isotropic turbulence.

A key feature of three-dimensional fluid turbulence is the stretching and realignment of vorticity by the action of the strain rate. It is shown in this paper, using the cumulant-generating function, that the cumulative vorticity stretching along a Lagrangian path in isotropic turbulence obeys a large deviation principle. As a result, the relevant statistics can be described by the vorticity stretching Cramér function. This function is computed from a direct numerical simulation data set at a Taylor-scale Reynolds number of Re(λ)=433 and compared to those of the finite-time Lyapunov exponents (FTLE) for material deformation. As expected, the mean cumulative vorticity stretching is slightly less than that of the most-stretched material line (largest FTLE), due to the vorticity's preferential alignment with the second-largest eigenvalue of strain rate and the material line's preferential alignment with the largest eigenvalue. However, the vorticity stretching tends to be significantly larger than the second-largest FTLE, and the Cramér functions reveal that the statistics of vorticity stretching fluctuations are more similar to those of the largest FTLE. In an attempt to relate the vorticity stretching statistics to the vorticity magnitude probability density function in statistically stationary conditions, a model Kramers-Moyal equation is constructed using the statistics encoded in the Cramér function. The model predicts a stretched-exponential tail for the vorticity magnitude probability density function, with good agreement for the exponent but significant difference (35%) in the prefactor.

Multiscale geometry and scaling of the turbulent-nonturbulent interface in high Reynolds number boundary layers.

The scaling and surface area properties of the wrinkled surface separating turbulent from nonturbulent regions in open shear flows are important to our understanding of entrainment mechanisms at the boundaries of turbulent flows. Particle image velocimetry data from high Reynolds number turbulent boundary layers covering three decades in scale are used to resolve the turbulent-nonturbulent interface experimentally and, for the first time, determine unambiguously whether such surfaces exhibit fractal scaling. Box counting of the interface intersection with the measurement plane exhibits power-law scaling, with an exponent between -1.3 and -1.4. A complementary analysis based on spatial filtering of the velocity fields also shows power-law behavior of the coarse-grained interface length as a function of filter width, with an exponent between -0.3 and -0.4. These results establish that the interface is fractal-like with a multiscale geometry and fractal dimension of Df≈2.3-2.4.

Flux-freezing breakdown in high-conductivity magnetohydrodynamic turbulence.

The idea of 'frozen-in' magnetic field lines for ideal plasmas is useful to explain diverse astrophysical phenomena, for example the shedding of excess angular momentum from protostars by twisting of field lines frozen into the interstellar medium. Frozen-in field lines, however, preclude the rapid changes in magnetic topology observed at high conductivities, as in solar flares. Microphysical plasma processes are a proposed explanation of the observed high rates, but it is an open question whether such processes can rapidly reconnect astrophysical flux structures much greater in extent than several thousand ion gyroradii. An alternative explanation is that turbulent Richardson advection brings field lines implosively together from distances far apart to separations of the order of gyroradii. Here we report an analysis of a simulation of magnetohydrodynamic turbulence at high conductivity that exhibits Richardson dispersion. This effect of advection in rough velocity fields, which appear non-differentiable in space, leads to line motions that are completely indeterministic or 'spontaneously stochastic', as predicted in analytical studies. The turbulent breakdown of standard flux freezing at scales greater than the ion gyroradius can explain fast reconnection of very large-scale flux structures, both observed (solar flares and coronal mass ejections) and predicted (the inner heliosheath, accretion disks, γ-ray bursts and so on). For laminar plasma flows with smooth velocity fields or for low turbulence intensity, stochastic flux freezing reduces to the usual frozen-in condition.

Synchronization of chaos in fully developed turbulence.

We investigate chaos synchronization of small-scale motions in the three-dimensional turbulent energy cascade, via pseudospectral simulations of the incompressible Navier-Stokes equations. The modes of the turbulent velocity field below about 20 Kolmogorov dissipation lengths are found to be slaved to the chaotic dynamics of larger-scale modes. The dynamics of all dissipation-range modes can be recovered to full numerical precision by solving small-scale dynamical equations with the given large-scale solution as an input, regardless of initial condition. The synchronization rate exponent scales with the Kolmogorov dissipation time scale, with possible weak corrections due to intermittency. Our results suggest that all sub-Kolmogorov length modes should be fully recoverable from numerical simulations with standard, Kolmogorov-length grid resolutions.

Lagrangian refined Kolmogorov similarity hypothesis for gradient time evolution and correlation in turbulent flows.

We study time evolution of velocity and pressure gradients in isotropic turbulence by quantifying their autocorrelation functions and decorrelation time scales. The Lagrangian analysis uses data in a public database generated by direct numerical simulation at a Reynolds number Re{lambda} approximately 433. It is confirmed that when averaging over the entire domain, correlation functions decay on time scales on the order of the global Kolmogorov turnover time scale. However, when performing the analysis in different subregions of the flow, turbulence intermittency leads to large spatial variability in the decay time scales. Remarkably, excellent collapse of the autocorrelation functions is recovered when using a locally defined Kolmogorov time scale. This provides new evidence for the validity of Kolmogorov's refined similarity hypothesis, but from a Lagrangian viewpoint that provides a natural frame to describe the dynamics of turbulence.

Matrix exponential-based closures for the turbulent subgrid-scale stress tensor.

Two approaches for closing the turbulence subgrid-scale stress tensor in terms of matrix exponentials are introduced and compared. The first approach is based on a formal solution of the stress transport equation in which the production terms can be integrated exactly in terms of matrix exponentials. This formal solution of the subgrid-scale stress transport equation is shown to be useful to explore special cases, such as the response to constant velocity gradient, but neglecting pressure-strain correlations and diffusion effects. The second approach is based on an Eulerian-Lagrangian change of variables, combined with the assumption of isotropy for the conditionally averaged Lagrangian velocity gradient tensor and with the recent fluid deformation approximation. It is shown that both approaches lead to the same basic closure in which the stress tensor is expressed as the matrix exponential of the resolved velocity gradient tensor multiplied by its transpose. Short-time expansions of the matrix exponentials are shown to provide an eddy-viscosity term and particular quadratic terms, and thus allow a reinterpretation of traditional eddy-viscosity and nonlinear stress closures. The basic feasibility of the matrix-exponential closure is illustrated by implementing it successfully in large eddy simulation of forced isotropic turbulence. The matrix-exponential closure employs the drastic approximation of entirely omitting the pressure-strain correlation and other nonlinear scrambling terms. But unlike eddy-viscosity closures, the matrix exponential approach provides a simple and local closure that can be derived directly from the stress transport equation with the production term, and using physically motivated assumptions about Lagrangian decorrelation and upstream isotropy.

Pollen clumping and wind dispersal in an invasive angiosperm.

Pollen dispersal is a fundamental aspect of plant reproductive biology that maintains connectivity between spatially separated populations. Pollen clumping, a characteristic feature of insect-pollinated plants, is generally assumed to be a detriment to wind pollination because clumps disperse shorter distances than do solitary pollen grains. Yet pollen clumps have been observed in dispersion studies of some widely distributed wind-pollinated species. We used Ambrosia artemisiifolia (common ragweed; Asteraceae), a successful invasive angiosperm, to investigate the effect of clumping on wind dispersal of pollen under natural conditions in a large field. Results of simultaneous measurements of clump size both in pollen shedding from male flowers and airborne pollen being dispersed in the atmosphere are combined with a transport model to show that rather than being detrimental, clumps may actually be advantageous for wind pollination. Initial clumps can pollinate the parent population, while smaller clumps that arise from breakup of larger clumps can cross-pollinate distant populations.

Anomalous scaling and intermittency in three-dimensional synthetic turbulence.

A simple method, the multiscale minimal Lagrangian map (MMLM) approach, to generate synthetic turbulent vector fields was previously introduced [C. Rosales and C. Meneveau, Phys. Fluids 18, 075104 (2006)]. It was shown that the synthesized fields reproduce many statistical and geometric properties observed in real, isotropic, turbulence. In this paper we investigate if this procedure, which applies a minimal Lagrangian map to deform an initial Gaussian field, can produce also anomalous scaling in the inertial range. It is found that the advection Lagrangian map time scale is crucial in determining anomalous scaling properties. With the sweeping time scale used in the MMLM approach, non-Gaussian statistics and realistic geometric features are reproduced at each scale, but anomalous exponents are not observed; i.e., we observe nearly 1941 Kolmogorov scaling. Conversely, if the appropriate Kolmogorov inertial-range turnover time scale is used in a modified approach [the multiscale turnover Lagrangian map (MTLM) method], fields with realistic anomalous scaling exponents are reproduced. Remarkably, the intermittency and multifractal nature of the energy dissipation is also found to be quite realistic. Finally, the properties of the pressure field derived from the MTLM velocity field are studied and found to be quite realistic also. The results shed new light on what are minimal dynamical requirements for the generation of anomalous scaling and intermittency in turbulent flow: at least one turnover time for small eddies to be sufficiently deformed, as well as the accumulation of spatially correlated deformations across scales.

Multiscale model of gradient evolution in turbulent flows.

A multiscale model for the evolution of the velocity gradient tensor in turbulence is proposed. The model couples "restricted Euler" (RE) dynamics describing gradient self-stretching with a cascade model allowing energy exchange between scales. We show that inclusion of the cascade process is sufficient to regularize the finite-time singularity of the RE dynamics. Also, the model retains geometrical features of real turbulence such as preferential alignments of vorticity and joint statistics of gradient tensor invariants. Furthermore, gradient fluctuations are non-Gaussian, skewed in the longitudinal case, and derivative flatness coefficients are in good agreement with experimental data.

Subgrid-scale modeling of helicity and energy dissipation in helical turbulence.

The subgrid-scale (SGS) modeling of helical, isotropic turbulence in large eddy simulation is investigated by quantifying rates of helicity and energy cascade. Assuming Kolmogorov spectra, the Smagorinsky model with its traditional coefficient is shown to underestimate the helicity dissipation rate by about 40%. Several two-term helical models are proposed with the model coefficients calculated from simultaneous energy and helicity dissipation balance. The helical models are also extended to include dynamic determination of their coefficients. The models are tested a priori in isotropic steady helical turbulence. Together with the dynamic Smagorinsky model and the dynamic mixed model, they are also tested a posteriori in both decaying and steady isotropic helical turbulence by comparing results to direct numerical simulations (DNS). The a priori tests confirm that the Smagorinsky model underestimates SGS helicity dissipation, although quantitative differences with the predictions are observed due to the finite Reynolds number of the DNS. Also, in a posteriori tests improvement can be achieved for the helicity decay rate with the proposed models, compared with the Smagorinsky model. Overall, however, the effect of the new helical terms added to obtain the correct rate of global helicity dissipation is found to be quite small. Within the small differences, the various versions of the dynamic model provide the results closest to the DNS. The dynamic model's good performance in capturing mean kinetic energy dissipation at the finite Reynolds number of the simulations appears to be the most important aspect in accounting also for accurate prediction of the helicity dissipation.

Modeling flow around bluff bodies and predicting urban dispersion using large eddy simulation.

Modeling air pollutant transport and dispersion in urban environments is especially challenging due to complex ground topography. In this study, we describe a large eddy simulation (LES) tool including a new dynamic subgrid closure and boundary treatment to model urban dispersion problems. The numerical model is developed, validated, and extended to a realistic urban layout. In such applications fairly coarse grids must be used in which each building can be represented using relatively few grid-points only. By carrying out LES of flow around a square cylinder and of flow over surface-mounted cubes, the coarsest resolution required to resolve the bluff body's cross section while still producing meaningful results is established. Specifically, we perform grid refinement studies showing that at least 6-8 grid points across the bluff body are required for reasonable results. The performance of several subgrid models is also compared. Although effects of the subgrid models on the mean flow are found to be small, dynamic Lagrangian models give a physically more realistic subgrid-scale (SGS) viscosity field. When scale-dependence is taken into consideration, these models lead to more realistic resolved fluctuating velocities and spectra. These results set the minimum grid resolution and subgrid model requirements needed to apply LES in simulations of neutral atmospheric boundary layer flow and scalar transport over a realistic urban geometry. The results also illustrate the advantages of LES over traditional modeling approaches, particularly its ability to take into account the complex boundary details and the unsteady nature of atmospheric boundary layer flow. Thus LES can be used to evaluate probabilities of extreme events (such as probabilities of exceeding threshold pollutant concentrations). Some comments about computer resources required for LES are also included.

Origin of non-Gaussian statistics in hydrodynamic turbulence.

Turbulent flows are notoriously difficult to describe and understand based on first principles. One reason is that turbulence contains highly intermittent bursts of vorticity and strain rate with highly non-Gaussian statistics. Quantitatively, intermittency is manifested in highly elongated tails in the probability density functions of the velocity increments between pairs of points. A long-standing open issue has been to predict the origins of intermittency and non-Gaussian statistics from the Navier-Stokes equations. Here we derive, from the Navier-Stokes equations, a simple nonlinear dynamical system for the Lagrangian evolution of longitudinal and transverse velocity increments. From this system we are able to show that the ubiquitous non-Gaussian tails in turbulence have their origin in the inherent self-amplification of longitudinal velocity increments, and cross amplification of the transverse velocity increments.