Lagrangian Turbulence Research Articles

Transport and Scale Interactions in Geophysical Flows

This interdisciplinary workshop brought together researchers working on different aspects of transport and scale interactions across the spectrum of geophysical fluid dynamics: geometry and computation of transport and exchange processes in geophysical flows, Lagrangian coherent structures, (geo-strophic) turbulence, nonlinear waves and coherent structures in the Eulerian description of fluids, and stochastic methods in multiscale systems. Each of these topics have their own vibrant communities as well as well-established and emerging connections. This meeting aimed to bridge across the entire span of topics from a dynamical systems perspective, and to connect classical approaches with new developments in data-driven modeling and stochastic modeling.

Synthetic Lagrangian turbulence by generative diffusion models

Lagrangian turbulence lies at the core of numerous applied and fundamental problems related to the physics of dispersion and mixing in engineering, biofluids, the atmosphere, oceans and astrophysics. Despite exceptional theoretical, numerical and experimental efforts conducted over the past 30 years, no existing models are capable of faithfully reproducing statistical and topological properties exhibited by particle trajectories in turbulence. We propose a machine learning approach, based on a state-of-the-art diffusion model, to generate single-particle trajectories in three-dimensional turbulence at high Reynolds numbers, thereby bypassing the need for direct numerical simulations or experiments to obtain reliable Lagrangian data. Our model demonstrates the ability to reproduce most statistical benchmarks across time scales, including the fat-tail distribution for velocity increments, the anomalous power law and the increased intermittency around the dissipative scale. Slight deviations are observed below the dissipative scale, particularly in the acceleration and flatness statistics. Surprisingly, the model exhibits strong generalizability for extreme events, producing events of higher intensity and rarity that still match the realistic statistics. This paves the way for producing synthetic high-quality datasets for pretraining various downstream applications of Lagrangian turbulence.

Lagrangian large eddy simulations via physics-informed machine learning

High-Reynolds number homogeneous isotropic turbulence (HIT) is fully described within the Navier-Stokes (NS) equations, which are notoriously difficult to solve numerically. Engineers, interested primarily in describing turbulence at a reduced range of resolved scales, have designed heuristics, known as large eddy simulation (LES). LES is described in terms of the temporally evolving Eulerian velocity field defined over a spatial grid with the mean-spacing correspondent to the resolved scale. This classic Eulerian LES depends on assumptions about effects of subgrid scales on the resolved scales. Here, we take an alternative approach and design LES heuristics stated in terms of Lagrangian particles moving with the flow. Our Lagrangian LES, thus L-LES, is described by equations generalizing the weakly compressible smoothed particle hydrodynamics formulation with extended parametric and functional freedom, which is then resolved via Machine Learning training on Lagrangian data from direct numerical simulations of the NS equations. The L-LES model includes physics-informed parameterization and functional form, by combining physics-based parameters and physics-inspired Neural Networks to describe the evolution of turbulence within the resolved range of scales. The subgrid-scale contributions are modeled separately with physical constraints to account for the effects from unresolved scales. We build the resulting model under the differentiable programming framework to facilitate efficient training. We experiment with loss functions of different types, including physics-informed ones accounting for statistics of Lagrangian particles. We show that our L-LES model is capable of reproducing Eulerian and unique Lagrangian turbulence structures and statistics over a range of turbulent Mach numbers.

Study of turbulent transport in magnetized plasmas with flow using symplectic maps

Turbulent transport in a magnetized plasma of the kind found in tokamaks is modeled by a 2D wave spectrum that allows reduction to a symplectic map. The properties of particle transport when chaos sets in are analyzed in various circumstances including finite Larmor radius (FLR) effects and a background plasma flow. For large wave amplitudes, regular particle orbits become chaotic, which represents a type of Lagrangian turbulence. When chaos becomes global, it leads to the loss of particle confinement. Poloidal flows tend to decrease the chaos in some regions, and they can give rise to the formation of transport barriers. FLR effects not only reduce chaos but also give rise to non-local behavior. Thus, when the particles have a thermal distribution of Larmor radii, a non-Gaussian particle distribution function in space is obtained. However, the transport preserves its diffusive scaling when there is no flow. Previous results about the dependence of the diffusion coefficient with amplitude are re-derived analytically and numerically taking into account FLR effects. In the presence of general poloidal flows, the transport has to be described by a two-step map. They modify the nature of transport in the direction of the flow from diffusive to ballistic to super-ballistic, depending on the type of flow. The transverse transport, in turn, shows suppression of the oscillations with wave amplitude that are present in the absence of flow. When the plasma flow varies linearly with radius, the transport can be studied with a similar single-step map, and the transverse diffusion coefficient is reduced while parallel transport can become super-ballistic. For non-monotonic flows, there are accelerating modes that can produce ballistic-like particles while the bulk of the particles behaves diffusively.

Acceleration scaling and stochastic dynamics of a fluid particle in turbulence

Fluid-particle acceleration in turbulent flows is related to turbulent kinetic energy and its rate of dissipation into heat. Focusing on the statistics of the fluid-particle acceleration conditioned on both the local dissipation rate and the kinetic energy, it is shown that the acceleration grows exponentially with kinetic energy and presents a power law dependence on the dissipation. Based on these observations, we propose a vectorial stochastic model for the dynamics of a fluid particle giving the essential characteristics of Lagrangian turbulence.

Extreme events and instantons in Lagrangian passive scalar turbulence models.

The advection and mixing of a scalar quantity by fluid flow is an important problem in engineering and natural sciences. The statistics of the passive scalar exhibit complex behavior even in the presence of a Gaussian velocity field. This paper is concerned with two Lagrangian turbulence models that are based on the recent fluid deformation model, but adding a passive scalar field with uniform mean gradient. For a range of Reynolds numbers, these models can reproduce the statistics of passive scalar turbulence. For these models, we demonstrate how events of extreme passive scalar gradients can be recovered by computing the instanton, i.e., the saddle-point configuration of the associated stochastic field theory. It allows us to both reproduce the heavy-tailed statistics associated with passive scalar turbulence, and recover the most likely mechanism leading to such extreme events. We further demonstrate that events of large negative strain in these models undergo spontaneous symmetry breaking.

Markov property of Lagrangian turbulence

Based on direct numerical simulations with point-like inertial particles, with Stokes numbers St = 0, 0.5, 3, and 6, transported by homogeneous and isotropic turbulent flows, we present in this letter for the first time evidence for the existence of Markov property in Lagrangian turbulence. We show that the Markov property is valid for a finite step size larger than a Stokes-number-dependent Einstein-Markov coherence time scale. This enables the description of multi-scale statistics of Lagrangian particles by Fokker-Planck equations, which can be embedded in an interdisciplinary approach linking the statistical description of turbulence with fluctuation theorems of non-equilibrium stochastic thermodynamics and local flow structures. The formalism allows estimation of the stochastic thermodynamics entropy exchange associated with the particles Lagrangian trajectories. Entropy-consuming trajectories of the particles are related to specific evolution of velocity increments through scales and may be seen as intermittent structures. Statistical features of Lagrangian paths and entropy values are thus fixed by the fluctuation theorems.

SCIENTIFIC APPROACHES TO GLOBAL TURBULENCE: FEATURES OF ORIGIN, CURRENT STATE, AND IMPACT PERSPECTIVES

Any crisis is always followed by development and vice versa; after a crisis comes development. For socio-economic systems, these components are inherent. Due to the properties' importance, the duration, scale, and power affecting the socio-economic systems can change. Today the sustainable development of regions must be studied under the influence of global changes, which are uncontrollable. It is under such conditions that today regional socio-economic systems are in conditions of global turbulence. Therefore, the study of scientific approaches to the peculiarities of the occurrence, the current state of development, and the prospects of the impact of global turbulence on the economy is quite relevant and important that is the aim of the study. Based on the above, it is possible to formulate the task of the research, which consists of researching the scientific approaches to the peculiarities of the occurrence, the current state of development, and the prospects of the global turbulence impact on the economy. Using epistemological approach to the concept of "turbulence", it was established that this concept was widely used: in natural sciences as quantum, chemical, optical, wave, Lagrangian turbulence, and plasma turbulence; in medicine as the turbulence of the heart rhythm, turbulence in the circulatory system; in social life as turbulent world, turbulent society; in the economy as the turbulence of the global economy, market turbulence. The dynamic characteristics of the level of the shadow economy in Ukraine demonstrate the consequences of the influence of systemic factors, the corona crisis, and military escalation. Ukraine's economy's definition depends on the implemented reforms' effectiveness and public recognition. The only way to a destination is the formation of a favorable environment for financial and economic activity in the legal sphere due to the improvement of the conditions of doing business and carrying out investment activities, in general, the creation of conditions in which the shadow economy will be uninteresting, unprofitable and ineffective for its subjects. The priority vector for economic activity in Ukraine is the legalization of business and labor relations, the increase of non-cash payments, and the increase in the level of the payment infrastructure use due to the reduction in prices. Keywords: global turbulence, socio-economic systems, crisis.

Modulating flow and mixing characteristics of an inclined jet in crossflow at a large backward inclination angle by acoustic excitation

Previous investigations revealed that the backward-inclined jet in crossflow exhibits seemingly lower transverse velocity and turbulence intensity at inclination angles higher than a critical value about 25°, thus resulting in significantly low jet fluid dispersion properties. In this article, the acoustic excitations were applied to a backward-inclined jet in crossflow at an inclination angle higher than the critical value to examine experimentally whether the flow and dispersion characteristics could be improved or not. The flow in the test section of an open-loop wind tunnel was used as the crossflow. A profiled nozzle assembly with a loudspeaker installed in the lower part of it was used to generate the pulsating jet. The instantaneous and time-averaged smoke flow patterns were obtained by the laser-light-sheet assisted flow visualization method. The binary edge detection method was employed to the long-exposure smoke flow images to measure the jet spread width. The turbulence intensities, as well as the Lagrangian integral turbulence time and length scales, were obtained using a hotwire anemometer. The jet-fluid dispersion characteristics were examined using the tracer-gas detection technique. The results revealed that in the domain of jet pulsation intensity and excitation Strouhal number, the pulsed backward-inclined jet in crossflow presented three characteristic flow modes: synchronized oscillating jet, transition, and synchronized shear-layer vortices. The synchronized oscillating jet exhibited violent transverse oscillations due to the high axial jet pulsations induced by the acoustic excitation. The transverse jet width and jet penetration height were enlarged. The turbulence intensities were significantly increased, and the turbulence time and length scales were decreased, therefore led to a significant enhancement in the jet-fluid dispersions and mixing capabilities.

Lagrangian turbulence in the woods

Abstract

Innovative Mini Ultralight Radioprobes to Track Lagrangian Turbulence Fluctuations within Warm Clouds: Electronic Design.

Characterization of dynamics inside clouds remains a challenging task for weather forecasting and climate modeling as cloud properties depend on interdependent natural processes at micro- and macro-scales. Turbulence plays an important role in particle dynamics inside clouds; however, turbulence mechanisms are not yet fully understood partly due to the difficulty of measuring clouds at the smallest scales. To address these knowledge gaps, an experimental method for measuring the influence of small-scale turbulence in cloud formation in situ and producing an in-field cloud Lagrangian dataset is being developed by means of innovative ultralight radioprobes. This paper presents the electronic system design along with the obtained results from laboratory and field experiments regarding these compact (diameter ≈30 cm), lightweight (≈20 g), and expendable devices designed to passively float and track small-scale turbulence fluctuations inside warm clouds. The fully customized mini-radioprobe board (5 cm × 5 cm) embeds sensors to measure local fluctuations and transmit data to the ground in near real time. The tests confirm that the newly developed probes perform well, providing accurate information about atmospheric turbulence as referenced in space. The integration of multiple radioprobes allows for a systematic and accurate monitoring of atmospheric turbulence and its impact on cloud formation.

On the Well-Mixed Condition and Consistency Issues in Hybrid Eulerian/Lagrangian Stochastic Models of Dispersion

We clarify issues related to the expression of Lagrangian stochastic models used for atmospheric dispersion applications. Two aspects are addressed: the need to verify the well-mixed criterion and the correspondence between Eulerian and Lagrangian turbulence models when they are combined in practical simulations. In particular, it is recalled that the fulfillment of the well-mixed criterion depends only on the proper incorporation of the mean pressure-gradient term as the mean drift term of the Langevin equation. New consistency issues between duplicate fields within Eulerian/Lagrangian hybrid formulations are also brought out, especially regarding turbulence models, boundary conditions, and divergence-free condition. Such hybrid methods, where mean flow quantities calculated with an Eulerian approach are provided to the Lagrangian approach, are commonly used in atmospheric dispersion simulations for their numerical efficiency. Nevertheless, it is shown that serious inconsistencies can result from coupling Eulerian and Lagrangian models that do not correspond to the same level of description of the fluid turbulence.

Pair dispersion in inhomogeneous turbulent thermal convection

Due to large scale flow inhomogeneities and the effects of temperature, turbulence small-scale structure in thermal convection is still an active field of investigation, especially considering sophis- ticated Lagrangian statistics. Here we experimentally study Lagrangian pair dispersion (one of the canonical problems of Lagrangian turbulence) in a Rayleigh-B enard convection cell. A sufficiently high temperature difference is imposed on a horizontal layer of fluid to observe a turbulent flow. We perform Lagrangian tracking of sub-millimetric particles on a large measurement volume in- cluding part of the Large Scale Circulation (LSC) revealing some large inhomogeneities. Our study brings to light several new insights regarding our understanding of turbulent thermal convection: (i) by decomposing particle Lagrangian dynamics into the LSC contribution and the turbulent fluc- tuations, we highlight the relative impact of both contributions on pair dispersion; (ii) using the same decomposition, we estimate the Eulerian second-order velocity structure functions from pair statistics and show that after removing the LSC contribution, the remaining statistics recover usual homogeneous and isotropic behaviours which are governed by a local energy dissipation rate to be distinguished from the global dissipation rate classically used to characterise turbulence in thermal convection; and (iii) we revisit the super-diffusive Richardson-Obukhov regime of particle dispersion and propose a refined estimate of the Richardson constant.

Irregular dynamics of cellular blood flow in a model microvessel.

The flow of red blood cells within cylindrical vessels is complex and irregular, so long as the vessel diameter is somewhat larger than the nominal cell size. Long-time-series simulations, in which cells flow 10^{5} vessel diameters, are used to characterize the chaotic kinematics, particularly to inform reduced-order models. The simulation model used includes full coupling between the elastic red blood cell membranes and surrounding viscous fluid, providing a faithful representation of the cell-scale dynamics. Results show that the flow has neither classifiable recurrent features nor a dominant frequency. Instead, its kinematics are sensitive to the initial flow configuration in a way consistent with chaos and Lagrangian turbulence. Phase-space reconstructions show that a low-dimensional attractor does not exist, so the observed long-time dynamics are effectively stochastic. Based on this, a simple Markov chain model for the dynamics is introduced and shown to reproduce the statistics of the cell positions.

Turbulent electric current in the marine convective atmospheric boundary layer

The atmospheric boundary layer considered a part of the planetary global electric circuit is known to exhibit a most dramatically changing in space and time atmospheric electrical variables. Extremely low specific electrical conductivity in the lower atmosphere is accompanied by the work of the electric generator associated with turbulent dynamo realizing itself through the space charge transport by boundary layer flows. The electromotive force of this generator acting in fair weather atmospheric regions provides a contribution to the global potential drop between the lower ionosphere and the earth's surface. In this study, the vertical electric current density produced by the turbulent transfer of space charge is investigated in the cases of the buoyancy-dominated and shear-dominated convective boundary layer (CBL) over the oceans based on second-order dissipation-conditioned Lagrangian stochastic model (LSM) applied near air-sea interface and conjugated with first-order LSM in the rest of the CBL. The total electric charge flux is treated in terms of mechanical transfer of atmospheric ions and charged aerosol particles by Lagrangian turbulence together with the drift of small ions in the self-consistent electric field. This approach based on a transported probability density function method offers persuasive advantages for quantitative estimates of local perturbations in the fair-weather electric field created by the atmospheric space charge carried by turbulent flows. It is found that the space charge density vertical profile only slightly depends on turbulence everywhere except for the wavy boundary layer about 10 m thick, a new parameterization of space charge vertical profile is proposed. Based on the simulation results, it can be predicted that in the buoyancy-dominated CBLs the electric field must be greater than in the sheared CBLs with other things being equal. Turbulent electromotive force and changes in total downward atmospheric electric current density are quantified. Simulated vertical profiles of electrical conductivity, space charge, electric field, and turbulent current density reasonably well reproduce previously reported observation results.

Extended 3D-PTV for direct measurements of Lagrangian statistics of canopy turbulence in a wind tunnel

Direct estimation of Lagrangian turbulence statistics is essential for the proper modeling of dispersion and transport in highly obstructed canopy flows. However, Lagrangian flow measurements demand very high rates of data acquisition, resulting in bottlenecks that prevented the estimation of Lagrangian statistics in canopy flows hitherto. We report on a new extension to the 3D Particle Tracking Velocimetry (3D-PTV) method, featuring real-time particle segmentation that outputs centroids and sizes of tracer particles and performed on dedicated hardware during high-speed digital video acquisition from multiple cameras. The proposed extension results in four orders of magnitude reduction in data transfer rate that enables to perform substantially longer experimental runs, facilitating measurements of convergent statistics. The extended method is demonstrated through an experimental wind tunnel investigation of the Lagrangian statistics in a heterogeneous canopy flow. We observe that acceleration statistics are affected by the mean shear at the top of the canopy layer and that Lagrangian particle dispersion at small scales is dominated by turbulence in the wake of the roughness elements. This approach enables to overcome major shortcomings from Eulerian-based measurements which rely on assumptions such as the Taylor’s frozen turbulence hypothesis, which is known to fail in highly turbulent flows.

Theoretical hydrodynamic efficiency of coccoliths

Abstract The sinking speed of coccoliths, considered as small particles, mainly depends on turbulence processes in the upper layer of the ocean. In deeper layers, the size, shape, buoyancy, and drag force experienced between the contact surface and the fluid in which particles are immersed are fundamental determinants of the sinking speed. For spherical bodies, the sinking speed is explained by the Stokes formula. For other geometries, it can be explained by the shape resistance factor of an equivalent sphere with the same density and volume as the original body. To model the sinking trajectories of coccoliths in the upper layer, a Lagrangian turbulence model was applied. To estimate how the size and shape of some coccoliths influence their sinking speed and trajectory in deeper layers, experimental videos were taken of sinking coccoliths made at amplified scales in a graduated water tank and analyzed. In the upper layer, the sinking speed only depends on the intensity of turbulence. Below this layer, the shape resistance factor reduced the sinking speed with respect to that of the equivalent sphere by an average of 50%. The Lagrangian model shows that, in the turbulent mixing layer, the distribution of particles is homogeneous, but once the particles fall below the laminar layer, the distribution takes on the form of a thin lens with a central thickness that is proportional to the sinking speed. The particles then flatten out to a thin strip as they continue along their path to the ocean bottom.

Near‐wake flow simulation of a vertical axis turbine using an actuator line model

AbstractIn the present work, the near‐wake generated for a vertical axis wind turbine (VAWT) was simulated using an actuator line model (ALM) in order to validate and evaluate its accuracy. The sensitivity of the model to the variation of the spatial and temporal discretization was studied and showed a bigger response to the variation in the mesh size as compared with the temporal discretization. The large eddy simulation (LES) approach was used to predict the turbulence effects. The performance of Smagorinsky, dynamic k‐equation, and dynamic Lagrangian turbulence models was tested, showing very little relevant differences between them. Generally, predicted results agree well with experimental data for velocity and vorticity fields in representative sections. The presented ALM was able to characterize the main phenomena involved in the flow pattern using a relatively low computational cost without stability concerns, identified the general wake structure (qualitatively and quantitatively), and the contribution from the blade tips and motion on it. Additionally, the effects of the tower and struts were investigated with respect to the overall structure of the wake, showing no significant modification. Similarities and discrepancies between numerical and experimental results are discussed. The obtained results from the various simulations carried out here can be used as a practical reference guideline for choosing parameters in VAWTs simulations using the ALM.

Non-intermittent turbulence: Lagrangian chaos and irreversibility

Simulations of Lagrangian turbulence with Fourier components removed (decimation) show no effect on the level of chaos but an emergent time reversality as indicated by the ratio of Lyapunov exponents shown in the figure.

Energy dissipation statistics along the Lagrangian trajectories in three-dimensional turbulent flows

Energy dissipation rate is relevant in the turbulent phenomenology theory, such as the classical Kolmogorov 1941 and 1962 refined similarity hypothesis. However, it is extremely difficult to retrieve experimentally or numerically. In this paper, the full energy dissipation, its proxy and the pseudo-energy dissipation rate along the Lagrangian trajectories in the three-dimensional turbulent flows are examined by using a state-of-art high resolution direct numerical simulation database with a Reynolds number Re λ = 400. It is found that the energy dissipation proxy e P is more correlated with the full energy dissipation rate e. The corresponding correlation coefficient ρ between the velocity gradient and e shows a Gaussian distribution. Furthermore, the coarse-grained dissipation rate is considered. The cross correlation ρ is found to be increased with the increasing of the scale τ. Finally, the hierarchical structure is extracted for the full energy dissipation rate, its proxy and the pseudo one. The results show a power-law behavior in the inertial range 10 ≤τ/τ η ≤ 100. The experimental scaling exponent of the full energy dissipation rate is found to be h L =0.69, agrees very well with the one found for the Eulerian velocity. The experimental values for e P and e S are around h L = 0.78, implying a more intermittent Lagrangian turbulence. Therefore, the intermittency parameter provided by e P and e S will be biased.