Turbulent Dynamics Research Articles

MRI turbulence in vertically stratified accretion discs at large magnetic Prandtl numbers

ABSTRACT The discovery of the first binary neutron star merger, GW170817, has spawned a plethora of global numerical relativity simulations. These simulations are often ideal (with dissipation determined by the grid) and/or axisymmetric (invoking ad hoc mean-field dynamos). However, binary neutron star mergers (similar to X-ray binaries and active galactic nuclei inner discs) are characterized by large magnetic Prandtl numbers, $\rm Pm$, (the ratio of viscosity to resistivity). $\rm Pm$ is a key parameter determining dynamo action and dissipation but it is ill-defined (and likely of order unity) in ideal simulations. To bridge this gap, we investigate the magnetorotational instability (MRI) and associated dynamo at large magnetic Prandtl numbers using fully compressible, three-dimensional, vertically stratified, isothermal simulations of a local patch of a disc. We find that, within the bulk of the disc (z ≲ 2H, where H is the scale-height), the turbulent intensity (parametrized by the stress-to-thermal-pressure ratio α), and the saturated magnetic field energy density, Emag, produced by the MRI dynamo, both scale as a power with Pm at moderate Pm (4 ≲ Pm ≲ 32): Emag ∼ Pm0.74 and α ∼ Pm0.71, respectively. At larger Pm (≳ 32), we find deviations from power-law scaling and the onset of a plateau. Compared to our recent unstratified study, this scaling with Pm becomes weaker further away from the disc mid-plane, where the Parker instability dominates. We perform a thorough spectral analysis to understand the underlying dynamics of small-scale MRI-driven turbulence in the mid-plane and of large-scale Parker-unstable structures in the atmosphere.

The evolution of whole-brain turbulent dynamics during recovery from traumatic brain injury.

It has been previously shown that traumatic brain injury (TBI) is associated with reductions in metastability in large-scale networks in resting-state fMRI (rsfMRI). However, little is known about how TBI affects the local level of synchronization and how this evolves during the recovery trajectory. Here, we applied a novel turbulent dynamics framework to investigate whole-brain dynamics using an rsfMRI dataset from a cohort of moderate to severe TBI patients and healthy controls (HCs). We first examined how several measures related to turbulent dynamics differ between HCs and TBI patients at 3, 6, and 12 months post-injury. We found a significant reduction in these empirical measures after TBI, with the largest change at 6 months post-injury. Next, we built a Hopf whole-brain model with coupled oscillators and conducted in silico perturbations to investigate the mechanistic principles underlying the reduced turbulent dynamics found in the empirical data. A simulated attack was used to account for the effect of focal lesions. This revealed a shift to lower coupling parameters in the TBI dataset and, critically, decreased susceptibility and information-encoding capability. These findings confirm the potential of the turbulent framework to characterize longitudinal changes in whole-brain dynamics and in the reactivity to external perturbations after TBI.

Effects of resonant magnetic perturbations on turbulence and flows in the edge of HL-2A plasmas

The influence of resonant magnetic perturbations (RMPs) on the dynamics of turbulence and flows at the edge of the HL-2A tokamak is analyzed utilizing transfer entropy technique. The results have shown that the RMP damps the poloidal flows as well as the E × B shearing rate, whereas enhances the toroidal flows and leads to a broadened particle spectrum with increased small scale turbulence transport. The causality analysis indicates that the regulation impact of poloidal flow on turbulent fluctuations and particle flux is weakened, while that of the toroidal rotation on the latter is strengthened by the RMP field. The impact of the changes in poloidal flow dominates over that of the modified toroidal flow on turbulent transport in the edge. The magnetic perturbation and the flows generally show predator–prey oscillations, where the causal effect between the former and the toroidal flow transits to a synchronization relation in the presence of RMP. In addition, the RMP field will weaken the causal effect on poloidal Reynolds stress while strengthening the parallel-radial component simultaneously. The present findings provide a possible explanation on the effects of external fields on the edge transport, which is suggested to be dominated by the complex interactions among external perturbations, flows, and ambient microturbulence.

Random matrix model of Kolmogorov-Zakharov turbulence.

We introduce and study a random matrix model of Kolmogorov-Zakharov turbulence in a nonlinear purely dynamical finite-size system with many degrees of freedom. For the case of a direct cascade, the energy and norm pumping takes place at low energy scales with absorption at high energies. For a pumping strength above a certain chaos border, a global chaotic attractor appears with a stationary energy flow through a Hamiltonian inertial energy interval. In this regime, the steady-state norm distribution is described by an algebraic decay with an exponent in agreement with the Kolmogorov-Zakharov theory. Below the chaos border, the system is located in the quasi-integrable regime similar to the Kolmogorov-Arnold-Moser theory and the turbulence is suppressed. For the inverse cascade, the system rapidly enters a strongly nonlinear regime where the weak turbulence description is invalid. We argue that such a dynamical turbulence is generic, showing that it is present in other lattice models with disorder and Anderson localization. We point out that such dynamical models can be realized in multimode optical fibers.

Periodic bursting cycles on the edge to square duct turbulence

The long-time behaviour of trajectories embedded in the edge manifold between the laminar and turbulent basins of attraction is investigated in order to identify simple invariant solutions to the Navier-Stokes equations in straight ducts with square cross-section. With the aid of the iterative bisection procedure of Toh and Itano (J. Fluid Mech., vol. 481, 2003, pp. 67-76), we detect three travelling waves that represent attracting ‘edge states’ within the separatrix and saddles w.r.t. the full state space. All three travelling waves are presumably connected to solutions known in the community. In other situations, the edge states to which trajectories are attracted seem to be invariant periodic cycles that feature a rich dynamics: Along each cycle, the flow oscillates periodically between two flow states, in each of which streamwise vorticity is predominantly residing near one set of parallel walls, while the vortical activity associated to the other pair of opposing walls is markedly reduced. This ‘switching’ dynamics is accompanied by intermittent bursting-like high-dissipation excursions. While we cannot rigorously prove that the identified periodic cycle is a periodic orbit rather than a finite-precision approximation to a heteroclinic cycle, sound arguments for the former supposition are given. Interestingly, the different phases of the periodic cycle qualitatively resemble a similar ‘switching’ behaviour observed in (chaotic) marginal turbulence, which suggests that the found periodic cycles could help understanding the characteristic dynamics of duct turbulence at low Reynolds numbers.

Are the dynamics of wall turbulence in minimal channels and larger domain channels equivalent? A graph-theoretic approach

This work proposes two algorithmic approaches to extract critical dynamical mechanisms in wall-bounded turbulence with minimum human bias. In both approaches, multiple types of coherent structures are spatiotemporally tracked, resulting in a complex multilayer network. Network motif analysis, i.e., extracting dominant non-random elemental patterns within these networks, is used to identify the most dominant dynamical mechanisms. Both approaches, combined with network motif analysis, are used to answer whether the main dynamical mechanisms of a minimal flow unit (MFU) and a larger unconstrained channel flow, labeled a full channel (FC), at Reτ ≈ 180, are equivalent. The first approach tracks traditional coherent structures defined as low- and high-speed streaks, ejections, and sweeps. It is found that the roll-streak pairing, consistent with the current understanding of self-sustaining processes, is the most significant and simplest dynamical mechanism in both flows. However, the MFU has a timescale for this mechanism that is approximately 2.83 times slower than that of the FC. In the second approach, we use semi-Lagrangian wavepackets and define coherent structures from their energetic streak, roll, and small-scale phase space. This method also shows similar motifs for both the MFU and FC. It indicates that, on average, the most dominant phase-space motifs are similar between the two flows, with the significant events taking place approximately 2.21 times slower in the MFU than in the FC. This value is more consistent with the implied timescale ratio of only the slow speed streaks taking part in the roll-streak pairing extracted using the first multi-type spatiotemporal approach, which is approximately 2.17 slower in the MFU than the FC.

Experimental study of the effect of particle–wall interactions on inertial particle dynamics in wall turbulence

Based on Voronoi analysis, the properties related to the near-wall motion of particles in a turbulent boundary layer were experimentally investigated via different release modes, with a friction Reynolds number $Re_\tau =3530$ . For high-inertia sand particles with Stokes number $St^+ \sim O(10^2\unicode{x2013}10^3)$ and a volume fraction $\varPhi _v \sim O(10^{-4})$ , particle image tracking velocimetry was used to determine the particle position and near-wall distribution properties. We established three particle release modes, including top-released, bottom overall-released and bottom partially released sand particles, under the same flow field conditions and calculated the differences in particle near-wall clustering and void properties. It was confirmed that wall effects (including collision and strike-splash) have a great influence on particle clustering and void behaviour near the wall. In the top-released sand particle and locally laid sand particle cases, particles bounced off the smooth walls and re-entered the carrier flow, causing significant clustering and sparsing of particles near the walls. In contrast, in the overall sand-laying case where the bottom wall was completely covered with sand particles, there is no apparent cluster or void phenomenon near the wall $(z/\delta <0.12)$ and the particles are randomly distributed, due to the combined effect of particle impact and splashing. In addition, the clustering and voids of particles become more pronounced with increasing wall-normal distance in the three release modes, and the particle distribution shows some self-similarity at each flow layer. The probability density function of the concentration of cluster particles decreases following a ‘ $-5/3$ ’ power law. However, due to the particle–wall interaction, the probability density function gradually deviates from the ‘ $-5/3$ ’ power law.

Analysis of the airflow features and ventilation efficiency of an Ultra-Clean-Air operating theatre by qDNS simulations and experimental validation

Ultra-Clean-Air (UCA) operating theatres aim to minimise surgical instrument contamination and wound infection through high flow rates of ultra-clean air, reducing the presence of Microbe Carrying Particles (MCPs). This study investigates the airflow patterns and ventilation characteristics of a UCA operating theatre (OT) under standard ventilation system operating conditions, considering both empty and partially occupied scenarios. Utilising a precise computational model, quasi-Direct Numerical Simulations (qDNS) were conducted to delineate flow velocity profiles, energy spectra, distributions of turbulent kinetic energy, energy dissipation rate, local Kolmogorov scales, and pressure-based coherent structures. These results were also complemented by a tracer gas decay analysis following ASHRAE standard guidelines. Simulations showed that contrary to the intended laminar regime, the OT’s geometry inherently fosters a predominantly turbulent airflow, sustained until evacuation through the exhaust vents, and facilitating recirculation zones irrespective of occupancy level. Notably, the occupied scenario demonstrated superior ventilation efficiency, a phenomenon attributed to enhanced kinetic energy induced by the additional obstructions. The findings underscore the critical role of UCA-OT design in mitigating MCP dissemination, highlighting the potential to augment the design to optimise airflow across a broader theatre spectrum, thereby diminishing recirculation zones and consequently reducing the propensity for Surgical Site Infections (SSIs). The study advocates for design refinements to harness the turbulent dynamics beneficially, steering towards a safer surgical environment.

Turbulent dynamics and whole-brain modeling: toward new clinical applications for traumatic brain injury.

Traumatic Brain Injury (TBI) is a prevalent disorder mostly characterized by persistent impairments in cognitive function that poses a substantial burden on caregivers and the healthcare system worldwide. Crucially, severity classification is primarily based on clinical evaluations, which are non-specific and poorly predictive of long-term disability. In this Mini Review, we first provide a description of our model-free and model-based approaches within the turbulent dynamics framework as well as our vision on how they can potentially contribute to provide new neuroimaging biomarkers for TBI. In addition, we report the main findings of our recent study examining longitudinal changes in moderate-severe TBI (msTBI) patients during a one year spontaneous recovery by applying the turbulent dynamics framework (model-free approach) and the Hopf whole-brain computational model (model-based approach) combined with in silico perturbations. Given the neuroinflammatory response and heightened risk for neurodegeneration after TBI, we also offer future directions to explore the association with genomic information. Moreover, we discuss how whole-brain computational modeling may advance our understanding of the impact of structural disconnection on whole-brain dynamics after msTBI in light of our recent findings. Lastly, we suggest future avenues whereby whole-brain computational modeling may assist the identification of optimal brain targets for deep brain stimulation to promote TBI recovery.

Multi-scale invariant solutions in plane Couette flow: a reduced-order model approach

Plane Couette flow at Reynolds number $Re=1200$ (based on the channel half-height and half the velocity difference between the top and bottom plates) is investigated with a spatial domain designed to retain only two spanwise integral length scales. In this system, the computation of invariant solutions that are physically representative of the turbulent state has been understood to be challenging. To address this challenge, our approach is to employ an accurate reduced-order model with 600 degrees of freedom (Cavalieri & Nogueira, Phys. Rev. Fluids, vol. 7, 2022, L102601). Using the two-scale energy budget and the temporal cross-correlation of key observables, it is first demonstrated that the model contains most of the multi-scale physical processes identified recently (Doohan et al., J. Fluid Mech., vol. 913, 2021, A8); i.e. the large- and small-scale self-sustaining processes, the energy cascade for turbulent dissipation, and an energy-cascade mediated small-scale production mechanism. Invariant solutions of the reduced-order model are subsequently computed, including 96 equilibria and 43 periodic orbits. It is found that none of the computed equilibrium solutions are able to reproduce an accurate energy balance associated with the multi-scale dynamics of the turbulent state. Incorporation of unsteadiness into invariant solutions is seen to be essential for a sensible description of the multi-scale turbulent dynamics and the related energetics, at least in this type of flow, as periodic orbits with a sufficiently long period are mainly able to describe the complex spatio-temporal dynamics associated with the known multi-scale phenomena.

Optimization of Reynolds stress model coefficients at multiple discrete flow regions for three-dimensional realizations of fractal-generated turbulence

The quantification of global turbulence statistical moments generated by grid turbulators is crucial for the enhancement of conjugate heat transfer in industrial thermo-fluid systems. As such, there is a need for precise, low-cost alternatives to numerically model three-dimensional flow dynamics of fractal-generated turbulence (FGT) behind multilength-scale square fractal grids (SFGs), in contrast to previously-reported direct numerical simulations. In this study, a numerical framework consisting of multiple applications of the Reynolds stress model (RSM), each employing its own distinct set of optimized coefficient values, is developed by segregating an FGT flow domain into its production and decay regions with Nelder-Mead optimization on key coefficients then performed independently for each region. The flow fields predicted by such RSM framework achieved overall disparities below 3% and 13% w.r.t. reported experimental measurements of mean velocity and turbulence intensity, respectively, considering the evolution in the flow domain along the streamwise, vertical, and spanwise directions. This is therefore the first documentation of any RANS-turbulence model being validated for mean velocity and turbulence intensity predictions of FGT in all three-dimensions. Thereafter, this proposed RSM framework is generalized to predict industry-relevant turbulence statistical moments of four additional FGT flows. The predicted centerline-statistics are verified against reported experiments, and the findings potentially enable realizations of FGT induced by arbitrary SFGs without relying on a posteriori validation while eliminating further reliance on the Nelder-Mead optimization algorithm on a case-by-case basis. The findings indicate a potential to apply the model coefficients as continuous functions of space to simulate the entire FGT domain. Overall, the accurate and numerically sustainable realizations of FGT in 3D provide valuable insights to engineer potent fluid-solid heat transfer via passive turbulence management within HVAC systems.

Impact of High-Pressure-Turbine Purge Flow on the Evolution of Turbulence in a Turbine Vane Frame

Abstract This paper describes the measurement and postprocessing of turbulence data. The experiments were carried out in a two-stage, two-spool transonic turbine test rig at the Institute for Thermal Turbomachinery and Machine Dynamics at the Graz University of Technology, which includes relevant purge and turbine rotor tip leakage flows. The test setup consists of a high-pressure turbine (HPT) stage, a turbine vane frame (TVF) with turning struts and splitters, and a counter-rotating low-pressure turbine (LPT) to allow engine realistic measurements. Time-resolved area traverse measurements have been performed for three different operating conditions in three measurement planes downstream of the HPT rotor, which enable the measurement of the turbulence quantities at the TVF inlet and outlet as well as the LPT outlet. The turbulence quantities are evaluated using triaxial- and single hot-film probes by means of Constant-Temperature-Anemometry, and their results were validated with five-hole probe (FHP) measurements. Ensemble- and time-averaging, as well as Fourier transforms, were applied for data reduction. It is shown how the turbulence intensity and integral length scale vary over different purge flowrates (PFR). The acquired measurement data illustrate that the interaction of the ejected purge flow with mean flow enhances the turbulent mixing in the secondary flow structures at the TVF inlet and TVF outlet, respectively. Furthermore, the flow downstream of the LPT rotor is affected by TVF and LPT rotor secondary flow structures, which are identified as high turbulence regions. These regions strongly depend on the purge flowrate. These results acquired under engine realistic rig flow conditions enable a deeper understanding of the relationship between loss and turbulence quantities and will help improve the application of computational fluid dynamics turbulence models to turbomachinery modeling.

Heat release and flame scale effects on turbulence dynamics in confined premixed flows

As industry transitions to a net-zero carbon future, turbulent premixed combustion will remain an integral process for power generating gas turbines, aviation engines, and high-speed propulsion due to their ability to minimize pollutant emissions. However, accurately predicting the behavior of a turbulent reacting flow field remains a challenge. To better understand the dynamics of premixed reacting flows, this study experimentally investigates the effects of combustion heat release and flame scales on the evolution of turbulence in a high-speed, confined bluff-body combustor. The combustor is operated across a range of equivalence ratios from 0.7 to 1 to isolate the role of chemical heat release, flame speed, and flame thickness on the evolution of turbulence as the flow progresses from reactants to products. High-speed particle image velocimetry and CH* chemiluminescence imaging systems are simultaneously employed to quantify turbulent flame and flow dynamics. The results notably demonstrate that the flame augments turbulence fluctuations as the flow evolves from reactants to products for all cases, which opposes most simulations of premixed turbulent reactions. Notably, turbulence fluctuations increase monotonically with the heat of combustion and corresponding turbulent flame speed. Spatial profiles of turbulence statistics are conditioned on the mean flame front, and nondimensionalizing the turbulence profiles using laminar flame properties is shown to collapse all conditions onto a single curve. The resulting nondimensional profile confirms that turbulence dynamics scales with the heat of combustion and was used to develop a novel correlation to predict the increase in turbulent fluctuations across the premixed flame. A Reynolds averaged Navier Stokes decomposition is also explored to further characterize the effects of combustion heat release on the dominant mechanisms of turbulent energy transport. The cumulative results can guide modeling capabilities to better predict flame and flow dynamics and accelerate design strategies for premixed turbines with carbon-free fuels.

A tale of missed opportunities: The Cold War in Brazil

AbstractBrazil was not at the forefront of initial Cold War events and US‐Brazil relations have been more often defined by alignment than conflict. Still, Brazil was not immune to the Cold War logic and when these turbulent dynamics became more prevalent in Latin America, Brazil was at the center of US concerns and influence. But though much was promised and attempted, recurrent opportunities for constructive interactions were missed at the price of growing violence and social injustice. The present piece reviews the scholarship on the Cold War in Brazil by focusing on some of the main works produced by US and Brazilian scholars working on central themes of Brazilian history during the period. Rather than attempting to provide a comprehensive list of works, which would have required more space than permitted here, the article is structured based on key studies that helped shape the conversation about Brazil's historical development in the second half of the 20th‐century.

An improved TDE technique for derivation of 2D turbulence structures based on GPI data in toroidal plasma

This paper reports an improved time-delay estimation (TDE) technique for the derivation of turbulence structures based on gas-puff imaging data. The improved TDE technique, integrating an inverse timing search and hierarchical strategy, offers superior accuracy in calculating turbulent velocity field maps and analyzing blob dynamics, which has the power to obtain the radial profiles of equilibrium poloidal velocity, blob size and its radial velocity, even the fluctuation analysis, such as geodesic acoustic modes and quasi-coherent mode, etc. This improved technique could provide important 2D information for the study of edge turbulence and blob dynamics, advancing the understanding of edge turbulence physics in fusion plasmas.

Average turbulence dynamics from a one-parameter kinetic theory: Estimation of the relaxation time

We provide a theoretical estimation of the relaxation time for the kinetic theoretical representation of homogeneous, isotropic, and stationary turbulent flow. The basic approach depends on the construction of a balance of fluctuation and dissipation between the relaxation process and the self-consistently generated fluctuating force. The kinetic theory representation generalizes the modeling of turbulence so that turbulent viscosity as well as all higher order transport coefficients are determined by the relaxation time. The resulting value of the relaxation time gives an estimation of the turbulent viscosity with the coefficient value comparable with those from most of the representative turbulence models, which have been obtained empirically or semi-empirically.

Buoyancy effects on very-large-scale motions and amplitude modulation in convective atmospheric surface layers

A large amount of high-Reynolds-number experimental data was obtained from long-term observations of the atmospheric surface layer in the Qingtu Lake Observation Array under different thermal stability conditions. To reveal the thermal effects, the variations of the scales of turbulent coherent structures, energy distribution and amplitude modulation as a function of thermal stability are investigated. Results show that in the convective atmospheric surface layer, the superposition of buoyancy and shear drives leads to a large enhancement of turbulent kinetic energy, an increase in the scales of coherent structures, and in particular, a more significant enhancement of the very-large-scale motions kinetic energy. This results in an increased energy proportion of very-large-scale motions, and thus enhancing the amplitude modulation effect on small scales. Moreover, the variations in the coherent structure scale, energy proportion of the very-large-scale motions, amplitude modulation coefficient and the corresponding modulating and carrier signal scales with the thermal stability parameter can all be characterized by the same parametric equation form. This study contributes to a better understanding of turbulence dynamics driven by both buoyancy and shear.

Turbulence on open string worldsheets under non-integrable boundary conditions

We demonstrate the turbulent dynamics of the Nambu-Goto open string in the AdS3 spacetime. While the motion of a classical closed string in AdS is known to be integrable, the integrability of an open string motion depends on the boundary conditions at the string endpoints. We numerically solve the equations of motion of the open string under the boundary conditions where the endpoints are i) fixed to a finite radial coordinate in AdS, and ii) free. For i), we find turbulence on the string, that shows a cascade in the energy and angular momentum spectra. This result indicates the non-integrability of the open string with this type of boundary conditions. For ii), we find no turbulence. This is consistent with the integrability of the open string with the free boundary conditions.

Beyond Cryptic Equations: Reimagining Concepts in Physics Through Metaheuristics and Fantasy Stories using Neutrosophic Venn Diagram

Physics, the grand narrative of the universe, has long been viewed as a realm of cold, hard equations. But what if we looked beyond the formulas and considered a more imaginative origin for some of its concepts? This article explores the intriguing possibility that physics, and even cosmology, might share a surprising kinship with metaheuristics and fantastical fiction. Metaheuristics, a branch of computer science, deals with finding approximate solutions to complex problems. Perhaps the universe, in its vastness, employs a set of "rules" that lead to the most likely outcomes, much like an algorithm searching for the best solution within a vast space of possibilities. The connection strengthens when we consider the fantastical. Argentine writer Jorge Luis Borges, known for his thought-provoking short stories, often explored themes of infinity, labyrinths, and forking realities. In this article, we discuss, among other things, how to look at physics laws from an alternative fundamental viewpoint that is fluid dynamics perspective. As an example, we provide an outline for deriving the Newton gravitational law from the Kutta-Joukowski theorem, and then deriving the Kutta-Joukowski theorem from Bernoulli principles. In the meantime, it is known that vortex flows, related to solar convective turbulent dynamics at granular scales and their interplay with magnetic fields within intergranular lanes, occur abundantly on the solar surface and in the atmosphere above.

Modeling and oblique transmission characteristics of an underwater wireless optical communication channel based on ocean depth layering.

Underwater wireless optical communication is widely considered in the field of underwater communication due to its high bandwidth and low latency. In a real transmission link, the temperature and salinity of seawater, chlorophyll concentration, and bubble density vary with ocean depth. Therefore, the depth of the optical transmitter in seawater and the tilt angle of the beam will exhibit different beam transmission characteristics. In this paper, an underwater oblique-range layered channel model considering the combined effects of dynamic turbulence, absorption, and scattering is developed based on real data of seawater at different depths measured by the Global Ocean Observing Buoy Argo and the Woods Hole Oceanographic Institution BCO-DMO. The effects of transmission distance, transmitter tilt angle, and transmitter depth on the oblique-range transmission characteristics of the beam in seawater are discussed. The simulation results show that, at the same transmission distance, the beam centroid displacement increases with an increase in transmitter depth only when the transmitter is located above the interior of the thermocline. When the transmitter is located below the interior of the thermocline, the influence of the transmitter tilt angle on the beam centroid displacement decreases. This indicates that at different depths within the interior of the thermocline, the optical beam transmission characteristics exhibit significant variations.