Signature Of Turbulence Research Articles

Asymptotic predictions on the velocity gradient statistics in low-Reynolds-number random flows: onset of skewness, intermittency and alignments

Stirring a fluid through a Gaussian forcing at a vanishingly small Reynolds number produces a Gaussian random field, while flows at higher Reynolds numbers exhibit non-Gaussianity, cascades, anomalous scaling and preferential alignments. Recent works (Yakhot & Donzis, Phys. Rev. Lett., vol. 119, 2017, 044501; Khurshid et al., Phys. Rev. E, vol. 107, 2023, 045102) investigated the onset of these turbulent hallmarks in low-Reynolds-number flows by focusing on the scaling of the velocity gradients and velocity increments. They showed that the onset of power-law scalings in the velocity gradient statistics occurs at low Reynolds numbers, with the scaling exponents being surprisingly similar to those in the inertial range of fully developed turbulence. In this work we address the onset of turbulent signatures in low-Reynolds-number flows from the viewpoint of the velocity gradient dynamics, giving insights into its rich statistical geometry. We combine a perturbation theory of the full Navier–Stokes equations with velocity gradient modelling. This procedure results in a stochastic model for the velocity gradient in which the model coefficients follow directly from the Navier–Stokes equations and statistical homogeneity constraints. The Fokker–Planck equation associated with our stochastic model admits an analytic solution that shows the onset of turbulent hallmarks at low Reynolds numbers: skewness, intermittency and preferential alignments arise in the velocity gradient statistics through a smooth transition as the Reynolds number increases. The model predictions are in excellent agreement with direct numerical simulations of low-Reynolds-number flows.

User authentication system based on human exhaled breath physics.

This work, in a pioneering approach, attempts to build a biometric system that works purely based on the fluid mechanics governing exhaled breath. We test the hypothesis that the structure of turbulence in exhaled human breath can be exploited to build biometric algorithms. This work relies on the idea that the extrathoracic airway is unique for every individual, making the exhaled breath a biomarker. Methods including classical multi-dimensional hypothesis testing approach and machine learning models are employed in building user authentication algorithms, namely user confirmation and user identification. A user confirmation algorithm tries to verify whether a user is the person they claim to be. A user identification algorithm tries to identify a user's identity with no prior information available. A dataset of exhaled breath time series samples from 94 human subjects was used to evaluate the performance of these algorithms. The user confirmation algorithms performed exceedingly well for the given dataset with over 97% true confirmation rate. The machine learning based algorithm achieved a good true confirmation rate, reiterating our understanding of why machine learning based algorithms typically outperform classical hypothesis test based algorithms. The user identification algorithm performs reasonably well with the provided dataset with over 50% of the users identified as being within two possible suspects. We show surprisingly unique turbulent signatures in the exhaled breath that have not been discovered before. In addition to discussions on a novel biometric system, we make arguments to utilise this idea as a tool to gain insights into the morphometric variation of extrathoracic airway across individuals. Such tools are expected to have future potential in the area of personalised medicines.

Unveiling the spatiotemporal evolution of liquid-lens coalescence: Self-similarity, vortex quadrupoles, and turbulence in a three-phase fluid system

The coalescence of liquid lenses represents a fundamental challenge within the domains of fluid dynamics and statistical physics, particularly in the context of complex multi-phase flows. We demonstrate that the three-phase Cahn–Hilliard–Navier–Stokes (CHNS3) system provides a natural theoretical framework for studying liquid-lens coalescence, which has been investigated in recent experiments. Our extensive direct numerical simulations of lens coalescence, in the two and three dimensional (2D and 3D) CHNS3, uncover the rich spatiotemporal evolution of the fluid velocity u and vorticity ω, the concentration fields c1, c2, and c3 of the three liquids, and an excess pressure PℓG, which we define in terms of these concentrations via a Poisson equation. We find, in agreement with experiments, that as the lenses coalesce, their neck height h(t)∼tαv, with αv≃1 in the viscous regime, and h(t)∼tαi, with αi≃2/3 in the inertial regime. We obtain the crossover from the viscous to the inertial regimes as a function of the Ohnesorge number Oh, a dimensionless combination of viscous stresses and inertial and surface tension forces. We show that a vortex quadrupole, which straddles the neck of the merging lenses, and PℓG play crucial roles in distinguishing between the viscous- and inertial-regime growths of the merging lenses. In the inertial regime, we find signatures of turbulence, which we quantify via kinetic-energy and concentration spectra. Finally, we examine the merger of asymmetric lenses, in which the initial stages of coalescence occur along the circular parts of the lens interfaces; in this case, we obtain power-law forms for the h(t) with inertial-regime exponents that lie between their droplet-coalescence and lens-merger counterparts.

Characteristics of the surface signatures induced by a sphere in a linearly stratified flow

Internal waves generated by a moving body submerged in a stratified fluid typically yield modest surface signatures. Large-eddy simulation (LES) is employed to capture the surface signatures generated using a moving sphere in a linearly stratified fluid with various Froude numbers (Fr) and diving depths (D). For surface Kelvin wakes, with increasing Froude numbers (Fr), the wake angle (θ) decreases, the wavelength (L) and the maximum surface wave amplitude (Amax) increases. Within the range of our simulation, the influence of diving depth (D) on wake angle (θ) and wavelength (L) is insignificant, while the maximum surface wave amplitude (Amax) decreases as diving depth (D) increases. Additionally, surface turbulent signatures characterised by horizontal divergence (divh) are identified in the near wake. The results demonstrated the following: the horizontal divergence (divh) is transported upstream and downstream from internal wakes to the free surface, whereas the vertical vorticity (ωy) is only transported downstream. And the horizontal divergence (divh) can be transmitted for a larger distance than the vertical vorticity (ωy).

On the Evolution of the Anisotropic Scaling of Magnetohydrodynamic Turbulence in the Inner Heliosphere

We analyze a merged Parker Solar Probe (PSP) and Solar Orbiter (SO) data set covering heliocentric distances 13 R ⊙ ≲ R ≲ 220 R ⊙ to investigate the radial evolution of power and spectral index anisotropy in the wavevector space of solar wind turbulence. Our results show that anisotropic signatures of turbulence display a distinct radial evolution when fast, V sw ≥ 400 km s−1, and slow, V sw ≤ 400 km s−1, wind streams are considered. The anisotropic properties of slow wind in Earth orbit are consistent with a “critically balanced” cascade, but both spectral index anisotropy and power anisotropy diminish with decreasing heliographic distance. Fast streams are observed to roughly retain their near-Sun anisotropic properties, with the observed spectral index and power anisotropies being more consistent with a “dynamically aligned” type of cascade, though the lack of extended fast wind intervals makes it difficult to accurately measure the anisotropic scaling. A high-resolution analysis during the first perihelion of PSP confirms the presence of two subranges within the inertial range, which may be associated with the transition from weak to strong turbulence. The transition occurs at κ d i ≈ 6 × 10−2 and signifies a shift from −5/3 to −2 and from −3/2 to −1.57 scaling in parallel and perpendicular spectra, respectively. Our results provide strong observational constraints for anisotropic theories of MHD turbulence in the solar wind.

Turbulence signatures of natural river morphology in four dimensions

AbstractTurbulent flow in natural river channels drives geophysical processes and exerts a fundamental influence on aquatic biota. An extensive range of turbulence properties have previously been synthesized into four categories or “dimensions” with ecological relevance: intensity, periodicity, orientation and scale (IPOS). We apply this framework across three rivers with differing morphologies in order to assess the statistical coherence of the four IPOS categories within turbulence field data and their utility in discriminating between fundamental units of river habitat. Intensity, periodicity‐scale and orientation were identified as the key gradients in the turbulence data set using multivariate analysis. These gradients all revealed statistically significant differences between rivers and/or geomorphic units. The intensity gradient accounted for the highest variance and most pronounced inter‐reach differences, but the periodicity‐scale and orientation gradients were also useful in distinguishing between certain combinations of rivers and/or geomorphic units. Different turbulence gradients, or combinations of gradients, were important in characterizing differences between rivers and geomorphic units (riffes, pools, steps). The gradients provided improved prediction of geomorphic units compared to standard hydraulic variables (mean velocity, depth), although the extent of improvement in prediction varied between river morphologies. The analysis reveals the statistical coherence of the four categories or “dimensions” of turbulence in multivariate space, connects the ecologically defined IPOS categories of turbulence properties with river types and fundamental units of river habitat (geomorphic units). Turbulence signatures of natural channel morphology are expressed across all four dimensions of turbulence, providing clear evidence that these four dimensions should be routinely considered in ecohydraulics and hydromorphology research to facilitate a full understanding hydraulic habitat.

Effects of classic psychedelic drugs on turbulent signatures in brain dynamics.

Psychedelic drugs show promise as safe and effective treatments for neuropsychiatric disorders, yet their mechanisms of action are not fully understood. A fundamental hypothesis is that psychedelics work by dose-dependently changing the functional hierarchy of brain dynamics, but it is unclear whether different psychedelics act similarly. Here, we investigated the changes in the brain's functional hierarchy associated with two different psychedelics (LSD and psilocybin). Using a novel turbulence framework, we were able to determine the vorticity, that is, the local level of synchronization, that allowed us to extend the standard global time-based measure of metastability to become a local-based measure of both space and time. This framework produced detailed signatures of turbulence-based hierarchical change for each psychedelic drug, revealing consistent and discriminate effects on a higher level network, that is, the default mode network. Overall, our findings directly support a prior hypothesis that psychedelics modulate (i.e., "compress") the functional hierarchy and provide a quantification of these changes for two different psychedelics. Implications for therapeutic applications of psychedelics are discussed.

Anisotropic turbulence in relativistic plasmas

Signs of turbulence have been observed at the relativistic heavy ion collision at high collision energies. We study the signatures of turbulence in this system and find that there are significant departures from isotropic turbulence in the initial and the pre-equilibrium stages of the collision. As the anisotropic fluctuations are subleading to the isotropic fluctuations, the Kolmogorov spectrum can usually be obtained even for the initial stages. However, the energy spectrum and the temperature fluctuations indicate deviations from isotropic turbulence. Since a strong momentum anisotropy exists between the transverse and the longitudinal plane, we study the energy density spectrum in these two planes by slicing the sphere into different planes. The geometrical anisotropy is reflected in the anisotropic turbulence generated in the rotating plasma and we find that the scaling exponent is different in the two planes. We also obtain the temperature spectrum in the pre-equilibrium stages. The spectrum deviates from the Gaussian spectra expected for an isotropic turbulence. All these seem to indicate that the large scale momentum anisotropy persists in the smaller length scales for the relativistic heavy ion collisions.

Coarsening in the two-dimensional incompressible Toner-Tu equation: Signatures of turbulence.

We investigate coarsening dynamics in the two-dimensional, incompressible Toner-Tu equation. We show that coarsening proceeds via vortex merger events, and the dynamics crucially depend on the Reynolds number Re. For low Re, the coarsening process has similarities to Ginzburg-Landau dynamics. On the other hand, for high Re, coarsening shows signatures of turbulence. In particular, we show the presence of an enstrophy cascade from the intervortex separation scale to the dissipation scale.

Seismic signature of turbulence during the 2017 Oroville Dam spillway erosion crisis

Abstract. Knowing the location of large-scale turbulent eddies during catastrophic flooding events improves predictions of erosive scour. The erosion damage to the Oroville Dam flood control spillway in early 2017 is an example of the erosive power of turbulent flow. During this event, a defect in the simple concrete channel quickly eroded into a 47 m deep chasm. Erosion by turbulent flow is difficult to evaluate in real time, but near-channel seismic monitoring provides a tool to evaluate flow dynamics from a safe distance. Previous studies have had limited ability to identify source location or the type of surface wave (i.e., Love or Rayleigh wave) excited by different river processes. Here we use a single three-component seismometer method (frequency-dependent polarization analysis) to characterize the dominant seismic source location and seismic surface waves produced by the Oroville Dam flood control spillway, using the abrupt change in spillway geometry as a natural experiment. We find that the scaling exponent between seismic power and release discharge is greater following damage to the spillway, suggesting additional sources of turbulent energy dissipation excite more seismic energy. The mean azimuth in the 5–10 Hz frequency band was used to resolve the location of spillway damage. Observed polarization attributes deviate from those expected for a Rayleigh wave, though numerical modeling indicates these deviations may be explained by propagation up the uneven hillside topography. Our results suggest frequency-dependent polarization analysis is a promising approach for locating areas of increased flow turbulence. This method could be applied to other erosion problems near engineered structures as well as to understanding energy dissipation, erosion, and channel morphology development in natural rivers, particularly at high discharges.

Influence of Intermittency on the Quasi-perpendicular Scaling in Three-dimensional Magnetohydrodynamic Turbulence

Abstract Solar wind fluctuations reveal the ubiquity of intermittency, which is believed to affect the spectral signatures of turbulence. In this work, based on simulation of driven compressible MHD turbulence, we apply the wavelet technique to the magnetic field and velocity to identify intermittency, and we analyze the influence of the intermittency on the quasi-perpendicular scaling in the inertial range. The numerical results show that the original magnetic and velocity fluctuations are anisotropic, and have a power anisotropy with a spectral index approaching the Iroshnikov–Kraichnan scaling in the direction quasi-perpendicular to the local mean magnetic field. As in observations of the solar wind fluctuations, as the scale decreases in the simulation, the calculated probability distribution functions (pdfs) of the wavelet coefficients become extended on both tails of the non-Gaussian distribution, with a rapid increase in flatness. After intermittency has been removed from the driven turbulence, at each scale, the pdfs approach a Gaussian distribution, with the flatness being ∼3. Meanwhile, the quasi-perpendicular scaling for both fluctuations becomes steeper and close to a Kolmogorov scaling, which may be a result of the stronger intermittency in the quasi-perpendicular direction and at the smaller scales. These results suggest that there is intermittency superposed on the “background” turbulence that seems to have the Kolmogorov scaling, whereby the overall slope is getting flatter with the involvement of intermittency.

Turbulence hierarchy in a random fibre laser

Turbulence is a challenging feature common to a wide range of complex phenomena. Random fibre lasers are a special class of lasers in which the feedback arises from multiple scattering in a one-dimensional disordered cavity-less medium. Here we report on statistical signatures of turbulence in the distribution of intensity fluctuations in a continuous-wave-pumped erbium-based random fibre laser, with random Bragg grating scatterers. The distribution of intensity fluctuations in an extensive data set exhibits three qualitatively distinct behaviours: a Gaussian regime below threshold, a mixture of two distributions with exponentially decaying tails near the threshold and a mixture of distributions with stretched-exponential tails above threshold. All distributions are well described by a hierarchical stochastic model that incorporates Kolmogorov’s theory of turbulence, which includes energy cascade and the intermittence phenomenon. Our findings have implications for explaining the remarkably challenging turbulent behaviour in photonics, using a random fibre laser as the experimental platform.

Gas kinematics in the H ii regions G351.69-1.15 and G351.63-1.25

We probe the structure and kinematics of two neighbouring H II regions identified as cometary and bipolar, using radio recombination lines (RRL). The H172{\alpha} RRLs from these H II regions: G351.6-1.15 and G351.6-1.25, are mapped using GMRT, India. We also detect carbon RRLs C172{\alpha} towards both these regions. The hydrogen RRLs display the effects of pressure and dynamical broadening in the line profiles, with the dynamical broadening (15 km/s) playing a major role in the observed profile of G351.6-1.15. We investigate the kinematics of molecular gas species towards this H II region from the MALT90 pilot survey. The molecular gas is mostly distributed towards the north and north-west of the cometary head. The molecular line profiles indicate signatures of turbulence and outflow in this region. The ionized gas at the cometary tail is blue shifted by 8 km/s with respect to the ambient molecular cloud, consistent with the earlier proposed champagne flow scenario. The relative velocity of 5 km/s between the northern and southern lobes of the bipolar H II region G351.6-1.25 is consistent with the premise that the bipolar morphology is a result of the expanding ionized lobes within a flat molecular cloud.

Fluid dynamics: Turbulence in a quantum gas.

The discovery of a cascade of sound waves across many wavelengths in an ultracold atomic gas advances our understanding of turbulence in fluids governed by quantum mechanics. See Letter p.72 An important signature of turbulence is the emergence of a cascade of excitations involving all length scales. While turbulence has been observed in quantum fluids—typically liquid helium—it is difficult to control such systems and to observe the properties of turbulence on demand, because the particles therein strongly interact. Here Nir Navon et al. trap a weakly interacting homogeneous Bose–Einstein condensate consisting of rubidium-87 atoms in a cylindrical optical box and shake the gas to produce turbulence. This methodology lets them observe the full turbulent cascade. This work demonstrates that ultracold atomic gases could serve as models for quantum turbulence.

CRAB FLARES DUE TO TURBULENT DISSIPATION OF THE PULSAR STRIPED WIND

ABSTRACT We interpret γ-ray flares from the Crab Nebula as the signature of turbulence in the pulsar’s electromagnetic outflow. Turbulence is triggered upstream by dynamical instability of the wind’s oscillating magnetic field and accelerates non-thermal particles. On impacting the wind-termination shock, these particles emit a distinct synchrotron component , which is constantly modulated by intermittency of the upstream plasma flow. Flares are observed when the high-energy cutoff of emerges above the fast-declining nebular emission around 0.1–1 GeV. Simulations carried out in the force-free electrodynamics approximation predict the striped wind to become fully turbulent well ahead of the wind-termination shock, provided its terminal Lorentz factor is .

Neutrino Flavor Evolution in Turbulent Supernova Matter

In order to decode the neutrino burst signal from a Galactic core-collapse supernova and reveal the complicated inner workings of the explosion, we need a thorough understanding of the neutrino flavor evolution from the proto-neutron-star outwards. The flavor content of the signal evolves due to both neutrino collective effects and matter effects which can lead to a highly interesting interplay and distinctive spectral features. In this paper we investigate the supernova neutrino flavor evolution by including collective flavor effects, the evolution of the Mikheyev, Smirnov & Wolfenstein (MSW) matter conversions due to the shock wave passing through the star, and the impact of turbulence. The density profiles utilized in our calculations represent a 10.8 MG progenitor and comes from a 1D numerical simulation by Fischer et al.[1]. We find that small amplitude turbulence, up to 10% of the average potential, leads to a minimal modification of the signal, and the emerging neutrino spectra retain both collective and MSW features. However, when larger amounts of turbulence are added, 30% and 50%, the features of collective and shock wave effects in the high density resonance channel are almost completely obscured at late times. At the same time we find the other mixing channels – the low density resonance channel and the non-resonant channels – begin to develop turbulence signatures. Large amplitude turbulent motions in the outer layers of massive, iron core-collapse supernovae may obscure the most obvious fingerprints of collective and shock wave effects in the neutrino signal but cannot remove them completely, and additionally bring about new features in the signal. We illustrate how the progression of the shock wave is reflected in the changing survival probabilities over time, and we show preliminary results on how some of these collective and shock wave induced signatures appear in a detector signal.

Electro-optic signatures of turbulent electroconvection in dielectric liquids

Signatures of turbulent electroconvection in transformer oil stressed by dc and ac voltages are identified from Kerr electro-optic measurement data. When the applied dc voltage is high enough, compared with the results with no applied voltage, the optical scintillation index and image entropy exhibit substantial enhancement and reduction, respectively, which are interpreted as temporal and spatial signatures of turbulence. Under low-frequency ac high voltages, spectral and correlational analyses indicate that there exist interacting flow and charge processes in the gap. This work also clarifies the meaning of dc steady state and the requirement on ac modulation frequency in Kerr measurements.

Combining collective, MSW, and turbulence effects in supernova neutrino flavor evolution

(Abridged) In order to decode the neutrino burst signal from a Galactic core-collapse supernova and reveal the complicated inner workings of the explosion we need a thorough understanding of the neutrino flavor evolution from the proto-neutron star outwards. The flavor content of the signal evolves due to both neutrino collective effects and matter effects which can lead to a highly interesting interplay and distinctive spectral features. In this paper we investigate the supernova neutrino flavor evolution in three different progenitors and include collective flavor effects, the evolution of the Mikheyev, Smirnov & Wolfenstein conversion due to the shock wave passage through the star, and the impact of turbulence. In the Oxygen-Neon-Magnesium supernova we find that the impact of turbulence is both brief and slight during a window of 1-2 seconds post bounce. Thus the spectral features of collective and shock effects in the neutrino signals from ONeMg supernovae may be almost turbulence free making them the easiest to interpret. For the more massive progenitors we again find that small amplitude turbulence, up to 10%, leads to a minimal modification of the signal, and the emerging neutrino spectra retain both collective and MSW features. However, when larger amounts of turbulence is added, 30% and 50%, the features of collective and shock wave effects in the high density resonance channel are almost completely obscured at late times. Yet at the same time we find the other mixing channels - the low density resonance channel and the non-resonant channels - begin to develop turbulence signatures. Large amplitude turbulent motions in the outer layers of more massive, iron core-collapse supernovae may obscure the most obvious fingerprints of collective and shock wave effects in the neutrino signal but cannot remove them completely, and additionally bring about new features in the signal.

Consequences of largeθ13for the turbulence signatures in supernova neutrinos

The transition probabilities for a single neutrino emitted from a point proto-neutron source after passage through a turbulent supernova density profile have been found to be random variates drawn from parent distributions whose properties depend upon the stage of the explosion, the neutrino energy and mixing parameters, the observed channel, and the properties of the turbulence such as the amplitude ${C}_{\ensuremath{\star}}$. In this paper we examine the consequences of the recently measured mixing angle ${\ensuremath{\theta}}_{13}$ upon the neutrino flavor transformation in supernova when passing through turbulence, in order to provide some clarity as to what one should expect in the way of turbulence effects in the next supernova neutrino burst signal. We find that the measurements of a relatively large value of ${\ensuremath{\theta}}_{13}$ means the neutrinos are relatively immune to small, ${C}_{\ensuremath{\star}}\ensuremath{\lesssim}1%$, amplitude turbulence but as ${C}_{\ensuremath{\star}}$ increases the turbulence effects grow rapidly and spread to all mixing channels. For ${C}_{\ensuremath{\star}}\ensuremath{\gtrsim}10%$ the turbulence effects in the high density resonance mixing channels are independent of ${\ensuremath{\theta}}_{13}$ but nonresonant mixing channels are more sensitive to turbulence when ${\ensuremath{\theta}}_{13}$ is large.

Macroturbulent coherent structures in an ice‐covered river flow using a pulse‐coherent acoustic Doppler profiler

ABSTRACTThe aim of this work is to compare macroturbulent coherent structures (MCS) geometry and organization between ice covered and open channel flow conditions. Velocity profiles were obtained using a Pulse‐Coherent Acoustic Doppler Profiler in both open channel and ice‐covered conditions. The friction imposed by the ice cover results in parabolic shaped velocity profiles. Reynolds stresses in the streamwise (u) and vertical (v) components of the flow show positive values near the channel bed and negative values near the ice cover, with two distinctive boundary layers with specific turbulent signatures. Vertically aligned stripes of coherent flow motions were revealed from statistics applied to space‐time matrices of flow velocities. In open channel conditions, the macroturbulent structures extended over the entire depth of the flow whereas they were discontinued and nested close to the boundary walls in ice‐covered conditions. The size of MCS is consequently reduced in scale under an ice cover. The average streamwise length scale is reduced from 2.5 to 0.4Y (u) and from 1.5 to 0.4Y (v) where Y is the flow depth. In open channel conditions, the vertical extent of MCS covers the entire flow depth, whereas the vertical extent was in the range 0.58Y–1Y (u) and 0.81Y–1Y (v) in ice‐covered conditions. Under an ice cover, each boundary wall generates its own set of MCS that compete with each other in the outer region of the flow, enhancing mixing and promoting the dissipation of coherent structures. Copyright © 2012 John Wiley & Sons, Ltd.