Hydrodynamic Turbulence Research Articles

Measurements of the imploding plasma sheath in triple-nozzle gas-puff z pinches

Gas-puff z-pinch implosions are characterized by the formation of a dense annular plasma shell, the sheath, that is driven to the axis by magnetic forces and therefore subject to the magneto-Rayleigh–Taylor instability. Here, the conditions within these sheaths are measured on the 1-MA COBRA generator at Cornell University [Greenly et al., Rev. Sci. Instrum. 79, 073501 (2008)] for various gas species and initial fill densities. The gas-puff loads are initialized by a 7 cm diameter triple-nozzle gas valve assembly with concentric outer and inner annular nozzles and a central gas jet. Thomson scattering and laser interferometry provide spatially resolved flow, temperature, and electron density profiles midway through the implosion, while extreme ultraviolet pinhole cameras record the evolution of the plasma column and photoconducting diodes measure x-ray emission. Analysis of the scattering spectra includes a means of discriminating between thermal and non-thermal broadening to test for the presence of hydrodynamic turbulence. Two types of sheath profiles are observed, those with sharp discontinuities at the leading edge and those with smooth gradients. In both cases, non-thermal broadening is generally peaked at the front of the sheath and exhibits a characteristic decay length that roughly scales with the sheath ion mean free path. We demonstrate that this non-thermal broadening term is inconsistent with laminar velocity gradients and is more consistent with dissipative turbulence driven by unstable plasma waves in a collisionless shock. The resulting differences in sheath profile are then set by the sheath ion collisionality in a manner consistent with recent 1D kinetic simulations [Angus et al., Phys. Plasmas 28, 010701 (2021)].

Major environmental drivers determining life and death of cold-water corals through time.

Cold-water corals (CWCs) are the engineers of complex ecosystems forming unique biodiversity hotspots in the deep sea. They are expected to suffer dramatically from future environmental changes in the oceans such as ocean warming, food depletion, deoxygenation, and acidification. However, over the last decades of intense deep-sea research, no extinction event of a CWC ecosystem is documented, leaving quite some uncertainty on their sensitivity to these environmental parameters. Paleoceanographic reconstructions offer the opportunity to align the on- and offsets of CWC proliferation to environmental parameters. Here, we present the synthesis of 6 case studies from the North Atlantic Ocean and the Mediterranean Sea, revealing that food supply controlled by export production and turbulent hydrodynamics at the seabed exerted the strongest impact on coral vitality during the past 20,000 years, whereas locally low oxygen concentrations in the bottom water can act as an additional relevant stressor. The fate of CWCs in a changing ocean will largely depend on how these oceanographic processes will be modulated. Future ocean deoxygenation may be compensated regionally where the food delivery and food quality are optimal.

Self-regularization in turbulence from the Kolmogorov 4/5-law and alignment.

A defining feature of three-dimensional hydrodynamic turbulence is that the rate of energy dissipation is bounded away from zero as viscosity is decreased (Reynolds number increased). This phenomenon-anomalous dissipation-is sometimes called the 'zeroth law of turbulence' as it underpins many celebrated theoretical predictions. Another robust feature observed in turbulence is that velocity structure functions [Formula: see text] exhibit persistent power-law scaling in the inertial range, namely [Formula: see text] for exponents [Formula: see text] over an ever increasing (with Reynolds) range of scales. This behaviour indicates that the velocity field retains some fractional differentiability uniformly in the Reynolds number. The Kolmogorov 1941 theory of turbulence predicts that [Formula: see text] for all [Formula: see text] and Onsager's 1949 theory establishes the requirement that [Formula: see text] for [Formula: see text] for consistency with the zeroth law. Empirically, [Formula: see text] and [Formula: see text], suggesting that turbulent Navier-Stokes solutions approximate dissipative weak solutions of the Euler equations possessing (nearly) the minimal degree of singularity required to sustain anomalous dissipation. In this note, we adopt an experimentally supported hypothesis on the anti-alignment of velocity increments with their separation vectors and demonstrate that the inertial dissipation provides a regularization mechanism via the Kolmogorov 4/5-law. This article is part of the theme issue 'Mathematical problems in physical fluid dynamics (part 2)'.

Von Karman correlation similarity in solar wind magnetohydrodynamic turbulence.

A major development underlying hydrodynamic turbulence theory is the similarity decay hypothesis due to von Karman and Howarth, here extended empirically to plasma turbulence in the solar wind. In similarity decay the second-order correlation experiences a continuous transformation based on a universal functional form and a rescaling of energy and characteristic length. Solar wind turbulence follows many principles adapted from classical fluid turbulence, but previously this similarity property has not been examined explicitly. Here, we analyze an ensemble of Elsässer autocorrelation functions computed from Advanced Composition Explorer data at 1 astronomical unit (AU), and demonstrate explicitly that the two-point correlation functions undergo a collapse to a similarity form of the type anticipated from von Karman's hypothesis applied to weakly compressive magnetohydrodynamic turbulence. This provides a firm empirical basis for employing the similarity decay hypothesis to the Elsässer correlations that represent the incompressive turbulence cascade. This approach is of substantial utility in space turbulence data analysis, and for adopting von Karman-type heating rates in global and subgrid-scale dynamical modeling.

Dynamics of finite-size spheroids in turbulent flow: the roles of flow structures and particle boundary layers

We study the translational and rotational dynamics of neutrally buoyant finite-size spheroids in hydrodynamic turbulence by means of fully resolved numerical simulations. We examine axisymmetric shapes, from oblate to prolate, and the particle volume dependences. We show that the accelerations and rotations experienced by non-spherical inertial-scale particles result from volume filtered fluid forces and torques, similar to spherical particles. However, the particle orientations carry signatures of preferential alignments with the surrounding flow structures, which are reflected in distinct axial and lateral fluctuations for accelerations and rotation rates. The randomization of orientations does not occur even for particles with volume-equivalent diameter size in the inertial range, here up to $60$ dissipative units ( $\eta$ ) at Taylor-scale Reynolds number ${Re_{\lambda }=120}$ . Additionally, we demonstrate that the role of fluid boundary layers around the particles cannot be neglected in reaching a quantitative understanding of particle statistical dynamics, as they affect the intensities of the angular velocities and the relative importance of tumbling with respect to spinning rotations. This study brings to the fore the importance of inertial-scale flow structures in homogeneous and isotropic turbulence and their impacts on the transport of neutrally buoyant bodies with sizes in the inertial range.

A self‐consistent κ‐model for anomalous transport due to electrostatic, interchange‐dominated E × B drift turbulence in the scrape‐off layer and implementation in SOLPS‐ITER

AbstractThe ad‐hoc description of anomalous transport through diffusive relations with manually tuned coefficients is currently one of the main limitations in mean‐field plasma edge codes, seriously restricting their interpretive and predictive capabilities. In this paper, we attempt to improve that description by relating the anomalous transport coefficients to the turbulent kinetic energy as a measure for the local intensity of the turbulence. Using RANS techniques from hydrodynamic turbulence and insights from their recent successful application to 2D electrostatic drift turbulence modelling for the scrape‐off layer, we propose a transport equation for and discuss its coupling with the mean‐field transport equations. The main features of the model include (a) an analytically exact interchange source of which introduces the ballooning character of the transport; (b) fast parallel transport of through the connection with parallel current fluctuations; and (c) consistent transport reduction due to the impact of mean flow shear. The resulting model has been implemented in the new extended grids version of SOLPS‐ITER, enabling for the first time mean‐field simulations self‐consistently combining classical parallel transport with mean‐field drifts and anomalous transport with the code. A first assessment of the model has been made for a representative C‐Mod case study, highlighting the promising features of the model. Further analysis is needed to investigate in detail the impact of the different new terms in the model across operational regimes, and determine the new closures constants based on larger sets of turbulence simulations and experimental data.

Emergence of active turbulence in microswimmer suspensions due to active hydrodynamic stress and volume exclusion

Microswimmers exhibit an intriguing, highly-dynamic collective motion with large-scale swirling and streaming patterns, denoted as active turbulence – reminiscent of classical high-Reynolds-number hydrodynamic turbulence. Various experimental, numerical, and theoretical approaches have been applied to elucidate similarities and differences of inertial hydrodynamic and active turbulence. We use squirmers embedded in a mesoscale fluid, modeled by the multiparticle collision dynamics (MPC) approach, to explore the collective behavior of bacteria-type microswimmers. Our model includes the active hydrodynamic stress generated by propulsion, and a rotlet dipole characteristic for flagellated bacteria. We find emergent clusters, activity-induced phase separation, and swarming behavior, depending on density, active stress, and the rotlet dipole strength. The analysis of the squirmer dynamics in the swarming phase yields Kolomogorov-Kraichnan-type hydrodynamic turbulence and energy spectra for sufficiently high concentrations and a strong rotlet dipole. This emphasizes the paramount importance of the hydrodynamic flow field for swarming motility and bacterial turbulence.

Effects of Oil and Sediment Properties and Mixing States on the Formation and Settling of Oil‐Particle Aggregates

AbstractUnderstanding the interaction of oil droplets with suspended particulate matter is important not only for sunken oil modeling but also for emergency response. In this study, the effects of mixing time and energy, oil type, and sediment concentration and size on the oil content, morphology, and density of oil‐particle aggregates (OPAs) were investigated through a series of wave tank experiments and sedimentation tests. The results showed that loads of oil and particles in OPAs are high under high mixing energy. Under turbulent hydrodynamics, moderately viscous oils form OPAs more easily and sink rapidly to the seabed. Moreover, an increase in the density and oil capacity of OPAs is observed at a higher sediment concentration. More oil is captured by finer sediments. However, the corresponding oil‐sediment aggregates generally show lower density compared with those formed by larger sediments. The oil‐seawater interfacial tension (IFTow) diminishes with the addition of sediments, further promoting oil dispersion. The increasing duration and mixing energy produce more flake OPAs and multiple‐droplet OPAs. Oil droplets tend to be surrounded by several small particles but attach to the surface of large particles. Regardless of oil type and sediment concentration, the structure of OPAs does not change significantly.

Anomalous Dissipation in Passive Scalar Transport

We study anomalous dissipation in hydrodynamic turbulence in the context of passive scalars. Our main result produces an incompressible \(C^\infty ([0,T)\times {\mathbb {T}}^d)\cap L^1([0,T]; C^{1-}({\mathbb {T}}^d))\) velocity field which explicitly exhibits anomalous dissipation. As a consequence, this example also shows the non-uniqueness of solutions to the transport equation with an incompressible \(L^1([0,T]; C^{1-}({\mathbb {T}}^d))\) drift, which is smooth except at one point in time. We also give a sufficient condition for anomalous dissipation based on solutions to the inviscid equation becoming singular in a controlled way. Finally, we discuss connections to the Obukhov-Corrsin monofractal theory of scalar turbulence along with other potential applications.

Fluctuation-Induced Interaction in Turbulent Flows.

Fluctuation-induced forces are observed in numerous physical systems spanning from quantum to macroscopic scale. However, there is as yet no experimental report of their existence in hydrodynamic turbulence. Here, we present evidence of an attraction force mediated via turbulent fluctuations by using two walls locally confining 2D turbulence. This long-range interaction is a function of the wall separation and the energy injection rate in the turbulent flow. As the wall spacing decreases, the confined flow becomes less energetic and more anisotropic in the bounded domain, producing stronger attraction. The mechanism of force generation is rooted in a nontrivial fluid-wall coupling where coherent flow structures are guided by the cavity walls. For the narrowest cavities studied, a resonance phenomenon at the flow forcing scale leads to a complex short-range interaction. The results could be relevant to problems encountered in a range of fields from industrial multiphase flows to modeling of planetary formation.

Efficient Approaches for Solving Systems of Nonlinear Time-Fractional Partial Differential Equations

In this work, we present a modified generalized Mittag–Leffler function method (MGMLFM) and Laplace Adomian decomposition method (LADM) to get an analytic-approximate solution for nonlinear systems of partial differential equations (PDEs) of fractional-order in the Caputo derivative. We apply the MGMLFM and LADM on systems of nonlinear time-fractional PDEs. Precisely, we consider some important fractional-order nonlinear systems, namely Broer–Kaup (BK) and Burgers, which have found major significance because they arise in many physical applications such as shock wave, wave processes, vorticity transport, dispersal in porous media, and hydrodynamic turbulence. The analysis of these methods is implemented on the BK, Burgers systems and solutions have been offered in a simple formula. We show our results in figures and tables to demonstrate the efficiency and reliability of the used methods. Furthermore, our outcome converges rapidly to the given exact solutions.

Design and Fabrication of Artificial Brain Coral: Evolution Principle, Turbulent Hydrodynamics and Matter Interchange

Design and Fabrication of Artificial Brain Coral: Evolution Principle, Turbulent Hydrodynamics and Matter Interchange

Gravitational waves generation in turbulent hypermagnetic fields before the electroweak phase transition

We study the production of relic gravitational waves (GWs) in turbulent hypermagnetic fields (HMFs) in the symmetric phase of the early universe before the electroweak phase transition (EWPT). The noise of HMFs is modeled by the analog of the magnetic hydrodynamics turbulence. The evolution of HMFs is driven by the analogs of the chiral magnetic effect and the Adler anomalies in the presence of the nonzero asymmetries of leptons and Higgs bosons. We track the evolution of the energy density of GWs from 10 TeV down to EWPT and analyze its dependence on the parameters of the system. We also discuss the possibility to observe the predicted GW background by the current GW detectors.

Fully-Resolved Numerical Simulations of the Turbulent Hydrodynamics and Airborne Particletransport and Deposition on Thermally Active Walls in Enclosed Cavities Atra=3.6 X 109

Fully-Resolved Numerical Simulations of the Turbulent Hydrodynamics and Airborne Particletransport and Deposition on Thermally Active Walls in Enclosed Cavities Atra=3.6 X 109

Application of the Correlation Measurement Method for Reconstructing of the Velocity Profile with Spatial and Temporal Discretization in Studies of the Hydrodynamics of Turbulent Flows Based on the Matrix Conductometry Method

The correlation method for measuring of the coolant fl rate is used in the operation of nuclear power plants and is widespread in research practice including study of turbulent fl hydrodynamics. However the question of its applicability and possibilities in studies using the matrix conductometry method remains open. Earlier the algorithm for determining of the correlation fl rate using a conductometric measuring system was highlighted and the error of the results obtained was estimated and the dependence of the influence of noise and the time of data collection on the reliability of results was investigated. These works were carried out using two independent mesh sensors and the issue of the resolution of local velocity components was not covered. The purpose of this work was to test the correlation method for measuring velocity with temporal and spatial sampling using two-layer mesh conductometric sensors.As the result velocity cartograms were obtained over the cross-section of the experimental model with quasi-stationary mixing and the value of the average flow rate is in good agreement with the values obtained from the standard flow meters of the stand. Also measurements were carried out at a non-stationary setting of the experiment and realizations of the flow rate and velocity components of the flow at the measuring points were obtained.Analysis of the obtained values allows to conclude about the optimal data collection time for correlation measurements, as well as the reliability of results.

A quadratic Reynolds stress development for the turbulent Kolmogorov flow

We study the three-dimensional turbulent Kolmogorov flow, i.e., the Navier–Stokes equations forced by a single-low-wave-number sinusoidal force in a periodic domain, by means of direct numerical simulations. This classical model system is a realization of anisotropic and non-homogeneous hydrodynamic turbulence. Boussinesq's eddy viscosity linear relation is checked and found to be approximately valid over half of the system volume. A more general quadratic Reynolds stress development is proposed, and its parameters are estimated at varying the Taylor scale-based Reynolds number in the flow up to the value 200. The case of a forcing with a different shape, here chosen Gaussian, is considered, and the differences with the sinusoidal forcing are emphasized.

Nonlinear amplification in hydrodynamic turbulence

Using direct numerical simulations performed on periodic cubes of various sizes, the largest being $8192^3$ , we examine the nonlinear advection term in the Navier–Stokes equations generating fully developed turbulence. We find significant dissipation even in flow regions where nonlinearity is locally absent. With increasing Reynolds number, the Navier–Stokes dynamics amplifies the nonlinearity in a global sense. This nonlinear amplification with increasing Reynolds number renders the vortex stretching mechanism more intermittent, with the global suppression of nonlinearity, reported previously, restricted to low Reynolds numbers. In regions where vortex stretching is absent, the angle and the ratio between the convective vorticity and solenoidal advection in three-dimensional isotropic turbulence are statistically similar to those in the two-dimensional case, despite the fundamental differences between them.

Identifying Performance-Defining Metrics of Ion Exchange Membranes for Non-Aqueous Redox Flow Batteries

Redox flow batteries stand out as a promising candidate for large-scale and multi-hour energy storage due to their ability to independently scale power and energy, long cycle life, and facile manufacturing[1,2]. However, current deployment is hampered by elevated costs which motivate research into alternative electrolyte chemistries and advanced reactor concepts. As a result of the limited electrochemical stability window of water and the scarcity of inorganic redox active molecules, non-aqueous redox flow batteries (NAqRFBs) have emerged as a promising technology for low-cost energy storage if a number of technical challenges can be overcome. Leveraging the extended electrochemical window of organic electrolytes, NAqRFBs can enable high cell voltage and high energy density[3] and the use of abundant elements (e.g. H, C, N, O, S) coupled with molecular engineering enables almost unlimited tunability of the redox active molecules[4]. However, NAqRFBs suffer from large ohmic overpotentials due to the low ionic conductivity of the electrolytes[5] and the lack of tailored membrane materials for non-aqueous electrolytes. While existing knowledge on materials and characterization techniques in ion exchange membranes (IEMs) for NAqRFBs has been borrowed from their aqueous counterparts, there are some unique challenges (e.g. different ion size, solvent polarity[6]) that motivate research into new methodologies and polymer chemistries. In this work, we aim to elucidate material-property-performance relationships for IEMs relevant to NAqRFBs.Here, we employ an array of electrochemical and spectroscopic techniques to assess relevant membrane metrics for NAqRFBs. We deploy methods to determine membrane resistance, redox species crossover, ion exchange capacity, and electrochemical performance. To demonstrate this methodology we selected a series of commercial anion exchange membranes. We elect to study a model non-aqueous electrolyte system with redox active molecules based on ferrocene and phtalimide precursors chosen for their stability and facile kinetics, using TBAPF6 as supporting electrolyte in acetonitrile. In an effort to measure the real ion-exchange capacity using polyatomic fluorinated anions typically employed in NAqRFBs, we introduce quantitative fluorine nuclear magnetic resonance as analytical tool to track the loading of fluorinated anions in anion exchange membranes. Interestingly, we find that the loading of PF6 - is significantly lower than the ion exchange capacity measured in aqueous conditions, highlighting a rate-limited ion loading in non-aqueous electrolytes with bulky anions. Furthermore, we correlate these results with complementary metrics such as membrane resistance obtained with electrochemical impedance spectroscopy. Additionally, we incorporate a three-electrode setup equipped with a microelectrode within the electrolyte tanks to track in operando changes in concentrations. Linear sweep voltammetry reveals a reproducible and linear current-concentration response over a wide range of analyte concentrations, matching with the requirements of high-performance NAqRFBs. The integrated microelectrode sensor is suitable for an accurate measurement of state of charge or analyte crossover rate over a wide range of flow rates due to its positioning in the external tanks which display limited hydrodynamic turbulence. Our results demonstrate the need to develop novel methodologies to characterize membranes in non-aqueous electrolytes and informs the design of tailored membrane materials for next-generation NAqRFBs.

Vertical settling of pebbles in turbulent circumbinary discs and the in situ formation of circumbinary planets

ABSTRACT The inner-most regions of circumbinary discs are unstable to a parametric instability whose non-linear evolution is hydrodynamical turbulence. This results in significant particle stirring, impacting on planetary growth processes such as the streaming instability or pebble accretion. In this paper, we present the results of three-dimensional, inviscid global hydrodynamical simulations of circumbinary discs with embedded particles of 1 cm size. Hydrodynamical turbulence develops in the disc, and we examine the effect of the particle back-reaction on vertical dust. We find that higher solid-to-gas ratios lead to smaller gas vertical velocity fluctuations, and therefore to smaller dust scale heights. For a metallicity Z = 0.1, the dust scale height near the edge of the tidally truncated cavity is $\sim 80{{\ \rm per\ cent}}$ of the gas scale height, such that growing a Ceres-mass object to a 10 M⊕ core via pebble accretion would take longer than the disc lifetime. Collision velocities for small particles are also higher than the critical velocity for fragmentation, which precludes grain growth and the possibility of forming a massive planetesimal seed for pebble accretion. At larger distances from the binary, turbulence is weak enough to enable not only efficient pebble accretion but also grain growth to sizes required to trigger the streaming instability. In these regions, an in situ formation scenario of circumbinary planets involving the streaming instability to form a massive planetesimal followed by pebble accretion on to this core is viable. In that case, planetary migration has to be invoked to explain the presence of circumbinary planets at their observed locations.

Reconnection-Controlled Decay of Magnetohydrodynamic Turbulence and the Role of Invariants

We present a new theoretical picture of magnetically dominated, decaying turbulence in the absence of a mean magnetic field. We demonstrate that such turbulence is governed by the reconnection of magnetic structures, and not by ideal dynamics, as has previously been assumed. We obtain predictions for the magnetic-energy decay laws by proposing that turbulence decays on reconnection timescales, while respecting the conservation of certain integral invariants representing topological constraints satisfied by the reconnecting magnetic field. As is well known, the magnetic helicity is such an invariant for initially helical field configurations, but does not constrain non-helical decay, where the volume-averaged magnetic-helicity density vanishes. For such a decay, we propose a new integral invariant, analogous to the Loitsyansky and Saffman invariants of hydrodynamic turbulence, that expresses the conservation of the random (scaling as $\mathrm{volume}^{1/2}$) magnetic helicity contained in any sufficiently large volume. Our treatment leads to novel predictions for the magnetic-energy decay laws: in particular, while we expect the canonical $t^{-2/3}$ power law for helical turbulence when reconnection is fast (i.e., plasmoid-dominated or stochastic), we find a shallower $t^{-4/7}$ decay in the slow `Sweet-Parker' reconnection regime, in better agreement with existing numerical simulations. For non-helical fields, for which there currently exists no definitive theory, we predict power laws of $t^{-10/9}$ and $t^{-20/17}$ in the fast- and slow-reconnection regimes, respectively. We formulate a general principle of decay of turbulent systems subject to conservation of Saffman-like invariants, and propose how it may be applied to MHD turbulence with a strong mean magnetic field and to isotropic MHD turbulence with initial equipartition between the magnetic and kinetic energies.