Quasi-coherent Structures Research Articles

A self-sustaining process theory for uniform momentum zones and internal shear layers in high Reynolds number shear flows

Abstract

Statistical study for ITG turbulent transport in flux-driven tokamak plasmas based on global gyro-kinetic simulation

Flux-driven ion temperature gradient (ITG) turbulence and associated transport regulated by non-local and non-diffusive processes are investigated based on GKNET simulations in a global toroidal geometry. Among these processes, the instantaneous formation of radially extended quasi-coherent structure, which leads to the transport burst, is found to play an important role in causing global profile formation and relaxation. To elucidate the characteristics of such a transport process, we introduce the size probability distribution function (size-PDF) to analyze heat flux eddies in the real space, with the eddy size, incorporated with Fourier-based approaches in spectral space. In the size-PDF to the quiescent phase, is found to be fitted by three piecewise power laws which transitions at two typical sizes, and , as , , and , where and in squared gyro-radius unit for the system with (a: the minor radius). On the other hand, the size-PDF in the bursting phase exhibits non-power-law irregular humps which corresponds to the quasi-coherent structures for reaching to . Such a coherent structure is ascribed to the spontaneous alignment of smaller scale eddies through phase matching in radial direction, which is classified as a quasi-deterministic process. Resultantly, a large amount of free energy is extracted from the system due to subsequent growth of the event, by which a self-organized profile is established. The coherent structure is then readily disintegrated by self-generated zonal flows, followed by the energy transferred to smaller eddies. Finally, turbulent transport in the steady state of a flux-driven system is found to be regulated by the mixture of such quasi-deterministic process and probabilistic processes, which leads to stiffness and resilience in the profile formation and self-similarity in the relaxation.

Flow Structure in a Shallow Mixing Layer Developing over 2-D Dunes

A high resolution Detached Eddy Simulation (DES) are used to characterize the evolution of a shallow mixing layer developing between two parallel streams in a long open channel over two-dimensional (2D) dunes. The study discusses the vertical non-uniformity in the mixing layer and provides a quantitative characterization of the growth of the large-scale quasi 2D coherent structures with the distance from the splitter plate. The presence of large-scale roughness elements in the form of an array of two-dimensional dunes with a maximum height of 0.25D (D is the channel depth) induces a very rapid and larger shift of the centerline of the mixing layer due to the increased influence of the bottom roughness. Results show that in streamwise sections situated after 100D (D is the channel depth) from the splitter plate, the width of the mixing layer close to the free surface stays constant. The tilting of the mixing layer interface toward the low speed stream is observed as the free surface is approached in all vertical sections.

Current flow instability and nonlinear structures in dissipative two-fluid plasmas

The current flow in two-fluid plasma is inherently unstable if plasma components (e.g., electrons and ions) are in different collisionality regimes. A typical example is a partially magnetized E×B plasma discharge supported by the energy released from the dissipation of the current in the direction of the applied electric field (perpendicular to the magnetic field). Ions are not magnetized so they respond to the fluctuations of the electric field ballistically on the inertial time scale. In contrast, the electron current in the direction of the applied electric field is dissipatively supported either by classical collisions or anomalous processes. The instability occurs due to a positive feedback between the electron and ion current coupled by the quasi-neutrality condition. The theory of this instability is further developed taking into account the electron inertia, finite Larmor radius and nonlinear effects. It is shown that this instability results in highly nonlinear quasi-coherent structures resembling breathing mode oscillations in Hall thrusters.

Quasi-coherent structures and flows in turbulent transport

The nonlinear effects that appear in test particle (tracer) transport in two-dimensional incompressible velocity fields are discussed. Test particle trajectories show both random and quasi-coherent aspects. The coherent motion is associated with trapping or eddying in the structure of the stochastic field. It generates quasi-coherent trajectory structures. The random motion leads to diffusive transport while the structures determine a micro-confinement process. The strength of each of these aspects depends on the parameters of the turbulence. The transport coefficients and the average size of the quasi-coherent structures are determined as function of the characteristics of the turbulence. The transport process is completely different in the presence of structures in the sense that the dependence on the parameters is different. The quasi-coherence of the motion can also be represented by the generation of flows. We show that tracers flows yield in a stochastic potential with space-dependent amplitude.

Preferential particle concentration in wall-bounded turbulence with zero skin friction

Inertial particles dispersed in turbulence distribute themselves unevenly. Besides their tendency to segregate near walls, they also concentrate preferentially in wall-parallel planes. We explore the latter phenomenon in a tailor-made flow with the view to examine the homogeneity and anisotropy of particle clustering in the absence of mean shear as compared with conventional, i.e., sheared, wall turbulence. Inertial particles with some different Stokes numbers are suspended in a turbulent Couette-Poiseuille flow, in which one of the walls moves such that the shear rate vanishes at that wall. The anisotropies of the velocity and vorticity fluctuations are therefore qualitatively different from those at the opposite non-moving wall, along which quasi-coherent streaky structures prevail, similarly as in turbulent pipe and channel flows. Preferential particle concentration is observed near both walls. The inhomogeneity of the concentration is caused by the strain-vorticity selection mechanism, whereas the anisotropy originates from coherent flow structures. In order to analyse anisotropic clustering, a two-dimensional Shannon entropy method is developed. Streaky particle structures are observed near the stationary wall where the flow field resembles typical wall-turbulence, whereas particle clusters near the moving friction-free wall are similar to randomly oriented clusters in homogeneous isotropic turbulence, albeit with a modest streamwise inclination. In the absence of mean-shear and near-wall streaks, the observed anisotropy is ascribed to the imprint of large-scale flow structures which reside in the bulk flow and are global in nature.

Particle segregation in turbulent Couette–Poiseuille flow with vanishing wall shear

Inertial particles dispersed in wall-bounded flows in pipes and channels are known to accumulate close to the walls. The segregation ability depends greatly on the inertia-selection effects of the near-wall quasi-coherent turbulent structures, which are formed near both walls where shear stresses are high. Here, however, we investigated if and how particles segregate in the vicinity of walls in absence of mean shear. A tailor-made turbulent Couette–Poiseuille flow was designed such that the mean shear vanished at the moving wall, thereby resulting in an asymmetric flow with conventional near-wall turbulent structures only at one wall. In addition, Large-Scale Structures (LSSs) were observed in the flow, which greatly influenced the distribution of the inertial particles. Particles of five different inertia groups were embedded in the directly simulated turbulence field and examined. It was found that particles of high inertia segregated near the stationary wall where mean shear prevailed, but also near the moving wall where mean shear was absent. However, due to the qualitatively distinct near-wall flow structures, the inertia effects on the actual segregation were different at the two walls. Mechanisms causing the asymmetric wall-normal segregation were explored with the focus on the moving-wall region, where the quasi-coherent turbulent structures were absent, and the local fluid structures were dominated by imprints of the LSSs.

Random and quasi-coherent aspects in particle motion and their effects on transport and turbulence evolution

The quasi-coherent effects in two-dimensional incompressible turbulence are analyzed starting from the test particle trajectories. They can acquire coherent aspects when the stochastic potential has slow time variation and the motion is not strongly perturbed. The trajectories are, in these conditions, random sequences of large jumps and trapping or eddying events. Trapping determines quasi-coherent trajectory structures, which have a micro-confinement effect that is reflected in the transport coefficients. They determine non-Gaussian statistics and flows associated to an average velocity. Trajectory structures also influence the test modes on turbulent plasmas. Nonlinear damping and generation of zonal flow modes is found in drift turbulence in uniform magnetic field. The coupling of test particle and test mode studies permitted to evaluate the self-consistent evolution of the drift turbulence in an iterated approach. The results show an important nonlinear effect of ion diffusion, which can prevent the transition to the nonlinear regime at small drive of the instability. At larger drive, quasi-coherent trajectory structures appear and they have complex effects on turbulence.

Spectral analysis of point-vortex dynamics: first application to vortex polygons in a circular domain*

The present study addresses the classical problem of the dynamics and stability of a cluster of N-point vortices of equal strength arranged in a polygonal configuration (‘N-vortex polygons’). In unbounded domains, such N-vortex polygons are unconditionally stable for . Confinement in a circular domain tightens the stability conditions to and a maximum polygon size relative to the domain radius. This work expands on existing studies on stability and integrability by a first giving an exploratory spectral analysis of the dynamics of N vortex polygons in circular domains. Key to this is that the spectral signature of the time evolution of vortex positions reflects their qualitative behaviour. Expressing vortex motion by a generic evolution operator (the so-called Koopman operator) provides a rigorous framework for such spectral analyses. This paves the way to further differentiation and classification of point-vortex behaviour beyond stability and integrability. The concept of Koopman-based spectral analysis is demonstrated for N-vortex polygons. This reveals that conditional stability can be seen as a local form of integrability and confirms an important generic link between spectrum and dynamics: discrete spectra imply regular (quasi-periodic) motion; continuous (sub-)spectra imply chaotic motion. Moreover, this exposes rich nonlinear dynamics as intermittency between regular and chaotic motion and quasi-coherent structures formed by chaotic vortices.

Effect of electron-cyclotron resonance heating conditions on the local parameters of short-wavelength plasma turbulence in the L-2M stellarator

Changes in the energy spectra of short-wavelength (ks ≈ 35 cm−1) plasma density fluctuations in the local region of the plasma column (r/a = 0.5–0.6) of the L-2M stellarator were studied by the method of collective scattering of 150-GHz radiation. The plasma was heated at the second harmonic of the electron gyrofrequency, the microwave heating power being in the range of 90–170 kW. A sector limiter was introduced in the peripheral plasma (r/a ≥ 0.8), and the Shafranov shift of the magnetic axis was varied by varying the vertical magnetic field. The results of measurements were averaged over 9–16 discharges. It is found that an increase in the heating power and/or the introduction of the sector limiter in the plasma lead to an increase in the energy of density fluctuations, which correlates with a decrease in the plasma energy lifetime. In the spectra of fluctuations, a broad spectral band in the range of 3–50 kHz was observed in which the spectral density was one order of magnitude higher than in the rest of the spectrum. Analysis of the Fourier spectra showed that the introduction of the sector limiter in the plasma resulted in an increase in both the spectral density of fluctuations in the range of 3–50 kHz and the fraction of quasi-coherent structures in turbulent density fluctuations.

ON THE SOURCE OF ASTROMETRIC ANOMALOUS REFRACTION

More than a century ago, astronomers using transit telescopes to determine precise stellar positions were hampered by an unexplained periodic shifting of the stars they were observing. With the advent of CCD transit telescopes in the past three decades, this unexplained motion, termed "anomalous refraction" by these early astronomers, is again being observed. Anomalous refraction is described as a low-frequency, large angular scale (∼2°) motion of the entire image plane with respect to the celestial coordinate system as observed and defined by astrometric catalogs. These motions, of typically several tenths of an arcsecond amplitude with timescales on the order of 10 minutes, are ubiquitous to ground-based drift-scan astrometric measurements regardless of location or telescopes used and have been attributed to the effect of tilting of equal-density layers of the atmosphere. The cause of this tilting has often been attributed to atmospheric gravity waves, but this cause has never been confirmed. Although theoretical models of atmospheric refraction show that atmospheric gravity waves are a plausible cause of anomalous refraction, an observational campaign specifically directed at defining this relationship provides clear evidence that anomalous refraction is not consistent with the passage of atmospheric gravity waves. The source of anomalous refraction is found to be meter-scale, slowly evolving quasi-coherent dynamical structures in the boundary layer below 60 m above ground level.

Vortical structures of trajectories and transport of tracers advected by turbulent fluids

Tracer transport in two-dimensional incompressible turbulent fluids is studied using the nested subensemble method, a semi-analytical statistical approach. Quasi-coherent vortical structures of trajectories are shown to appear when the stream function has slow time variation. In the presence of weak perturbation the structures are not destroyed and they determine anomalous transport regimes.

Measuring turbulent large-eddy structures with an ADCP. 1. Vertical velocity variance

Two different turbulent flows, Langmuir supercells and unstable convection, have been sampled with a VADCP, an acoustic Doppler current profiler (ADCP) with an additional vertical (V) beam. Direct measurements of the profile of vertical velocity variance provided by the vertical beam are used to calculate observational response functions for algorithms used to derive vertical velocity from the 4 beams of a standard ADCP. A theoretical response function derived for the vertical velocity estimate from a single pair of opposed slant beams illustrates the importance of large-scale quasi-coherent flow structures, as well as effects of different angles of slant beams from vertical. Different large-eddy characteristics for Langmuir supercells and unstable convection yield different theoretical response: however in both cases, the theoretical response agrees qualitatively with that derived from observations. For Langmuir supercells, there is additional agreement with numerical response functions generated by using the geometry of a VADCP to sample three-dimensional flow fields available from large eddy simulations (LES). The results from all three approaches show that there can be significant error in vertical velocity inferred from slant beam velocities. The error may be either overor under-estimation, depending upon (usually unknown) features of the large eddies of the turbulent field, such as vertical/horizontal anisotropy, phase coherence, and orientation of horizontally anisotropic turbulent structures relative to the instrument. Given only a standard ADCP, the “best” estimate of vertical velocity variance is not the usual 4-beam estimate, but the larger of the two pair estimates.

A turbulent boundary layer over a two-dimensional rough wall

Particle image velocimetry (PIV) measurements and planar laser induced fluorescence (PLIF) visualizations have been made in a turbulent boundary layer over a rough wall. The wall roughness consisted of square bars placed transversely to the flow at a pitch to height ratio of λ/k = 11 for the PLIF experiments and λ/k = 8 and 16 for the PIV measurements. The ratio between the boundary layer thickness and the roughness height k/δ was about 20 for the PLIF and 38 for the PIV. Both the PLIF and PIV data showed that the near-wall region of the flow was populated by unstable quasi-coherent structures which could be associated to shear layers originating at the trailing edge of the roughness elements. The streamwise mean velocity profile presented a downward shift which varied marginally between the two cases of λ/k, in agreement with previous measurements and DNS results. The data indicated that the Reynolds stresses normalized by the wall units are higher for the case λ/k = 16 than those for λ/k = 8 in the outer region of the flow, suggesting that the roughness density effects could be felt well beyond the near-wall region of the flow. As expected the roughness disturbed dramatically the sublayer which in turn altered the turbulence production mechanism. The turbulence production is maximum at a distance of about 0.5k above the roughness elements. When normalized by the wall units, the turbulence production is found to be smaller than that of a smooth wall. It is argued that the production of turbulence is correlated with the form drag.

Topological instability along invariant surfaces and pseudochaotic transport

The paper describes the complex topological structure of invariant surfaces that appears in a quasi-stationary regime of the tokamak plasma, and it considers in detail anomalous transport of particles along the invariant surfaces (isosurfaces) that have topological genus greater than 1. Such dynamics is pseudochaotic; i.e. it has a zero Lyapunov exponent. Simulations discover such surfaces in confined plasmas under a fairly low ratio of pressure to the magnetic field energy (beta). The isosurfaces correspond to quasi-coherent structures called "streamers" and the streamers are connected by filaments. We study distribution of time of particle separation, Poincaré; recurrences of trajectories, and first time arrival to the system's edge. A model of a multibar-in-square billiard, introduced by Carreras et al. [Chaos 13, 1175 (2003)] is studied with renormalization group method to obtain a distribution of the first time of particles arrival to the edge as a function of the number of bars, which appears to be power-like. The characteristic exponent of this distribution is discussed with respect to its dependence on the number of filaments that connect adjacent streamers.

Experiments on the stability of sinusoidal flow over a circular cylinder

The instabilities in a sinusoidally oscillating non-separated flow over smooth circular cylinders in the range of Keulegan–Carpenter numbers, K, from about 0.02 to 1 and Stokes numbers, β, from about 103 to 1.4 × 106 have been observed from inception to chaos using several high-speed imagers and laser-induced fluorescence. The instabilities ranged from small quasi-coherent structures, as in Stokes flow over a flat wall (Sarpkaya 1993), to three-dimensional spanwise perturbations because of the centrifugal forces induced by the curvature of the boundary layer (Taylor–Görtler instability). These gave rise to streamwise-oriented counter-rotating vortices or mushroom-shaped coherent structures as K approached the Kh values theoretically predicted by Hall (1984). Further increases in K for a given β led first to complex interactions between the coherent structures and then to chaotic motion. The mapping of the observations led to the delineation of four states of flow in the (K, β)-plane: stable, marginal, unstable, and chaotic.

Engineering Applications of Noncommutative Harmonic Analysis: With Emphasis on Rotation and Motion Groups

<i>Engineering Applications of Noncommutative Harmonic Analysis: With Emphasis on Rotation and Motion Groups</i>

HYDRODYNAMIC DAMPING AND QUASI-COHERENT STRUCTURES AT LARGE STOKES NUMBERS

Unsteady flow about solid and perforated cylinders at large Stokes numbers and very small Keulegan–Carpenter numbers has not been sufficiently understood to predict the hydroelastic response of compliant structures subjected to high frequency excitation. It is impossible to compute, difficult to quantify, and extremely difficult to visualize. Here, following a brief review of the previous research, new results for both forced and pluck-induced oscillations are presented. It is shown that: (a) the measured drag coefficients are larger (about double for smooth cylinders) than those predicted from the Stokes–Wang analysis (in the region of its applicability); (b) there is an unstable flow regime in which the oscillatory boundary layer develops quasicoherent structures (QCS) over a range of K values before giving rise to Honji-type coherent structures (HTCS); (c) the drag coefficients for perforated cylinders are much larger than those for solid cylinders and do not follow the Stokes–Wang prediction even at small β. As expected, their inertia coefficients are considerably smaller than those for solid cylinders.

Effects of freestream on turbulent combined-convection boundary layer along a vertical heated plate

A turbulent combined-convection boundary layer, created by imposing an aiding freestream on a turbulent natural-convection boundary layer along a vertical heated plate, was examined with normal hot- and cold-wires and a particle image velocimetry (PIV), with attention to the laminarization process of the boundary layer due to the freestream effects. As the freestream velocity increases, the wall shear stress monotonously increases, whereas the local heat transfer rate suddenly decreases. The reduction in heat transfer rates and the decays in velocity and temperature fluctuations, showing the transition from turbulent to laminar, arise at Grx/ Rex≃3×10 6. With the laminarization of the boundary layer, a similar change in the turbulent quantities appears independently of Grx. For instantaneous velocity vectors obtained with PIV, large-scale fluid motions, which play a predominant role in the generation of turbulence, are frequently observed in the outer layer, while quasi-coherent structures do not exist in the near-wall region. The increasing freestream then restricts large-scale fluid motions in the outer layer, and consequently the generation of turbulence is suppressed and the boundary layer becomes laminar.

Direct Numerical Simulation of a Fully Developed Turbulent Channel Flow With Respect to the Reynolds Number Dependence

Direct numerical simulation (DNS) of a fully developed turbulent channel flow for various Reynolds numbers has been carried out to investigate the Reynolds number dependence. The Reynolds number is set to be Reτ=180, 395, and 640, where Reτ is the Reynolds number based on the friction velocity and the channel half width. The computation has been executed with the use of the finite difference method. Various turbulence statistics such as turbulence intensities, vorticity fluctuations, Reynolds stresses, their budget terms, two-point correlation coefficients, and energy spectra are obtained and discussed. The present results are compared with the ones of the DNSs for the turbulent boundary layer and the plane turbulent Poiseuille flow and the experiments for the channel flow. The closure models are also tested using the present results for the dissipation rate of the Reynolds normal stresses. In addition, the instantaneous flow field is visualized in order to examine the Reynolds number dependence for the quasi-coherent structures such as the vortices and streaks.