Turbulence Spreading Research Articles

Effect of secondary convective cells on turbulence intensity profiles, flow generation, and transport

This paper reports the results of gyrokinetic simulation studies of ion temperature gradient driven turbulence which investigate the role of non-resonant modes in turbulence spreading, turbulence regulation, and self-generated plasma rotation. Non-resonant modes, which are those without a rational surface within the simulation domain, are identified as nonlinearly driven, radially extended convective cells. Even though the amplitudes of such convective cells are much smaller than that of the resonant, localized turbulence eddies, we find from bicoherence analysis that the mode-mode interactions in the presence of such convective cells increase the efficiency of turbulence spreading associated with nonlocality phenomena. Artificial suppression of the convective cells shows that turbulence spreading is reduced, and that the turbulence intensity profile is more localized. The more localized turbulence intensity profile produces stronger Reynolds stress and E × B shear flows, which in turn results in more effective turbulence self-regulation. This suggests that models without non-resonant modes may significantly underestimate turbulent fluctuation levels and transport.

Ballistic propagation of turbulence front in tokamak edge plasmas

The flux-driven nonlinear simulation of resistive ballooning mode turbulence with tokamak edge geometry is performed to study the non-steady component in the edge turbulence. The large-scale and dynamical events in transport are investigated in a situation where the mean flow is suppressed. Two types of dynamics are observed. One is the radial propagation of the pulse of pressure gradient, the other is the appearance/disappearance of radially elongated global structure of turbulent heat flux. The ballistic propagation is observed in the pulse of pressure gradient, which is associated with the front of turbulent heat flux. We focus on this ballistic propagation phenomenon. Both of the bump of pressure gradient and the front of heat flux propagate inward and outward direction. It is confirmed that the strong fluctuation propagates with the pulse front. It is observed that the number of pulses going outward is close to those going inward. This ballistic phenomenon does not contradict to the turbulence spreading theory. Statistical characteristics of the ballistic propagation of pulses are evaluated and compared with scaling laws which is given by the turbulence spreading theory. It is found that they give qualitatively good agreement.

Response of the deep chlorophyll maximum to fluctuations in vertical mixing intensity

Extreme atmospheric events, such as storms, can temporarily increase the vertical diffusivity in the upper ocean by several orders of magnitude, causing variability in the deep chlorophyll maximum (DCM). In this study, we investigate the impact of intermittent vertical mixing on the deep chlorophyll maximum. For this purpose, we analyze a one-dimensional phytoplankton-nutrient model exposed to short-term fluctuations in vertical diffusivity generated by internal waves. As a first step, we use singular perturbations to analyze the impact of a single burst of turbulence on the DCM characteristics. The simulations show that the DCM exhibits a long transient response, even after a single short perturbation. In particular, a single burst of turbulence (i) spreads out the DCM, thereby reducing the local phytoplankton maximum, and (ii) gives rise to a diffusion-driven enhancement of nutrient availability, producing a temporary increase in the phytoplankton growth rates at and above the DCM. Subsequently, we introduce a realistic annual sequence of fluctuations in vertical diffusivity in our model, and we also incorporate the seasonal cycle of light conditions. Fluctuations in vertical diffusivity were derived from high-resolution measurements from the POMME experiment in the north-east Atlantic Ocean, where the contribution of internal waves to the variation in vertical mixing has been characterized for more than one year. The annual light cycle, in combination with intermittent vertical mixing, leads to the superposition of a series of complex dynamical responses. At seasonal and shorter time scales, the vertically integrated productivity is temporally augmented by periods of medium/high diffusivity. Seasonal variation in light availability modifies the DCM response to mixing variability.

Hot-electron production and suprathermal heat flux scaling with laser intensity from the two-plasmon–decay instability

The fully kinetic reduced-description particle-in-cell (RPIC) method has been applied to simulations of two-plasmon–decay (TPD) instability, driven by crossed laser beams, in an inhomogeneous plasma for parameters consistent with recent direct-drive experiments related to laser-driven inertial fusion. The nonlinear saturated state is characterized by very spiky electric fields, with Langmuir cavitation occurring preferentially inside density channels produced by the ponderomotive beating of the crossed laser beams and the primary TPD Langmuir waves (LWs). The heated electron distribution function is, in all cases, bi-Maxwellian, with instantaneous hot-electron temperatures in the range 60–100 keV. The net hot-electron energy flux out of the system is a small fraction (∼1% to 2%) of the input laser intensity in these simulations. Scalings of the hot-electron temperature and suprathermal heat flux as functions of the laser intensity are obtained numerically from RPIC simulations. These simulations lead to the preliminary conclusion that Langmuir cavitation and collapse provide dissipation by producing suprathermal electrons, which stabilize the system in saturation and drive the LW spectrum to the small dissipation scales at the Landau cutoff. The Langmuir turbulence originates at an electron density 0.241× the laser's critical density, where the crossed laser beams excite a “triad” mode—a common forward LW plus a pair of backward LWs. Remnants of this “triad” evolve in k-space and dominate the time-averaged energy spectrum. At times exceeding 10 ps, the excited Langmuir turbulence spreads toward lower densities. Comparisons of RPIC simulations with the extended Zakharov model are presented in appropriate regimes, and the necessary requirements for the validity of a quasi-linear Zakharov model (where the spatially averaged electron-velocity distribution is evolved) are verified by RPIC simulation results.

Statistical modeling of the point spread function for imaging through turbulence

We use a rigorous Markov approximation-based propagation model to calculate statistical properties of the instantaneous turbulent point spread function (PSF) for weak and strong turbulence conditions. Long-exposure PSF is well-known, and is currently widely used for estimates of optical system performance and simulation of the image distortions caused by turbulence. We discuss some peculiarities of the long-exposure PSF that are related to specifics of propagation in turbulence, which are often overlooked in the literature. Models for the short-exposure PSF have been used since the mid-1960s, and were the subject of some recent publications. We review a recently published model, and present sample calculations of the short-exposure PSF. Based on the available results of the optical propagation theory, we calculate variances of power fluctuations in the instantaneous PSF and the Strehl ratio, and covariance of the total power and the Strehl ratio. Analysis of the calculation results shows that for the most practical situations, the random Strehl ratio is a product of two uncorrelated, random variables-power and axial directivity. This information enables modeling of the instantaneous PSF with random width and height.

Hybrid LES — RANS of Complex Geometry Jets

Large eddy simulation (LES) type studies are made of a realistic geometry coaxial nozzle with a pylon. For the LES, since the solver being used tends towards having dissipative qualities, the subgrid scale (SGS) model is omitted, giving Numerical LES (NLES). To overcome near wall streak resolution problems a near wall RANS (Reynolds averaged Navier Stokes) model is used giving a hybrid NLES-RANS approach. The pylon is shown to influence the flow development, having a significant impact on peak turbulence levels and spreading rates. The results show that real geometry effects are influential and should be taken into account when moving towards real engine simulations. If their effects are ignored then, based on the studies here, key turbulence parameters will have significant error.

Turbulence propagation in heat flux-driven plasmas: implications for temperature profile structure

Turbulence propagation and temperature profile evolution are studied in heat flux-driven plasmas. A simple model consisting of coupled non-linear reaction–diffusion equations for both turbulence and heat transport is proposed to elucidate several aspects of apparent non-local profile dynamics. Self-consistent E × B shear feedback on turbulence intensity growth and transport is also included in the model. Temperature profile evolution is studied in the presence of an intensity pulse propagating inwards but also interacting with an outward propagating heat pulse. It is found that as the heat flux Q increases, the intensity pulse speed first grows as and then decays as 1/Q, while the heat pulse speed finally saturates at the level given by neoclassical transport. Intensity pulse propagation can be effectively saturated at or above a critical heat flux, so that the formation of an internal transport barrier (ITB) can be triggered. This suggests that the ITB location is ultimately determined by both heat flux and edge turbulence conditions, and thus the ITB inhibits both the inward turbulence propagation and the outward turbulent heat transport. As a test of turbulence spreading dynamics, the intensity pulse propagation through gaps in turbulence excitation and its implications for profile response to off-axis heat deposition are also investigated. It is shown that the profile resilience phenomena can be recovered by taking into account intensity pulse propagation.

Influence of sidewalls on width effects of upward flame spread

A previous study has reported width effects for turbulent diffusion upward flame spread on thermally thick materials with sidewalls. However, sidewalls are not realistic. The present study has revisited this topic by performing experiments without sidewalls using 9 mm thick and 1000 mm tall PMMA slabs with widths of 100, 200, 300, 500 and 700 mm and by providing a hypothesis of the sidewall effects. Experimental data have revealed that the width effects still exist when sidewalls are absent. Flame heights and spread rates were higher for wider flames, although heat feedback to the fuel did not vary much with flame width. Compared to flames without sidewalls, the existence of sidewalls lengthened flame heights and generally reduced heat feedback along the central lines of the flames, resulting in higher flame spread rates for narrower flames and lower flame spread rates for wider flames. In addition, the absence of sidewalls enhanced the delivery of pyrolyzate towards the central line of the flames throughout the whole flame width.

Laminar Superlayer at the Turbulence Boundary

In this Letter we present results from particle tracking velocimetry and direct numerical simulation that are congruent with the existence of a laminar superlayer, as proposed in the pioneering work of Corrsin and Kistler (NACA, Technical Report No. 1244, 1955). We find that the local superlayer velocity is dominated by a viscous component and its magnitude is comparable to the characteristic velocity of the smallest scales of motion. This slow viscous process involves a large surface area so that the global rate of turbulence spreading is set by the largest scales of motion. These findings are important for a better understanding of mixing of mass and momentum in a variety of flows where thin layers of shear exist. Examples are boundary layers, clouds, planetary atmospheres, and oceans.

Turbulence intensity pulse propagation with self-consistent nonlinear noise

A model of turbulence intensity spreading with self-consistent nonlinear noise is derived systematically for the simple dynamical model of resistivity gradient driven turbulence. Local effective drive, thermal conduction damping, nonlinear coupling, and spatial scattering effects are included. As a consequence of nonlinear mode coupling processes (i.e., triad mode interactions), turbulence energy can be spatially scattered, leading to turbulence propagation and spreading. However, the range of any nonlinear mode interactions of the background with a test mode is restricted to within a few mode scale widths from the test mode rational surface. The speed of a turbulent spreading front is calculated. This front speed is effectively constant on macroscopic scales. We show that the effect of self-consistent nonlinear noise on the intensity front speed is modest, as a consequence of the ordering Δc<Lf, where Δc is the turbulence correlation length and Lf is the scale length of the front’s leading edge. The implications of these results for turbulence spreading models and the important differences between self-consistent mode coupling noise and ad hoc external noise are discussed. The broader implications of these results for turbulence front propagation are identified and explained.

Solar wind turbulence and shear: A superposed‐epoch analysis of corotating interaction regions at 1 AU

A superposed‐epoch analysis of ACE and OMNI2 measurements is performed on 27 corotating interaction regions (CIRs) in 2003–2008, with the zero epoch taken to be the stream interface as determined by the maximum of the plasma vorticity. When the measurements are rotated into the local‐Parker‐spiral coordinate system, the shear is seen to be abrupt. Converging flows are seen; about half of the CIRs show a layer of divergent rebound flow away from the stream interface. Analysis of the turbulence across the CIRs is performed. When possible, the effects of discontinuities are removed. Fluctuation amplitudes, the Alfvenicity, and the level of Alfvenic correlations all vary smoothly across the CIR. The Alfven ratio exhibits a decrease at the shear zone of the stream interface. Fourier analysis of subintervals is performed, and the results are superposed averaged as an ensemble of realizations. The spectral slopes of the velocity, magnetic field, and total energy vary smoothly across the CIR. The total‐energy spectral index is ∼3/2 in the slow and fast wind and in the CIRs. Fourier analysis of Elsasser fluctuations shows a smooth transition across the CIR from an inward‐outward balance in the slow wind to an outward dominance in the fast wind. Spreading of turbulence away from the region where it is produced is limited to ∼106 km. A number of signatures of turbulence driving at the shear zone are sought (entropy change, turbulence amplitude, Alfvenicity, spectral slopes, and in‐out nature): none show evidence of driving of turbulence by shear.

The nonlinear coupling between gyroradius scale turbulence and mesoscale magnetic islands in fusion plasmas

The interaction between small scale turbulence (of the order of the ion Larmor radius) and mesoscale magnetic islands is investigated within the gyrokinetic framework. Turbulence, driven by background temperature and density gradients, over nonlinear mode coupling, pumps energy into long wavelength modes, and can result in an electrostatic vortex mode that coincides with the magnetic island. The strength of the vortex is strongly enhanced by the modified plasma flow response connected with the change in topology, and the transport it generates can compete with the parallel motion along the perturbed magnetic field. Despite the stabilizing effect of sheared plasma flows in and around the island, the net effect of the island is a degradation of the confinement. When density and temperature gradients inside the island are below the threshold for turbulence generation, turbulent fluctuations still persist through turbulence convection and spreading. The latter mechanisms then generate a finite transport flux and, consequently, a finite pressure gradient in the island. A finite radial temperature gradient inside the island is also shown to persist due to the trapped particles, which do not move along the field around the island. In the low collisionality regime, the finite gradient in the trapped population leads to the generation of a bootstrap current, which reduces the neoclassical drive.

Role of the geodesic acoustic mode shearing feedback loop in transport bifurcations and turbulence spreading

A theory of the effect of the geodesic acoustic mode (GAM) on turbulence is presented. Two synergistic issues are elucidated: namely, the physics of the zonal flow modulation and its role in the L-H transition, and the role of the GAM wave group propagation in turbulence spreading. Using a wavekinetic modulational analysis, the response of the turbulence intensity field to the GAM is calculated. This analysis differs from previous studies of zero-frequency zonal flows since it accounts for resonance between the drift wave group speed and the GAM strain field, which induces secularity. This mechanism is referred to as secular stochastic shearing. Finite real frequency and radial group velocity are intrinsic to the GAM, so its propagation can induce nonlocal phenomena at the edge and pedestal regions. To understand the effect of the GAM on turbulence and transition dynamics, a predator-prey model incorporating the dynamics of both turbulence and the GAMs is constructed and analyzed for stability around fixed points. Three possible states are identified, namely, an L-modelike stationary state, a reduced turbulence state, and a GAM limit-cycle state. The system is attracted to the state with the minimum turbulence level.

Gyrokinetic Study of the Local Entropy Dynamics in Turbulent Plasmas with Zonal Flow

An entropy balance equation that maintains the dynamics in the radial direction is derived to study the role of zonal flows in turbulent transport. The equation describes the dynamics not only of the entropy density production related to zonal flow and local heat flux, but also of entropy density convection. We investigated these spatio-temporal dynamics of entropy in ion temperature gradient driven turbulence based on a global gyrokinetic Vlasov simulations in a slab geometry. The contribution of zonal flow to entropy production is observed to be small in the strong instability case, whereas the zonal flow energy is sufficiently large. We also found that the entropy density with n = 2 in the Hermite polynomial expansion in velocity space plays an important role in convecting the entropy density, causing turbulent spreading.

Properties of microturbulence in toroidal plasmas with reversed magnetic shear

Electrostatic drift wave turbulence in tokamak plasmas with reversed magnetic shear is studied using global gyrokinetic particle simulations. The linear eigenmode of the ion temperature gradient (ITG) instability exhibits a mode gap around the minimum safety factor (qmin) region, particularly when qmin is an integer, due to the rarefaction of rational surfaces. The collisionless trapped electron mode (CTEM) instability is suppressed in the negative-shear region due to the reversal of the toroidal precessional drift of trapped electrons. However, after nonlinear saturation, the ITG gap is filled up by the turbulence spreading and the CTEM fluctuation propagates into the stable negative-shear region. The steady state turbulence occupies the whole volume without any identifiable gap or coherent structures of the heat conductivity, perturbed temperature, or zonal flows in the qmin location or the reversed shear region. Our finding indicates that the electrostatic drift wave turbulence itself does not support either linear or nonlinear mechanism for the formation of internal transport barriers in the reversed magnetic shear when qmin crossing an integer.

Experiments on the spreading of shear-free turbulence under the influence of confinement and rotation

From Lie-group (symmetry) analysis of the multi-point correlation equation Oberlack and Gunther (Fluid Dyn Res 33:453-476, 2003) found three different solutions for the behavior of shear-free turbulence: (i) a diffusion like solution, in which turbulence diffuses freely into the adjacent calm fluid, (ii) a deceleration wave like solution when there is an upper bound for the integral length scale and (iii) a finite domain solution for the case when rotation is applied to the system. This paper deals with the experimental validation of the theory. We use an oscillating grid to generate turbulence in a water tank and Particle Image Velocimetry (PIV) to determine the two-dimensional velocity and out-of-plane vorticity components. The whole setup is placed on a rotating table. After the forcing is initiated, a turbulent layer develops which is separated from the initially irrotational fluid by a sharp interface, the so-called turbulent/non-turbulent interface (TNTI). The turbulent region grows in time through entrainment of surrounding fluid. We measure the propagation of the TNTI and find quantitative agreement with the predicted spreading laws for case one and two. For case three (system rotation), we observe that there is a sharp transition between a 3D turbulent flow close to the source of energy and a more 2D-like wavy flow further away. We measure that the separation depth becomes constant and in this sense, we confirm the theoretical finite domain solution.

Radial Spreading of Drift-Wave–Zonal-Flow Turbulence via Soliton Formation

The self-consistent spatiotemporal evolution of a drift-wave (DW) radial envelope and a zonal-flow (ZF) amplitude is investigated in a slab model. The stationary solution of the coupled partial differential equations in a simple limit yields the formation of DW-ZF soliton structures, which propagate radially with speed depending on the envelope peak amplitude. Additional interesting physics, e.g., the generation, destruction, collision, and reflection of solitons, as well as turbulence bursting can also be observed due to the effects of linear growth or damping, dissipation, equilibrium nonuniformities and soliton dynamics. The propagation of soliton causes significant radial spreading of DW turbulence and therefore can affect transport scaling with the system size by broadening of the turbulent region. The correspondence of the present analysis with the description of DW-ZF interactions in toroidal geometry is also discussed.

Advanced simulation of electron heat transport in fusion plasmas

Electron transport in burning plasmas is more important since fusion products first heat electrons. First-principles simulations of electron turbulence are much more challenging due to the multi-scale dynamics of the electron turbulence, and have been made possible by close collaborations between plasma physicists and computational scientists. The GTC simulations of collisionless trapped electron mode (CTEM) turbulence show that the electron heat transport exhibits a gradual transition from Bohm to gyroBohm scaling when the device size is increased. The deviation from the gyroBohm scaling can be induced by large turbulence eddies, turbulence spreading, and non-diffusive transport processes. Analysis of radial correlation function shows that CTEM turbulence eddies are predominantly microscopic but with a significant tail in the mesoscale. A comprehensive analysis of kinetic and fluid time scales shows that zonal flow shearing is the dominant decorrelation mechanism. The mesoscale eddies result from a dynamical process of linear streamers breaking by zonal flows and merging of microscopic eddies. The radial profile of the electron heat conductivity only follows the profile of fluctuation intensity on a global scale, whereas the ion transport tracks more sensitively the local fluctuation intensity. This suggests the existence of a nondiffusive component in the electron heat flux, which arises from the ballistic radial E X B drift of trapped electrons due to a combination of the presence of mesoscale eddies and the weak de-tuning of the toroidal precessional resonance that drives the CTEM instability. On the other hand, the ion radial excursion is not affected by the mesoscale eddies due to a parallel decorrelation, which is not operational for the trapped electrons because of a bounce averaging process associated with the electron fast motion along magnetic field lines. The presence of the nondiffusive component raises question on the applicability of the usual quasilinear theory for the CTEM electron transport. This is in contrast to the good agreement between the quasilinear transport theory and simulation results of the electron heat transport in electron temperature gradient (ETG) turbulence, which is regulated by a wave-particle decorrelation. Therefore, the transport in the CTEM turbulence is a fluid-like eddy mixing process even though the linear CTEM instability is driven by a kinetic resonance. In contrast, a kinetic process dominates the transport in the ETG turbulence, which is characterized by macroscopic streamers.

Momentum theorems and the structure of atmospheric jets and zonal flows in plasmas

The inviscid invariance of potential vorticity is used to derive momentum balance relations for zonal flows in drift wave turbulence. The relations are constructed by exploiting potential enstrophy balance and the Taylor identity, and link flow momentum to turbulence pseudomomentum, along with the driving flux, the dissipation and turbulence spreading. Applications to atmospheric jets and to zonal flows in plasmas are discussed.

Decay of Turbulence Generated by Spin-Down to Rest in Superfluid 4He

We report on the extension of the experiments (P. M. Walmsley et al., Phys. Rev. Lett. 99, 265302 (2007)) on the decay of quasiclassical turbulence generated by an impulsive spin-down from angular velocity Omega to rest of superfluid 4He in a cubic container at temperatures 0.15 K - 1.6 K. The density of quantized vortex lines L is measured by scattering negative ions. Following the spin-down, the maximal density of vortices is observed after time t ~ 10 Omega^-1. By observing the propagation of ions along the axis of the initial rotation, the transient dynamics of the turbulence spreading from the perimeter of the container into its central region is investigated. Nearly homogeneous turbulence develops after time t ~ 100 Omega^-1 and decays as L proportional to t^(-3/2). The effective kinematic viscosity in T=0 limit is nu = 0.003 kappa, where kappa=10^-3 cm^2 / s is the circulation quantum.