Dynamics of zonal flows in helical systems

A theory for describing collisionless long-time behavior of zonal flows in helical systems is presented and its validity is verified by gyrokinetic-Vlasov simulation. It is shown that, under the influence of particles trapped in helical ripples, the response of zonal flows to a given source becomes weaker for lower radial wave numbers and deeper helical ripples while a high-level zonal-flow response, which is not affected by helical-ripple-trapped particles, can be maintained for a longer time by reducing their bounce-averaged radial drift velocity. This implies a possibility that helical configurations optimized for reducing neoclassical ripple transport can simultaneously enhance zonal flows which lower anomalous transport.     

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基于Hasegawa-Wakatani湍流模型,数值模拟了托卡马克边缘等离子体中漂移波湍流和相关的反常粒子输运.从等离子体动量守恒方程出发导出了不采用常规的布辛涅斯克近似的带状流方程,论证了大振幅密度扰动和湍性粒子流对激发带状流的贡献可等效地对应于低阶负粘滞阻尼效果.数值模拟表明,大振幅密度扰动的非线性大大增强了带状流饱和振幅,从而有效抑制了湍性粒子输运.研究结果阐明了托卡马克边缘等离子体大振幅密度扰动的非线性对驱动等离子体旋转、动量输运和带状流的重要性.     

托卡马克边缘湍流中带状流的负粘滞阻尼

基于Hasegawa-Wakatani湍流模型,数值模拟了托卡马克边缘等离子体中漂移波湍流和相关的反常粒子输运。从等离子体动量守恒方程出发导出了不采用常规的布辛涅斯克近似的带状流方程,论证了大振幅密度扰动和湍性粒子流对激发带状流的贡献可等效地对应于低阶负粘滞阻尼效果。数值模拟表明,大振幅密度扰动的非线性大大增强了带状流饱和振幅,从而有效抑制了湍性粒子输运。研究结果阐明了托卡马克边缘等离子体大振幅密度扰动的非线性对驱动等离子体旋转、动量输运和带状流的重要性。     

In search of the elusive zonal flow using cross-bicoherence analysis

We show that the modulational instability growth rate of zonal flows is determined directly from the quasilinear wave kinetic equation. We also demonstrate the relation between zonal-flow growth and the cross bispectrum of the high-frequency drift-wave-driven Reynolds stress and the low-frequency plasma potential by explicit calculation. Experimental measurements of the spatiotemporal evolution of the spectrum integrated bicoherence at the L-->H transition near the edge shear layer indicate a modification in the nonlinear phase coupling, which might be linked to the generation of sheared ExB flows.     

Nonlinear damping of plasma zonal flows excited by inverse spectral transfer

Plasma zonal-flow excitation and saturation in fluid electron-drift-wave turbulence are studied spectrally. The zonal flow is a spectral condensation onto the zero-frequency linear-wave structure. In the representation diagonalizing the wave coupling that dominates interactions at long wavelengths, nonlinear triad interactions involving zero-frequency waves are greatly enhanced. Zonal modes are excited on both unstable and purely stable eigenmode branches. Coupling to the latter introduces robust, finite amplitude-induced damping of zonal flows, providing saturation.     

Intrinsic ambipolarity and rotation in stellarators

It is shown that collisional plasma transport is intrinsically ambipolar only in quasiaxisymmetric or quasihelically symmetric magnetic configurations. Only in such fields can the plasma rotate freely, and then only in the direction of quasisymmetry. In a non-quasi-symmetric magnetic field, the average radial electric field is determined by parallel viscosity, which in turn is usually governed by collisional processes. Locally, the radial electric field may be affected by turbulent Reynolds stress producing zonal flows, but on a radial average taken over several ion gyroradii, it is determined by parallel viscosity, at least if the turbulence is electrostatic and obeys the conventional gyrokinetic orderings. This differs from the situation in a tokamak, where there is no flow damping by parallel viscosity in the symmetry direction and the turbulent Reynolds stress may affect the global radial electric field.     

Successive bifurcations in a simple model of atmospheric zonal-flow vacillation

Low-frequency variability of the atmospheric flow in the Southern Hemisphere is dominated by irregular changes in the latitude and intensity of the mid-latitude eastward jet about its climatological mean state. This phenomenon, known as atmospheric zonal-flow vacillation, is characterized by the existence of two persistent states of the zonal (i.e., east-west oriented) jet and irregular transitions between them. Nonlinear interactions between the mean flow and the waves play a key role in the dynamics of this vacillation. In the present study, we develop a low-order, deterministic model for the nonlinear dynamics of atmospheric zonal-flow vacillation. Multiple equilibria arise in this model's zonal-mean flow, that is, in the longitudinal flow averaged along a given latitude circle. These equilibria bear a strong resemblance to the two persistent flow regimes found in Southern Hemisphere observations. The two equilibrium states are maintained by wave forcing against surface drag, as in the observations. Successive bifurcations to periodic and chaotic zonal-mean flow regimes occur as the model's dissipation parameter is reduced. (c) 2002 American Institute of Physics.     

Signature of turbulent zonal flows observed in the DIII-D tokamak

The spectrum of turbulent density fluctuations at long poloidal wavelengths in the edge plasma of the DIII-D tokamak peaks at nonzero radial wave number. The associated electric-potential fluctuations cause sheared E x B flows primarily in the poloidal direction. These zonal flows have been predicted by theory and are believed to regulate the overall level of turbulence and anomalous transport. This study provides the first indirect experimental identification of zonal flows.     

Dimits shift in realistic gyrokinetic plasma-turbulence simulations

In simulations of turbulent plasma transport due to long wavelength (k perpendicular rhoi < or = 1) electrostatic drift-type instabilities, we find a persistent nonlinear up-shift of the effective threshold. Next-generation tokamaks will likely benefit from the higher effective threshold for turbulent transport, and transport models should incorporate suitable corrections to linear thresholds. The gyrokinetic simulations reported here are more realistic than previous reports of a Dimits shift because they include nonadiabatic electron dynamics, strong collisional damping of zonal flows, and finite electron and ion collisionality together with realistic shaped magnetic geometry. Reversing previously reported results based on idealized adiabatic electrons, we find that increasing collisionality reduces the heat flux because collisionality reduces the nonadiabatic electron microinstability drive.     

用非正交曲线坐标系数值计算航空发动机加力燃烧室无化学反应的湍流流场

本文采用非正交曲线坐标系下非交错网格的SIMPLE方法对航空发动机加力燃烧室无化学反应的湍流流场进行了数值计算，湍流模型采用k-ε双方程模型．差分网格采用分区方法生成，计算时对整个流场进行分区迭代直至得到收敛结果．加力燃烧室湍流流场数值计算结果合理．     

Nondiffusive transport in tokamaks: three-dimensional structure of bursts and the role of zonal flows

Large scale transport events are studied in simulations of resistive ballooning turbulence in a tokamak plasma. The spatial structure of the turbulent flux is analyzed, indicating radially elongated structures (streamers) at the low field side which are distorted by magnetic shear at different toroidal positions. The interplay between self-generated zonal flows and transport events is investigated, resulting in significant modifications of the frequency and the amplitude of bursts. The propagation of bursts is studied in the presence of a transport barrier generated by a strong shear flow.     

Generation and stability of zonal flows in ion-temperature-gradient mode turbulence

We address the mechanisms underlying zonal flow generation and stability in turbulent systems driven by the electrostatic ion-temperature-gradient (ITG) mode. In the case of zonal flow stability, we show the poloidal flows typical of numerical simulations become unstable when they exceed a critical level. Near marginal stability of the linear ITG mode, the system can generate zonal flows that are sufficiently weak to remain stable and sufficiently strong to suppress the linear ITG mode. This stable region corresponds to the parameter regime of the nonlinear Dimits up-shift.     

Nonlinear generation of zonal flows by ion-acoustic waves in a uniform magnetoplasma

It is shown that large-scale zonal flows (ZFs) can be excited by Reynolds stress of nonlinearly interacting random phase ion-acoustic waves (EIAWs) in a uniform magnetoplasma. Since ZFs are associated with poloidal sheared flows, they can tear apart short scale EIAW turbulence eddies, and hence contribute to the reduction of the cross-field turbulent transport in a magnetized plasma.     

Turbulent saturation of tokamak-core zonal flows

Current theories of zonal flow dynamics focus on the transport of poloidal momentum. Different from a cylinder, stationary poloidal flows in a tokamak are accompanied by (possibly kinetic) flows along the magnetic field, which maintain incompressibility, and comprise the major part of the flow energy. In numerical turbulence studies, the flows saturate by the turbulent diffusion of the parallel flow, whereas the poloidal momentum transport continues to strongly drive the flows.     

Predictions of Conjugate Heat Transfer in Turbulent Channel Flow Using Advanced Wall-Modeled Large Eddy Simulation Techniques

In this paper, advanced wall-modeled large eddy simulation (LES) techniques are used to predict conjugate heat transfer processes in turbulent channel flow. Thereby, the thermal energy transfer process involves an interaction of conduction within a solid body and convection from the solid surface by fluid motion. The approaches comprise a two-layer RANS–LES approach (zonal LES), a hybrid RANS–LES representative, the so-called improved delayed detached eddy simulation method (IDDES) and a non-equilibrium wall function model (WFLES), respectively. The results obtained are evaluated in comparison with direct numerical simulation (DNS) data and wall-resolved LES including thermal cases of large Reynolds numbers where DNS data are not available in the literature. It turns out that zonal LES, IDDES and WFLES are able to predict heat and fluid flow statistics along with wall shear stresses and Nusselt numbers accurately and that are physically consistent. Furthermore, it is found that IDDES, WFLES and zonal LES exhibit significantly lower computational costs than wall-resolved LES. Since IDDES and especially zonal LES require considerable extra work to generate numerical grids, this study indicates in particular that WFLES offers a promising near-wall modeling strategy for LES of conjugated heat transfer problems. Finally, an entropy generation analysis using the various models showed that the viscous entropy production is zero inside the solid region, peaks at the solid–fluid interface and decreases rapidly with increasing wall distance within the fluid region. Except inside the solid region, where steep temperature gradients lead to high (thermal) entropy generation rates, a similar behavior is monitored for the entropy generation by heat transfer process.     

Direct measurement of poloidal long-wavelength E x B flows in the HT-7 tokamak

The poloidal long-wavelength E x B time-varying flows were directly measured using a forked Langmuir probe in the HT-7 tokamak. Low-frequency (<10 kHz) E x B flows were observed at the plasma edge, which possess many of the characteristics of zonal flows, including a poloidal long-wavelength (k(theta)rho(i) approximately 0) and narrow radial extent (k(r)rho(i) approximately 0.1). The cross bicoherence of turbulent Reynolds stress indicates the existence of nonlinear three-wave coupling processes and the generation of low-frequency E x B flows. The estimated flow-shearing rate is of the same order of magnitude as the turbulence decorrelation rate and may thus regulate the fluctuation level and thereby the turbulence-driven transport.     

Consistent theory of turbulent transport in two-dimensional magnetohydrodynamics

A theory of turbulent transport is presented in two-dimensional magnetohydrodynamics with background shear and magnetic fields. We provide theoretical predictions for the transport of magnetic flux, momentum, and particles and turbulent intensities, which show stronger reduction compared with the hydrodynamic case, with different dependences on shearing rate, magnetic field, and values of viscosity, Ohmic diffusion, and particle diffusivity. In particular, particle transport is more severely suppressed than momentum transport, effectively leading to a more efficient momentum transport. The role of magnetic fields in quenching transport without altering the amplitude of flow velocity and in inhibiting the generation of shear flows is elucidated. Implications of the results are discussed.     

Large-eddy simulation of a bluff-body stabilised turbulent premixed flame using the transported flame surface density approach

A premixed propane–air flame stabilised on a triangular bluff body in a model jet-engine afterburner configuration is investigated using large-eddy simulation (LES). The reaction rate source term for turbulent premixed combustion is closed using the transported flame surface density (TFSD) model. In this approach, there is no need to assume local equilibrium between the generation and destruction of subgrid FSD, as commonly done in simple algebraic closure models. Instead, the key processes that create and destroy FSD are accounted for explicitly. This allows the model to capture large-scale unsteady flame propagation in the presence of combustion instabilities, or in situations where the flame encounters progressive wrinkling with time. In this study, comprehensive validation of the numerical method is carried out. For the non-reacting flow, good agreement for both the time-averaged and root-mean-square velocity fields are obtained, and the Karman type vortex shedding behaviour seen in the experiment is well represented. For the reacting flow, two mesh configurations are used to investigate the sensitivity of the LES results to the numerical resolution. Profiles for the velocity and temperature fields exhibit good agreement with the experimental data for both the coarse and dense mesh. This demonstrates the capability of LES coupled with the TFSD approach in representing the highly unsteady premixed combustion observed in this configuration. The instantaneous flow pattern and turbulent flame behaviour are discussed, and the differences between the non-reacting and reacting flow are described through visualisation of vortical structures and their interaction with the flame. Lastly, the generation and destruction of FSD are evaluated by examining the individual terms in the FSD transport equation. Localised regions where straining, curvature and propagation are each dominant are observed, highlighting the importance of non-equilibrium effects of FSD generation and destruction in the model afterburner.     

Influence of the static Dynamic Ergodic Divertor on edge turbulence properties in TEXTOR

Systematic measurements on the edge turbulence and turbulent transport have been made by Langmuir probe arrays on TEXTOR under various static Dynamic Ergodic Divertor (DED) configurations. Common features are observed. With the DED, in the ergodic zone the local turbulent flux reverses sign from radially outwards to inwards. The turbulence properties are profoundly modified by energy redistribution in frequency spectra and suppression of large scale eddies. The fluctuation poloidal phase velocity changes direction from electron to ion diamagnetic drift, consistent with the observed reversal of the Er x B flow. In the laminar region, the turbulence is found to react to an observed reduced flow shear.     

Nonlinear dynamics of surface dust vortex and dust zonal flow systems

We present analytical and simulation studies of highly resolved dust fluid flows involving nonlinearly coupled incompressible surface dust vortex modes (SDVMs) and dust zonal flows (DZFs) in nonuniform unmagnetized dusty plasmas. For this purpose, we use the hydrodynamic equations for the dust fluid and Boltzmann distributed electrons and ions and obtain a set of equations that exhibit nonlinear couplings between the SDVMs and DZFs. The nonlinear equations are then used to investigate the parametric excitation of DZFs by the Reynolds stresses of the SDVMs. Large scale SDVMs emerge through nonlinear interactions with DZFs, and they suppress the dust particle transport across the density gradient. In contrast, DZFs possess short scale vortices with a higher turbulent transport. The relevance of our investigation into the role of coherent structures in a nonuniform dusty plasma is discussed.