Universal threshold of the transition to localized turbulence in shear flows

Experimental and numerical studies have shown similarities between localized turbulence in channel and pipe flows.By scaling analysis of a disturbed-flow model,this paper proposes a local Reynolds number Re M to characterize the threshold of transition triggered by finite-amplitude disturbances.The Re M represents the maximum contribution of the basic flow to the momentum ratio between the nonlinear convection and the viscous diffusion.The lower critical Re M observed in experiments of plane Poiseuille flow,pipe Poiseuille flow and plane Couette flow are all close to 323,indicating the uniformity of mechanism governing the transition to localized turbulence.

Direct and noisy transitions in a model shear flow

The transition to turbulence in flows where the laminar profile is linearly stable requires perturbations of finite amplitude. ＂Optimal＂ perturbations are distinguished as extrema of certain functionals, and different functionals give different optima. We here discuss the phase space structure of a 2D simplified model of the transition to turbulence and discuss optimal perturbations with respect to three criteria： energy of the initial condition, energy dissipation of the initial condition, and amplitude of noise in a stochastic transition. We find that the states triggering the transition are different in the three cases, but show the same scaling with Reynolds number.

Local Reynolds number and thresholds of transition in shear flows

Recent experimental and numerical investigations reveal that the onset of turbulence in plane-Poiseuille flow and planeCouette flow has some similar stages separated with different threshold Reynolds numbers.Based on these observations and the energy equation of a disturbed fluid element,a local Reynolds number Re L is derived to represent the maximum ratio of the energy supplement to the energy dissipation in a cross section.It is shown that along the sequence of transition stages,which include transient localized turbulence,"equilibrium" localized turbulence,spatially intermittent but temporally persistent turbulence and uniform turbulence,the corresponding thresholds of Re L for plane-Couette flow,Hagen-Poiseuille flow and plane-Poiseuille flow are consistent,indicating that the critical(threshold) states during the laminar-turbulent transition are determined by the local properties of the base flow and are independent of global features,such as flow geometries(pipe or channel) and types of driving forces(shear driving or pressure driving).

Laminar-to-Turbulence Transition Revealed Through a Reynolds Number Equivalence

Flow transition from laminar to turbulent mode (and vice versa)—that is, the initiation of turbulence—is one of the most important research subjects in the history of engineering. Even for pipe flow, predicting the onset of turbulence requires sophisticated instrumentation and/or direct numerical simulation, based on observing the instantaneous flow structure formation and evolution. In this work, a local Reynolds number equivalence c (ratio of local inertia effect to viscous effect) is seen to conform to the Universal Law of the Wall, where c = 1 represents a quantitative balance between the abovementioned two effects. This coincides with the wall layer thickness (y+= 1, where y+ is the dimensionless distance from the wall surface defined in the Universal Law of the Wall). It is found that the characteristic of how the local derivative of c against the local velocity changes with increasing velocity determines the onset of turbulence. For pipe flow, c - 25, and for plate flow, c - 151.5. These findings suggest that a certain combination of c and velocity (nonlinearity) can qualify the source of turbulence (i.e., generate turbulent energy). Similarly, a re-evaluation of the previous findings reveals that only the geometrically narrow domain can act locally as the source of turbulence, with the rest of the flow field largely being left for transporting and dissipating. This understanding will have an impact on the future large-scale modeling of turbulence.

Understanding L-H transition in tokamak fusion plasmas

This paper reviews the current state of understanding of the L-H transition phenomenon in tokamak plasmas with a focus on two central issues： （a） the mechanism for turbulence quick suppression at the L-H transition; （b） the mechanism for subsequent generation of sheared flow. We briefly review recent advances in the understanding of the fast suppression of edge turbulence across the L-H transition. We uncover a comprehensive physical picture of the L-H transition by piecing together a number of recent experimental observations and insights obtained from 1D and 2D simulation models. Different roles played by diamagnetic mean flow, neoclassical-driven mean flow, turbulence-driven mean flow, and turbulence-driven zonal flows are discussed and clarified. It is found that the L-H transition occurs spontaneously mediated by a shift in the radial wavenumber spectrum of edge turbulence, which provides a critical evidence for the theory of turbulence quench by the flow shear. Remaining questions and some key directions for future investigations are proposed.

A new model of the L–H transition and H-mode power threshold

In order to understand the mechanism of the confinement bifurcation and H-mode power threshold in magnetically confined plasma,a new dynamical model of the L-H transition based on edge instability phase transition（EIPT） has been developed.With the typical plasma parameters of the EAST tokamak,the self-consistent turbulence growth rate is analyzed using the simplest case of pressure-driven ballooning-type instability,which indicates that the L-H transition can be caused by the stabilization of the edge instability through EIPT.The weak E？×？B flow shear in L-mode is able to increase the ion inertia of the electrostatic motion by increasing the radial wave number of the tilted turbulence structures,which play an important role for accelerating the trigger process of EIPT rather than directly to suppress the turbulent transport.With the acceleration mechanism of E？×？B flow shear,fast L-H and H-L transitions are demonstrated under the control of the input heating power.Due to the simplified scrape-offlayer boundary condition applied,the ratio between the heating powers at the H-L and L-H transition respectively differs from the ratio by Nusselt number.The results of the modeling reveal a scaling of the power threshold of the L-H transition,P_（L-H）？∝？n^（0.76） B^（0.8） for deuterium plasma.It is found finite Larmor radius induces an isotope effect of the H-mode power threshold.

Dynamics of oscillatory plasma flows prior to the H-mode in the HL-2A tokamak

This paper discusses edge oscillatory plasma flows, geodesic acoustic mode （GAM） and limit cycle oscillations （LCOs）, which have been measured by Doppler reflectometry prior to the high confinement mode （H-mode） in the HL-2A tokamak. The complex relations between the flows and background turbulence have been analyzed. It was observed that the GAM and LCO coexist, and these two flows and turbulence have strong nonlinear interactions during the intermediate confinement phase （I-phase）. Dynamics of the shear flows and turbulence prior to the H-mode shows that the oscillatory flows quench the turbulence along with the increase of the mean E x B flow at the early stage of the I-phase, then the oscillatory flows are damped and the further increased mean flow takes over the role in turbulence suppression. The reduced turbulent transport results in the formation of a steep edge transport barrier. It suggests that the oscillatory flows can initiate the L-H transition through providing a positive feedback for the increase of the mean E × B flow strength.

槽流的亚临界转捩与局地湍流

在中低雷诺数时,处于线性稳定的槽道流若受到强扰动可发生亚临界转捩变为湍流。近年人们对该类转捩机理的研究取得重要进展。对于平板泊肃叶流,亚临界转捩之初是稀疏湍流态,其特征结构是远间隔的包含小尺度涡和高低速条带的大尺度的湍流带,可倾斜伸长。该阶段的湍流占比有上限但并非雷诺数的单值函数。随着雷诺数的增加转捩进入平衡局地湍流态,即存在统计定常态,其湍流占比是雷诺数单值函数,可由定向逾渗模型描述。进一步增加雷诺数,湍流带的分裂愈发频繁,最终流场会布满湍流带,在更高的雷诺数时变为均匀湍流。论文概述了为比拟亚临界转捩过程所提出的动力学模型,以及为定量表征管流、平板库艾特流和平板泊肃叶流转捩过程的相似性所提出的局地稳定性参数,并在最后对槽道流亚临界转捩研究的发展做了简要展望。

径向电场对等离子体约束的影响

讨论了由径向电场产生的剪切极向流对托卡马克中等离子体的约束的影响。采用考虑了剪切极向转动效应的新经典离子热输运系数模型，这种模型导致的热通量函数在相同的密度和温度下是多值的，将它用于电子与离子之间有碰撞的ＭＨＤ方程，数值结果显示了Ｈ模情形等离子体上边缘陡峭的离子温度梯度。

超声速喷流混合流场大涡模拟

以光学窗口外冷喷流为研究背景,采用大涡模拟方法对后台阶外形切向喷流混合流场进行了研究。数值方法基于隐式亚格子模型,采用高精度WENO格式进行空间离散,并通过超声速平面混合层流动对数值方法进行了考核验证。喷流混合流场计算模型与试验一致,来流和喷流马赫数分别为3.4和2.5。数值模拟清晰地捕捉到了流场波系以及混合剪切层、壁面边界层等典型流场结构,并精细预测了混合层发生失稳、转捩及发展为充分发展湍流的时空发展过程。数值模拟得到的湍流大尺度结构的位置和形态与实验图像一致。通过对瞬时流场、统计平均流场和脉动参数的分析,揭示了流场结构特征及其时空演化规律,并获得了流场密度脉动特性。