Transition to turbulence in a shear flow

We analyze the properties of a 19-dimensional Galerkin approximation to a parallel shear flow. The laminar flow with a sinusoidal shape is stable for all Reynolds numbers Re. For sufficiently large Re additional stationary flows occur; they are all unstable. The lifetimes of finite amplitude perturbations shows a fractal dependence on amplitude and Reynolds number. These findings are in accord with observations on plane Couette flow and suggest a universality of this transition scenario in shear flows.     

A minimal flow unit for the study of turbulence with passive scalars

The concept of a minimal flow unit (MFU) for the study of the basic physics of turbulent flows is introduced. The MFU is an initial vorticity configuration that consists of a few simple well-defined large-scale vortex structures. The form and position of these structures are chosen so that their interaction produces turbulence capturing many of the essential characteristics of isotropic homogeneous turbulence produced from random-phase initial conditions or that produced by continual random-phase forcing. The advantage of using the MFU is that the evolution of the vortex structures can be followed more clearly and the relationship between the evolving vortex structures and the various ranges in the energy spectrum can be more clearly defined. The addition of passive scalar fields to the MFU permits an investigation of passive scalar mixing that is relevant to the study of combustion. With a particular choice of the MFU, one that produces a trend to a finite-time singularity in the vorticity field, it is demonstrated that passive scalar distributed in the original large-scale vortices will develop intense gradients in the region where the vorticity is tending toward a singularity. In viscous flow, the evolution of the MFU clearly shows how the volume of the regions where originally well-separated passive scalars come into contact increases with increasing Reynolds number.     

Decay and growth laws in homogeneous shear turbulence

Homogeneous anisotropic turbulence has been widely studied in the past decades, both numerically and experimentally. Shear flows have received a particular attention because of the numerous physical phenomena they exhibit. In the present paper, both the decay and growth of anisotropy in homogeneous shear flows at high Reynolds numbers are revisited thanks to a recent eddy-damped quasi-normal Markovian closure adapted to homogeneous anisotropic turbulence. The emphasis is put on several aspects: an asymptotic model for the slow part of the pressure–strain tensor is derived for the return to isotropy process when mean velocity gradients are released. Then, a general decay law for purely anisotropic quantities in Batchelor turbulence is proposed. At last, a discussion is proposed to explain the scattering of global quantities obtained in DNS and experiments in sustained shear flows: the emphasis is put on the exponential growth rate of the kinetic energy and on the shear parameter.     

Statistics of velocity gradients in wall-bounded shear flow turbulence

The statistical properties of velocity gradients in a wall-bounded turbulent channel flow are discussed on the basis of three-dimensional direct numerical simulations. Our analysis is concentrated on the trend of the statistical properties of the local enstrophy and the energy dissipation rate with increasing distance from the wall. We detect a sensitive dependence of the largest amplitudes of both fields (which correspond with the tail of the distribution) on the spectral resolution. The probability density functions of each single field as well as their joint distribution vary significantly with increasing distance from the wall. The largest fluctuations of the velocity gradients are found in the logarithmic layer. This is in agreement with recent experiments which observe a bursting of hairpin vortex packets into the logarithmic region.     

Using symbolic computation to construct travelling wave solutions to nonlinear partial differential equations

Based upon the symbolic computation and the coupled projective Riccati equation, the tanh function method is further improved. As its applications, Wu－Zhang equation (which describes a (2+1)-dimensional dispersive long wave) and the (1+1)-dimensional dispersive long wave equation obtained from Wu－Zhang equation by scaling transformation and symmetry reduction are chosen to illustrate the validity of the proposed approach.     

Self-regulation of E x B flow shear via plasma turbulence

The momentum balance has been applied to the ExB flow in the edge region of a reversed field pinch (RFP) configuration. All terms, including those involving fluctuations, have been measured in stationary condition in the edge region of the Extrap-T2R RFP experiment. It is found that the component of the Reynolds stress driven by electrostatic fluctuations is the term playing the major role in driving the shear of the ExB flow to a value marginal for turbulent suppression, so that the results are in favor of a turbulence self-regulating mechanism underlying the momentum balance at the edge. Balancing the sheared flow driving and damping terms, the plasma viscosity is found anomalous and consistent with the diffusivity due to electrostatic turbulence.     

磁场剪切对离子温度梯度模带状流产生的影响

对离子温度梯度模湍流非线性流体方程进行了解耦处理,得到包含磁场剪切效应的带状流与漂移波相互作用的非线性动力学方程.采用调制不稳定性的四波相互作用模型,研究了磁场剪切对带状流产生的影响.研究表明,在k_//值较小的范围内,当|k_//|增加时,带状流的增长率也呈增加的趋势. 关键词： 托卡马克等离子体 离子温度梯度模湍流 带状流 磁场剪切     

Role of the zonal flow in multi-scale multi-mode turbulence with small-scale shear flow in tokamak plasmas

The structural characteristics of zonal flows and their roles in the nonlinear interaction of multi-scale multi-mode turbulence are investigated numerically via a self-consistent Landau-fluid model. The multi-mode turbulence here is composed of a shorter wavelength electromagnetic (EM) ion temperature gradient (ITG) mode and a Kelvin-Helmholtz (KH) instability with long wavelengths excited by externally imposed small-scale shear flows. For strong shear flow, a prominent periodic intermittency of fluctuation intensity except for dominant ITG component is revealed in turbulence evolution, which onset time depends on the ion temperature gradient and the shear flow amplitudes corresponding to different KH instabilities. It is identified that the intermittency phenomenon results from the zonal flow dynamics, which is mainly generated by the KH mode and back-reacts on it. It is demonstrated that the odd symmetric components of zonal flow (same symmetry as the external flow) make the radial parity of the KH mode alteration through adjusting the drift velocities at two sides of the resonant surface so that the KH mode becomes bursty first. Afterwards, the ITG intermittency follows due to nonlinear mode coupling. Parametric dependences of the features of the intermittency are elaborated. Finally, associated turbulent heat transport is evaluated.     

交变暨静态剪切流对湍流抑制的互斥性分析

把剪切流对湍流抑制的解析理论应用于同时包含静态剪切流和周期交变剪切流的情况。所得到的结果表明：当两者单独存在时对湍流有定量上大体相同的抑制效应;当两者同时存在时对湍流的抑制效应不仅不是简单的迭加,反而在很大的区域上呈现互相削弱的趋势,特别是这种互斥性在两种剪切流强度相等时为最大。这与Maeyama等人的数值模拟结果相符合-。采用的渐近理论平均法表明导致两种剪切流在抑制湍流上不对等是由交变剪切流与它所诱发的交变相对位移之间的耦合所造成。     

Dynamics of fully nonlinear drift wave-zonal flow turbulence system in plasmas

We present numerical simulations of fully nonlinear drift wave-zonal flow (DW-ZF) turbulence systems in a nonuniform magnetoplasma. In our model, the drift wave (DW) dynamics is pseudo-three-dimensional (pseudo-3D) and accounts for self-interactions among finite amplitude DWs and their coupling to the two-dimensional (2D) large amplitude zonal flows (ZFs). The dynamics of the 2D ZFs in the presence of the Reynolds stress of the pseudo-3D DWs is governed by the driven Euler equation. Numerical simulations of the fully nonlinear coupled DW-ZF equations reveal that short scale DW turbulence leads to nonlinear saturated dipolar vortices, whereas the ZF sets in spontaneously and is dominated by a monopolar vortex structure. The ZFs are found to suppress the cross-field turbulent particle transport. The present results provide a better model for understanding the coexistence of short and large scale coherent structures, as well as associated subdued cross-field particle transport in magnetically confined fusion plasmas.     

离子温度梯度模湍流的带状流最小自由度模型

在离子温度梯度模(ITG)湍流背景中,通过最小自由度模型中模耦合方式产生带状流,对此模型做了动力学稳定性分析及数值求解.并在此基础上初步探讨了湍流中漂移波与带状流的能量转移,以及雷诺协强与带状流的关系. 关键词： 等离子体 离子温度梯度模 湍流 带状流     

Nonequilibrium thermodynamics and the optimal path to turbulence in shear flows

We determine the initial condition on the laminar-turbulent boundary closest to the laminar state using nonlinear optimization for plane Couette flow. Resorting to the general evolution criterion of nonequilibrium systems we optimize the route to the statistically steady turbulent state, i.e., the state characterized by the largest entropy production. This is the first time information from the fully turbulent state is included in the optimization procedure. We demonstrate that the optimal initial condition is localized in space for realistic flow domains.     

非线性波方程求解的新方法

从Legendre椭圆积分和Jacobi椭圆函数的定义出发，得到了新的变换，并把它用于非线性演化方程的求解.用三个具体的例子，如非线性Klein-Gordon方程、Boussinesq方程和耦合的mKdV方程组，说明了具体的求解步骤.比较方便地得到非线性演化方程或方程组的新解析解，如周期解、孤子解等. 关键词： Jacobi椭圆函数 非线性方程 周期解 孤子解     

Homoclinic tangle on the edge of shear turbulence

Experiments and simulations lend mounting evidence for the edge state hypothesis on subcritical transition to turbulence, which asserts that simple states of fluid motion mediate between laminar and turbulent shear flow as their stable manifolds separate the two in state space. In this Letter we describe flows homoclinic to a time-periodic edge state that display the essential properties of turbulent bursting. During a burst, vortical structures and the associated energy dissipation are highly localized near the wall, in contrast with the familiar regeneration cycle.     

Transition to turbulence in particulate pipe flow

We investigate experimentally the influence of suspended particles on the transition to turbulence. The particles are monodisperse and neutrally buoyant with the liquid. The role of the particles on the transition depends upon both the pipe to particle diameter ratios and the concentration. For large pipe-to-particle diameter ratios the transition is delayed while it is lowered for small ratios. A scaling is proposed to collapse the departure from the critical Reynolds number for pure fluid as a function of concentration into a single master curve.     

Physical processes underlying the development of shear turbulence

A physical model of the development of turbulence in free shear flows is proposed. The model is based on the results of numerical simulations of turbulent flow development. The main ideas of the proposed theory of turbulence are stated as follows: the onset of turbulence begins with the formation of large vortices; spectral energy transfer involves both direct and inverse cascades; and the inertial range of the energy spectrum develops as a result of concurrent direct and inverse cascades. The dominant physical factors that determine the spectrum include Joukowski forces.     

切向流动作用下的胞晶定向生长机理研究

实时观测了切向流动作用下SCN-0.2%Salol透明合金的定向胞晶生长过程,研究了切向流动作用对胞晶间距调整的作用机理. 实验发现,切向流动使得胞晶阵列发生顺流偏转,并且稳态平均间距随流速的增高而减小. 分析表明,这主要是由于流动作用导致胞端失稳波长减小而引起. 施加切向流动使得胞晶间距的调整过程中的分裂机理多样化. 顶端分裂由均匀分岔转变为多枝分岔和不对称分岔;同时,胞晶迎流侧容易产生分枝,且分枝生长方向在流动作用下转变为与胞晶主干方向相同. 胞晶的淘汰机理由静态条件下的弱势生长胞晶被相邻两侧胞晶淘汰 关键词： 切向流动 定向胞晶生长 间距调整     

A procedure to construct exact solutions of nonlinear evolution equations

In this paper, we implemented the functional variable method for the exact solutions of the Zakharov?CKuznetsov-modified equal-width (ZK-MEW), the modified Benjamin?CBona?CMahony (mBBM) and the modified KdV?CKadomtsev?CPetviashvili (KdV?CKP) equations. By using this scheme, we found some exact solutions of the above-mentioned equations. The obtained solutions include solitary wave solutions, periodic wave solutions and combined formal solutions. The functional variable method presents a wider applicability for handling nonlinear wave equations.