W. D. McComb, S. R. Yoffe
From a critical review of Onsager's pioneering paper which was published in 1949 we conclude that his analysis was at odds with other workers in the field because instead of taking the infinite Reynolds number limit he simply set the viscosity equal to zero which is not the same thing.
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Using the unique capabilities of the Variable Density Turbulence Tunnel at the Max Planck Institute for Dynamics and Self-Organization, Göttingen, we report experimental result on classical grid turbulence that uncover fine, yet important details of the structure functions in the inertial range. This was made possible by measuring extremely long time series of up to $10^{10}$ samples of the turbulent fluctuating velocity, which corresponds to $\mathcal{O}\left(10^5\right)$ large eddy turnover times. These classical grid measurements were conducted in a well-controlled environment at a wide ran…
Reynolds number effect on the velocity increment skewness in isotropic turbulence
利用EDQNM模型计算了各向同性湍流的二阶和三阶纵向结构函数和波数谱，并与多重分形模型的结果进行了比较。在风洞实验中可获得的最高雷诺数$R_λ=2500$下，多重分形模型和EDQNM都对速度增量偏度的惯性范围标度给出幂律修正。对于EDQNM，这种校正是有限雷诺数效应，而对于多重分形形式主义，它是在任何高雷诺数下持续存在的不稳定性校正。此外，这两种方法产生的耗散和近耗散范围内的速度波动的二阶和三阶统计的现实行为。相似性和差异突出，特别是雷诺数的依赖性。
In this work we address the open problem of high Reynolds number limit in hydrodynamic turbulence, which we modify by considering a vanishing random (instead of deterministic) viscosity. In this formulation, a small-scale noise propagates to large scales in an inverse cascade, which can be described using qualitative arguments of the Kolmogorov-Obukhov theory. We conjecture that the limit of the resulting probability distribution exists as $\mathrm{Re} \to \infty$, and the limiting flow at finite time remains stochastic even if forcing, initial and boundary conditions are deterministic. This c…
The decay of Kadomtsev - Petviashvili lumps is considered for a few typical dissipations - Rayleigh dissipation, Reynolds dissipation, Landau damping, Chezy bottom friction, viscous dissipation in the laminar boundary layer, and radiative losses caused by large-scale dispersion. It is shown that the straight-line motion of lumps is unstable under the influence of dissipation. The lump trajectories are calculated for two most typical models of dissipation - the Rayleigh and Reynolds dissipations. A comparison of analytical results obtained within the framework of asymptotic theory with the dire…
Mach-number-dependent dissipative anomaly in isothermal compressible turbulence
该研究通过高分辨率直接数值模拟，发现等温可压缩湍流的耗散异常呈依赖马赫数的双分支特性，虽为耗散异常提供证据，但未明确其强弱属性。
We consider the evolution equations for the bulk viscous pressure, diffusion current and shear tensor derived within second-order relativistic dissipative hydrodynamics from kinetic theory. By matching the higher order moments directly to the dissipative quantities, all terms which are of second order in the Knudsen number Kn vanish, leaving only terms of order $\mathcal{O}(\textrm{Re}^{-1} \textrm{Kn})$ and $\mathcal{O}(\textrm{Re}^{-2})$ in the relaxation equations, where $\textrm{Re}^{-1}$ is the inverse Reynolds number. We therefore refer to this scheme as the Inverse-Reynolds-Dominance (I…
On the relative importance of second-order terms in relativistic dissipative fluid dynamics
在Denicol等人的研究中，Phys.Rev.D85，114047（2012）中，相对论耗散流体动力学的运动方程是从相对论玻尔兹曼方程导出的。这些方程包含大量的克努森数、雷诺数倒数或它们的乘积的二阶项。克努森数中的二阶项产生非双曲（因此是非因果）行为，在相对论耗散流体动力学的（数值）解中必须忽略。在上述参考文献中，在无质量玻尔兹曼气体的极限下，克努森数和雷诺数的倒数的乘积的数量级的项的系数已经被明确地计算。逆雷诺数中的二阶项来自玻尔兹曼方程中的碰撞项，在局部热力学平衡中偏离单粒子分布函数扩展到二阶时。在这项工作中，我们计算这些二阶项的无质量玻尔兹曼气体具有恒定的散射截面。因此，我们评估它们的相对重要性相比，这是克努森和逆雷诺数的产品的顺序的条款。
Critical Reynolds Number as a Topological Phase Transition in Adaptive Fractional Hydrodynamics
通过将分数阶拉普拉斯算子阶数提升为动态场并建立谱平衡条件，推导出临界雷诺数的解析表达式，将层流-湍流转变建模为耗散算子的拓扑变化。
Probing quantum and classical turbulence analogy through global bifurcations in a von Kármán liquid Helium experiment
我们报告测量的耗散在超流氦高雷诺数冯卡门流（SHREK）实验不同的强制条件下，通过一个制度的全球滞后分岔。我们的宏观测量表明经典流体和超流政权之间没有明显的差异，从而提供了相同的耗散异常和响应的不对称性的流体和超流政权的证据。在后一种情况下，对滞后周期随雷诺数变化的详细研究支持了这样的观点：（i）在这种封闭流动中，经典湍流分叉态的稳定性部分地受耗散尺度的控制，（ii）在这些温度（1.6K）下，正常和超流分量被锁定在耗散长度尺度之内。
When the intensity of turbulence is increased (by increasing the Reynolds number, e.g. by reducing the viscosity of the fluid), the rate of the dissipation of kinetic energy decreases but does not tend asymptotically to zero: it levels off to a non-zero constant as smaller and smaller vortical flow structures are generated. This fundamental property, called the dissipation anomaly, is sometimes referred to as the zeroth law of turbulence. The question of what happens in the limit of vanishing viscosity (purely hypothetical in classical fluids) acquires a particular physical significance in the…
The condition of linear instability for a converging cylindrical strong shock wave (SW) in an arbitrary viscous medium is obtained in the limit of a large stationary SW radius, when it is possible to consider the same Rankine-Hugoniot jump relations as for the plane SW. This condition of instability is substantially different from the condition of instability for the plane SW because a cylindrical SW does not have chiral symmetry in the direction of the SW velocity (from left to right or vice versa) as in the case of a plane SW. The exponential growth rate of perturbations for the converging c…
We consider the hydrodynamic regime of a 2+1 dimensions QFT with the parity anomaly. Beyond the known constraints from positivity of entropy production, we show that the anomaly inflow mechanism, from a corresponding bulk SPT phase, together with thermodynamic consistency of equilibrium partition functions, restricts the form of non-dissipative transport coefficients. This included the known form of quantised Hall conductivity, which is fixed to be $σ_{xy} = e^2/2h$, along with new constraints on other three non-dissipative parity-odd transport coefficients.
Direct Numerical Simulations of Low-$Rm$ MHD turbulence based on the least dissipative modes
本文提出了一种新的谱方法用于低磁雷诺数下磁流体动力学湍流的直接数值模拟。我们的方法的独创性是，而不是使用传统的基地的功能，它依赖于本征模的基础上的耗散运营商，这代表粘性和焦耳耗散。我们应用这个想法的简单情况下，一个周期域在空间的三个方向，在$\mathbf e_z$方向的均匀磁场。然后基仍然是傅立叶空间的子集，但是通过增长的线性衰减率$|λ|$（根据\emph{least dissipative modes}的\emph{i.e}）来排序。我们表明，因为在傅立叶空间中的恒定能量线倾向于遵循恒定$|λ|$的线，所以在强迫流中最小尺度$|λ^{\rm max}|$的标度可以使用这个单一参数表示，作为雷诺数的函数为$\sqrt{|λ^{\rm max}|}/(2πk_f)\simeq 0.5\Rey^{1/2}$，其中$k_f$是强迫波长，或者作为Grashof数$\Gr_f$的函数，其给出强迫的无量纲度量，作为$|λ^{\rm max}|^{1/2}/(2πk_f)\simeq 0.47\Gr_f^{0.20}$。还发现这种缩放与启发式缩放一致，并且我们能够将其数值量化为$k_\perp^{\rm max}/k_f\simeq 0.5 \Rey^{1/2}$和$k_z^{\rm max}/k_f\simeq 0.8k_f \Rey/Ha$。最后，我们表明，一组最少的耗散模式给出了一个相…
Non-local interactions in hydrodynamic turbulence at high Reynolds numbers: the slow emergence of scaling laws
我们分析了在2048^3个规则间隔点的网格上进行的强制不可压缩流体动力学模拟的数据，泰勒雷诺数为Re~1300。强迫是由泰勒-格林流，它与几个实验室实验中的流动有相似之处，计算在湍流稳定状态下运行了十个周转时间。在此雷诺数下，各向异性大尺度流动模式、惯性范围、瓶颈和耗散范围清晰可见，从而为研究自然界中出现的湍流提供了一个很好的测试案例。三元相互作用，局部的能量通量，和结构函数的速度增量计算。与运行在较低的雷诺数进行比较，并显示出出现的局部和非局部相互作用的相对振幅在谱空间的标度律。的Kolmogorov常数的缩放，以及速度增量的偏斜度和平坦度，以及执行，并与以前的实验结果是一致的。此外，在小尺度上与瓶颈的能量积累似乎发生在一个跨度的波数是独立的雷诺数，可能排除了惯性范围的解释it. Finally，不透明度指数似乎偏离标准模型在高Re，离开不透明度的解释一个悬而未决的问题。
Exact two-dimensionalization of rapidly rotating large-Reynolds-number flows
该研究严格证明强整体旋转下，大雷诺数三维旋转流动的二维解对竖直扰动稳定，长时间极限下呈二维特性，揭示了小Rossby数时系统趋向纯二维流的规律，挑战了波湍流理论在有界定常旋转湍流中的适用性。
Scaling and structural evolutions are contemplated in a new perspective for turbulent channel flows. The total integrated turbulence kinetic energy remains constant when normalized by the friction velocity squared, while the total dissipation increases linearly with respect to the Reynolds number. This serves as a global constraint on the turbulence structure. Motivated by the flux balances in the root turbulence variables, we also discover dissipative scaling for u2 and v2, respectively through its first and second gradients. This self-similarity allows for profile reconstructions at any Reyn…
We investigate aspects of low-magnetic-Reynolds-number flow between two parallel, perfectly insulating walls, in the presence of an imposed magnetic field parallel to the bounding walls. We find a functional basis to describe the flow, well adapted to the problem of finding the attractor dimension, and which is also used in subsequent direct numerical simulation of these flows. For given Reynolds and Hartmann numbers, we obtain an upper bound for the dimension of the attractor by means of known bounds on the nonlinear inertial term and this functional basis for the flow. Three distinct flow re…
Turbulence without inertia in quantum fluids
氦-II流体动力学的数值计算表明，超流涡的密集缠结在初始静止的正常流体中诱导出具有-2.2能谱标度指数和单位阶数的波动雷诺数的高度耗散的、复杂的旋涡流型（“湍流”）。在这种正常的流体流动中，来自超流涡的相互摩擦激励的影响和粘性应力的影响是相同量级的。结果表明，在以前的实验中，衰减，高雷诺数，量子湍流的动力学只能微弱地影响到量子化的旋涡。因此，它们的能谱将是（非常好的近似）经典的，纳维尔-斯托克斯型，正常流体成分的能谱。
Mesoscale particle-based simulations of flow in expansion-contraction microchannels at low Reynolds number
本文通过粒子基方法研究低雷诺数下微通道中流体流动，比较了DPD和MPCD模拟与系列解的准确性，发现其在多数情况下表现良好，但系列解在微通道长度短或振幅大时失效。
Large Eddy Simulations of Turbulent Pipe Flows At Moderate-To-High Reynolds Numbers
本文利用OpenFOAM中的WALE大涡模拟研究高雷诺数湍流管道流动，验证了WALE模型在低计算成本下与DNS高度一致，并给出了保证精度的网格分辨率条件。
Turbulence at Low Reynolds Numbers
本文证明湍流可在雷诺数约为1时存在，通过方向性偏置扰动将准二维电磁驱动流中的谱能量通量放大两个数量级以上，建立了二维Navier-Stokes湍流新状态，为微流控和低雷诺数生物系统提供了多尺度输运工程策略。
Spheres and fibres in turbulent flows at various Reynolds numbers
本研究通过浸入边界法模拟不同泰勒雷诺数和固体质量分数下湍流中有限尺寸球体与纤维的行为，揭示了两类颗粒对湍流强度、耗散、谱结构及涡旋的不同作用机制。
Data-driven low-dimensional model for the onset of turbulence in plane Couette flow
本研究用核分位数回归从直接数值模拟数据构建平面库埃特流低雷诺数湍流的低维模型，准确再现周期、混沌动力学及统计特性，并开发参数依赖模型重现分岔结构，验证了机器学习降阶建模的有效性。
A variable-coefficient model for decay of isotropic turbulence capturing effects of finite cascade time and Reynolds number
通过高保真数值模拟，研究各向同性湍流衰减中C_epsilon2系数的瞬时依赖性，提出一个考虑有限级联时间和雷诺数的变系数模型，准确预测宽雷诺数范围内的耗散和动能演化。
Dynamical relevance of periodic orbits under increasing Reynolds number and connections to inviscid dynamics
本文通过弧长延拓研究Kolmogorov流中相对周期轨道随雷诺数增加的动力学相关性，发现其迅速变得无关紧要，并与Euler方程解及点涡系统精确解相关联。
Exact two-dimensionalization of low-magnetic-Reynolds-number flows subject to a strong magnetic field
本研究针对强磁场下低磁雷诺数流动的二维化问题，分别在准静态近似和完整磁流体方程框架下证明了绝对二维化与线性二维化现象，为磁流体耗散反常性研究提供了理论支撑。
We report on a investigation of turbulent bubbly flows. Bubbles of a size larger than the dissipative scale, cannot be treated as point-wise inclusions, and generate important hydrodynamic fields in the carrier fluid when in motion. Furthermore, when the volume fraction of bubbles is large enough, the bubble motion may induce a collective agitation due to hydrodynamic interactions which display some turbulent-like features. We tackle this complex phenomenon numerically, performing direct numerical simulations (DNS) with a Volume-of-fluid (VOF) method. In the first part of the work, we perform …
Alfvén waves at low magnetic Reynolds number: Transitions between diffusion, dispersive Alfvén waves and nonlinear propagation
本研究在低磁雷诺数液态金属实验中通过交变电流激发阿尔文波，推导低Rm MHD近似的波动扩展形式识别出两种线性区域，经FLOWCUBE实验验证模型吻合度高，还观测到共振附近的非线性特征，为模拟天体和地球物理相关过程提供了实验基础。
Large/small eddy simulations: A posteriori analysis in high Reynolds number isotropic turbulence
本研究提出大/小涡模拟方法，用于高雷诺数各向同性湍流的后验分析，展示了其在计算效率和精度上的优势。
Passive scalars advected by three-dimensional Navier-Stokes turbulence exhibit a fundamental anomaly in odd-order moments because of the characteristic ramp-cliff structures, violating small-scale isotropy. We use data from direct numerical simulations with grid resolution of up to $8192^3$ at high Péclet numbers to understand this anomaly as the scalar diffusivity, $D$, diminishes, or as the Schmidt number, $Sc = ν/D$, increases; here $ν$ is the kinematic viscosity of the fluid. The microscale Reynolds number varies from 140 to 650 and $Sc$ varies from 1 to 512. A simple model for the ramp-cl…
Disentangling temperature and Reynolds number effects in quantum turbulence
本文基于HVBK模型推导逐尺度能量收支，提出有效雷诺数以解耦量子湍流中温度与雷诺数效应，并预测涡间距标度律，进而阐明间歇性变化源于雷诺数而非温度。
Aligned superhydrophobic surfaces with the same texture orientation reduce drag in the channel and generate secondary flows transverse to the direction of the applied pressure gradient. Here we show that a transverse shear can be easily generated by using superhydrophobic channels with misaligned textured surfaces. We propose a general theoretical approach to quantify this transverse flow by introducing the concept of an effective shear tensor. To illustrate its use, we present approximate theoretical solutions and Dissipative Particle Dynamics simulations for striped superhydrophobic channels…
In 1959, Batchelor predicted that the stationary statistics of passive scalars advected in fluids with small diffusivity $κ$ should display a $|k|^{-1}$ power spectrum along an inertial range contained in the viscous-convective range of the fluid model. This prediction has been extensively tested, both experimentally and numerically, and is a core prediction of passive scalar turbulence. In this article we provide a rigorous proof of a version of Batchelor's prediction in the $κ\to 0$ limit when the scalar is subjected to a spatially-smooth, white-in-time stochastic source and is advected by t…
Dissipation scaling in wind turbine wakes exposed to free-stream turbulence
本实验探究风力机尾流在不同强度自由流湍流下的湍动能耗散尺度，发现低/中等强度湍流下叶尖区域耗散呈特定尺度规律，高强度湍流下大尺度间歇性被抑制。
Whither the Zeroth Law of Turbulence?
针对湍流第零定律的反常行为，本文通过周期性边界条件方盒中不可压缩Navier-Stokes方程的直接数值模拟，发现该反常现象随雷诺数增大以绝对速度增量三阶矩标度的速率消失，指出无界湍流或无法维持第零定律。
We develop first-principles theory of relativistic fluid turbulence at high Reynolds and Péclet numbers. We follow an exact approach pioneered by Onsager, which we explain as a non-perturbative application of the principle of renormalization-group invariance. We obtain results very similar to those for non-relativistic turbulence, with hydrodynamic fields in the inertial-range described as distributional or "coarse-grained" solutions of the relativistic Euler equations. These solutions do not, however, satisfy the naive conservation-laws of smooth Euler solutions but are afflicted with dissipa…
Vortex topology in the lee of a 6:1 prolate spheroid
本文通过大涡模拟系统研究了6:1长椭球体绕流在多个雷诺数和攻角下的分离与尾流拓扑，归纳出原始涡、相干涡和回流尾流三类状态，并揭示了流动演化与载荷的关联。
Two-dimensional turbulent condensates without bottom drag
本文通过直接数值模拟研究无底阻尼下二维湍流大尺度凝聚态的稳态，发现临界雷诺数约为4.19，揭示了能量谱在不同雷诺数下从绝对平衡向幂律演化的规律，并阐明了强凝聚态偏离平衡动力学的机制。
Turbulent signals are known to exhibit burst-like activities, which affect the turbulence statistics at both large and small scales of the flow. In our study, we pursue this problem from the perspective of an event-based framework, where bursting events are studied across multiple scales in terms of both their size and duration. To illustrate our method and assess any dependence on the Reynolds number, we use two datasets - from the Melbourne wind tunnel and from SLTEST - an atmospheric surface layer experiment. We show that an index, namely the burstiness index, can be used successfully to de…
A defining feature of 3D hydrodynamic turbulence is that the rate of energy dissipation is bounded away from zero as viscosity is decreased (Reynolds number increased). This phenomenon - anomalous dissipation - is sometimes called the `zeroth law of turbulence' as it underpins many celebrated theoretical predictions. Another robust feature observed in turbulence is that velocity structure functions $S_p(\ell) :=\langle |δ_\ell u|^p\rangle$ exhibit persistent power-law scaling in the inertial range, namely $S_p(\ell) \sim |\ell|^{ζ_p}$ for exponents $ζ_p>0$ over an ever-increasing (with Reynold…
Scalar dissipation anomaly and scalar-gradient scaling in turbulence: A joint velocity-scalar multifractal view
通过理论分析和高达8192³网格的DNS数据，基于联合多重分形框架，揭示了标量耗散异常与标量梯度标度的普适规律，并预测了标量梯度高阶矩对Schmidt数的独立性。
Onsager's "Ideal Turbulence" Theory
本文回顾昂萨格理想湍流理论的发展，该理论以理想Euler方程弱解描述高雷诺数湍流，证实1/3 Hölder奇异性为反常耗散阈值，还拓展至壁面湍流应用，为大涡模拟提供新视角。
Universal constants and equations of turbulent motion
在1926年普朗特猜想的精神，湍流在高雷诺数，我们提出了一个类比与气体的动力学理论，与偶极子制成的准刚性和'打扮'涡流管作为无摩擦，不可压缩，但可变形的准粒子。它们的运动受局部应用的Helmholtz基本涡旋规则支配。接触相互作用或“碰撞”导致轨迹的随机散射或导致形成两个同样旋转的、基本上不稳定的漩涡，形成围绕其几乎静止的质心缓慢旋转的耗散片。该方法预测冯卡门常数为1/sqrt（2 pi）= 0.399，含能时间和长度尺度的时空动力学控制湍流混合[Baumert 2009]。到目前为止，与湍流光谱的联系还没有找到。本文表明，如果耗散斑块从两个同样旋转的涡旋开始，局部地演变成Herrmann [1990]意义上的空间填充轴承，即演变成“阿波罗齿轮”，则上述随机涡旋偶极运动的图像与Kolmogorov湍流谱是相容的。它的部件和零件是不可压缩的和柔性变形的涡管，除了零尺寸的耗散尺度外，是无摩擦的。对于稳定和局部均匀条件，我们的方法预测三维欧拉波数谱中的无量纲前因子为[（4 pi）^2/3]/3 = 1.8，拉格朗日频谱中的无量纲前因子为2。我们的推导依赖于几何学、多粒子物理学的方法和基本守恒定律。
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