Alexei A. Mailybaev
We introduce a shell model of turbulence featuring intermittent behaviour with anomalous power-law scaling of structure functions. This model is solved analytically with the explicit derivation of anomalous exponents. The solution associates the intermittency with the hidden symmetry for Kolmogorov multipliers, making our approach relevant for real turbulence.
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Synthetic turbulence models are a useful tool that provide realistic representations of turbulence, necessary to test theoretical results, to serve as background fields in some numerical simulations, and to test analysis tools. Models of 1D and 3D synthetic turbulence previously developed still required large computational resources. A new wavelet-based model of synthetic turbulence, able to produce a field with tunable spectral law, intermittency and anisotropy, is presented here. The rapid algorithm introduced, based on the classic $p$-model of intermittent turbulence, allows to reach a broa…
It is known that scale invariance is broken in the developed hydrodynamic turbulence due to intermittency, substantiating complexity of turbulent flows. Here we challenge the concept of broken scale invariance by establishing a hidden self-similarity in intermittent turbulence. Using a simplified (shell) model, we derive a nonlinear spatiotemporal scaling symmetry of inviscid equations, which are reformulated in terms of intrinsic times introduced at different scales of motion. Numerical analysis persuasively confirms that this symmetry is restored in a statistical sense within the inertial in…
Disentangling intermittent flow structure contributions to anomalous scaling and multifractality in turbulence
本研究通过阈值化涡量并反演毕奥-萨伐尔定律的滤波方法，解耦了湍流中间歇性流动结构对反常标度和多重分形性的贡献，揭示了其对相关物理量的选择性影响。
Superfluid flow around an oscillating microsphere is investigated at temperatures down to 25 mK. Stable laminar flow below a critical velocity and turbulence at large drives are found to be separated below 0.5 K by an intermediate range of driving forces where the flow is unstable, intermittently switching between laminar and turbulent phases. We have recorded time series of this switching phenomenon and have made a statistical analysis of the switching probability. The mean lifetime of the turbulent phases grows with increasing drive and becomes infinite at a critical value. Stability of the …
Synergy of turbulence and thermo-diffusive effects on the intermittent boundary-layer flashback of swirling flames
研究通过LES-FSD方法揭示了湍流与热扩散效应协同作用下，富氢旋流火焰间歇边界层闪火的形成机制与影响因素。
Intermittent turbulence in inclined gravity currents
本研究通过直接数值模拟探究倾斜重力流的间歇性湍流，构建延迟微分模型揭示其为延迟诱导振荡，发现增大初始雷诺数可抑制该间歇性。
We have found that in two-dimensional Kolmogorov flow a single spatially-localized turbulence (SLT) exists stably and travels with a constant speed on average switching the moving direction randomly and intermittently for moderate values of control parameters: Reynolds number and the flow rate. We define the coarse-grained position and velocity of an SLT and separate the motion of the SLT from its internal turbulent dynamics by introducing a co-moving frame. The switching process of an SLT represented by the coarse-grained velocity seems to be a random telegraph signal. Focusing on the asymmet…
Turbulence is ubiquitous in plasmas, leading to rich dynamics characterized by irregularity, irreversibility, energy fluctuations across many scales, and energy transfer across many scales. Another fundamental and generic feature of turbulence, although sometimes overlooked, is the inhomogeneous dissipation of energy in space and in time. This is a consequence of intermittency, the scale-dependent inhomogeneity of dynamics caused by fluctuations in the turbulent cascade. Intermittency causes turbulent plasmas to self-organize into coherent dissipative structures, which may govern heating, diff…
On an Analytical Criterion for Detecting Intermittent Turbulent Behaviour of Solutions of Partial Differential Equations
本文提出基于峰因子的分析准则，用于检测偏微分方程解的间歇湍流行为。
Intermittent fluctuations determine the nature of chaos in turbulence
本研究利用多体混沌去相关器分析充分发展湍流中 Lyapunov 指数对 Reynolds 数的标度，测得 α=0.59±0.04，并证明其偏离 Kolmogorov 平均场预测源于速度梯度张量的间歇性涨落。
Bioluminescence in turbulence: intermittent straining lights up dinoflagellates
研究湍流如何增强鞭毛虫生物发光，揭示湍流波动对发光强度和频率的影响。
Enhanced Activity Reduces the Duration of Intermittent Lévy Walks in Bacterial Turbulence
该研究通过实验揭示了细菌悬浮液中微观动力学与集体运动涌现的相关性，发现细菌在集体运动中经历弹道动力学、间歇性Lévy游走至随机涨落的转变，且增强的活性会缩短Lévy游走持续时间，微观动力学转变受流动有效活性的内在时间尺度控制。
Thermal plumes are the energy containing eddy motions that carry heat and momentum in a convective boundary layer. The detailed understanding of their structure is of fundamental interest for a range of applications, from wall-bounded engineering flows to quantifying surface-atmosphere flux exchanges. We address the aspect of Reynolds stress anisotropy associated with the intermittent nature of heat transport in thermal plumes by performing an invariant analysis of the Reynolds stress tensor in an unstable atmospheric surface layer flow, using a field-experimental dataset. Given the intermitte…
Low-dimensional representation of intermittent geophysical turbulence with High-Order Statistics-informed Neural Networks (H-SiNN)
本文提出高阶统计量信息神经网络H-SiNN，通过在卷积自编码器中引入约束高阶统计矩精度的定制损失函数，实现对分层间歇地球物理湍流的高效低维表示与精确重建。
Exact intermittent solutions in a turbulence multi branch shell model
本研究探讨了一个多分支湍流壳模型，构建了表现出间歇性的精确惯性区解，揭示了速度幅度比值具有尺度不变性，并利用大偏差理论将速度模式概率分布重缩放为尺度无关形式，为理解真实湍流提供了启示。
The turbulence statistics of the intermittent region in a supersonic turbulent boundary layer are studied by direct numerical simulation. Recently, Kwon et al. (2016) have shown that this intermittent behavior, consisting of the coexistence of turbulent and non-turbulent flows separated by an interface, could result in perils when the traditional Reynolds decomposition is used to analyze data. Here, we extend the study of turbulent/non-turbulent interfaces to the supersonic regime and report turbulence statistics conditioned to the interface. We show that the mathematical artefact of the tradi…
Wave turbulence: A solvable problem applied to Navier-Stokes
本文介绍波湍流理论，通过多时间尺度方法以波幅为小参数推导动力学方程，从而避开涡湍流的闭合问题，并在毛细波和惯性波中分别得到各向同性与各向异性湍流的精确结果。
Intermittent turbulent gusts lift eagles
研究通过金雕飞行加速度数据与非线性模型，揭示翱翔鸟类会优先利用间歇性湍流上升气流，提出棘轮式阵风收获机制。
Routes to stratified turbulence revealed by unsupervised classification of experimental data
本文利用无监督聚类和降维方法分析分层倾斜管道实验数据，识别出多种能量湍流类型及间歇性转变路径，为多物理场湍流降阶建模提供新途径。
Multiscale passive scalar turbulence in a compressed subspace via tensor trains
针对降阶建模中捕捉湍流多尺度统计的挑战，提出混合张量列方法以改进被动标量间歇性波动表征，为压缩张量形式下演化其线性动力学提供了途径。
The scaling of the longitudinal velocity structure functions, $S_q(r) = < | δu (r) |^q > \sim r^{ζ_q}$, is analyzed up to order $q=8$ in a decaying rotating turbulence experiment from a large Particle Image Velocimetry (PIV) dataset. The exponent of the second-order structure function, $ζ_2$, increases throughout the self-similar decay regime, up to the Ekman time scale. The normalized higher-order exponents, $ζ_q / ζ_2$, are close to those of the intermittent non-rotating case at small times, but show a marked departure at larger times, on a time scale $Ω^{-1}$ ($Ω$ is the rotation rate), alt…
Spatio-Temporal Signatures of Intermittency in Helically Rotating Turbulence through Topological Data Analysis
本文通过拓扑数据分析方法，揭示了低分辨率螺旋旋转湍流中间歇性现象的空间-时间特征，该方法能够更敏感地检测局部和短暂的流体变化，从而更清晰地识别间歇性行为。
Routes to stratified turbulence and temporal intermittency revealed by a cluster-based network model of experimental data
本文提出结合降维和无监督聚类的数据驱动方法，识别分层倾斜管道实验的湍流骨架，揭示多种湍流类型及间歇性转变路径，为多物理场湍流降阶模型奠定基础。
Stochastic Multiscale Reconstruction of Lagrangian Turbulence via Guided Diffusion Models
利用扩散模型以小波粗粒化的大尺度动力学为条件，从粗粒化轨迹中重建未解析的细尺度拉格朗日湍流波动，恢复间歇性统计和跨尺度相关性。
The intermittent small-scale structure of turbulence governs energy dissipation in many astrophysical plasmas and is often believed to have universal properties for sufficiently large systems. In this work, we argue that small-scale turbulence in accretion disks is universal in the sense that it is insensitive to the magnetorotational instability (MRI) and background shear, and therefore indistinguishable from standard homogeneous magnetohydrodynamic (MHD) turbulence at small scales. We investigate the intermittency of current density, vorticity, and energy dissipation in numerical simulations…
From directed percolation to patterned turbulence
本研究针对湍流转捩中条纹图案的形成机制问题，发现图案并非源于经典不稳定性的波长选择，而是从有向渗流临界点出发、由局部随机规则自组装形成，揭示了随机过程中宏观有序性的新产生机制。
Statistical properties of the Sun's photospheric turbulent magnetic field, especially those of the Active Regions (ARs), have been studied using the line-of-sight data from magnetograms taken by SOHO and several other instruments (see e.g. Abramenko et al (2002, 2003),Abramenko and Yurchyshyn (2010)). This includes structure functions and their exponents, flatness curves and correlation functions. In these works, the dependence of structure function exponents ($ζ_p$) of the order of the structure functions ($\it{p}$) was modeled using a non-intermittent K41 model. It is now well known that the…
We study steady vortex sheet solutions of the Navier-Stokes in the limit of vanishing viscosity at fixed energy flow. We refer to this as the turbulent limit. These steady flows correspond to a minimum of the Euler Hamiltonian as a functional of the tangent discontinuity of the local velocity parametrized as $Δ\vec v_t =\vec \nabla Γ$. This observation means that the steady flow represents the low-temperature limit of the Gibbs distribution for vortex sheet dynamics. The normal displacement $δr_\perp$ of the vortex sheet as a Hamiltonian coordinate and $Γ$ as a conjugate momentum. An infinite …
Inertial-range features of turbulence are investigated using data from experimental measurements of grid turbulence and direct numerical simulations of isotropic turbulence simulated in a periodic box, both at the Taylor-scale Reynolds number $R_λ\sim 1000$. In particular, oscillations modulating the power-law scaling in the inertial range are examined for structure functions up to sixth order moments. The oscillations in exponent ratios decrease with increasing sample size in simulations though, in experiments, they survive at a low value of $4$ parts in $1000$ even after massive averaging. T…
A Numerical Proof of Shell Model Turbulence Closure
本文提出一种基于深度循环神经网络的湍流闭合模型，在壳模型中定量重现欧拉和拉格朗日结构函数及能量级联间歇统计，为三维纳维-斯托克斯湍流建模提供新思路。
The characterization of heat and momentum fluxes in wall-bounded turbulence is of paramount importance for a plethora of applications, ranging from engineering to Earth sciences. However, how the turbulent structures associated with velocity and temperature fluctuations interact to produce the emergent flux signatures, is not evident till date. In this work, we investigate this fundamental issue by studying the switching patterns of intermittently occurring turbulent fluctuations from one state to another, a phenomenon called persistence. We discover that the persistence patterns for heat and …
We present a model describing evolution of the small-scale Navier-Stokes turbulence due to its stochastic distortions by much larger turbulent scales. This study is motivated by numerical findings (laval, 2001) that such interactions of separated scales play important role in turbulence intermittency. We introduce description of turbulence in terms of the moments of the k-space quantities using a method previously developed for the kinematic dynamo problem (Nazarenko, 2003). Working with the $k$-space moments allows to introduce new useful measures of intermittency such as the mean polarizatio…
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