Eric Falcon, Sebastien Aumaitre, Claudio Falcon, Claude Laroche, Stephan Fauve
We report that the power driving gravity and capillary wave turbulence in a statistically stationary regime displays fluctuations much stronger than its mean value. We show that its probability density function (PDF) has a most probable value close to zero and involves two asymmetric roughly exponential tails. We understand the qualitative features of the PDF using a simple Langevin type model.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
继续探索
Using fluctuating hydrodynamics we investigate the effect of thermal fluctuations in the dissipation range of homogeneous, isotropic turbulence. Simulations confirm theoretical predictions that the energy spectrum is dominated by these fluctuations at length scales comparable to the Kolmogorov length. We also find that the extreme intermittency in the far-dissipation range predicted by Kraichnan is replaced by Gaussian thermal equipartition.
On dissipation time scales of the basic second-order moments: the effect on the Energy and Flux-Budget (EFB) turbulence closure for stably stratified turbulence
本文利用直接数值模拟（DNS）评估基本二阶矩耗散率，修订稳定分层湍流的EFB湍流闭合理论，揭示TKE、浮力通量与TPE间的关键反馈机制，维持任意Richardson数下的剪切稳定分层湍流。
The origin of wall-shear stress fluctuations in wall-bounded turbulence
本文通过壁面能量耗散研究壁面剪切应力波动的起源，发现大尺度耗散源于近壁尺度相互作用，且随雷诺数增大，小尺度向大尺度的能量输运因对数层中间尺度增多而增强。
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 …
Within wall turbulence, there is a sublayer where the mean velocity and the variance of velocity fluctuations vary logarithmically with the height from the wall. This logarithmic scaling is also known for the mean concentration of a passive scalar. By using heat as such a scalar in a laboratory experiment of a turbulent boundary layer, the existence of the logarithmic scaling is shown here for the variance of fluctuations of the scalar concentration. It is reproduced by a model of energy-containing eddies that are attached to the wall.
In ferrofluids the suspended ferromagnetic particles agglomerate due to the interaction between the particle magnetic moment and the external magnetic field, which in turn, influences the turbulence and relaxation time. The relaxation time becomes large when we are considering turbulence drag force instead of viscous drag force in Brownian motion. We investigate that the total energy conservation in ferrofluids taking into interaction between the external magnetic field and the ferrofluid.
The irregular reversals of wind direction in convective turbulence are found to have fluctuating intervals that can be related to critical behavior. It is shown that the net magnetization of a 2D Ising lattice of finite size fluctuates in the same way. Detrended fluctuation analysis of the wind reversal time series results in a scaling behavior that agrees with that of the Ising problem. The properties found suggest that the wind reversal phenomenon exhibits signs of self-organized criticality.
For wall turbulence, moments of velocity fluctuations are known to be logarithmic functions of the height from the wall. This logarithmic scaling is due to the existence of a characteristic velocity and to the nonexistence of any characteristic height in the range of the scaling. By using mathematics of random variables, we obtain its necessary and sufficient conditions. They are compared with characteristics of a phenomenological model of eddies attached to the wall and also with those of the logarithmic scaling of the mean velocity.
Entropy and fluctuation relations in isotropic turbulence
该研究基于广义局部Kolmogorov-Hill方程，提出湍流熵及熵产生定义，并通过各向同性湍流直接数值模拟验证了惯性区间内涨落关系的有效性，发现正逆级联概率密度比呈指数行为，与含湍流温度的熵产生率相关。
A temporal study of energy transfer across length scales is performed in 3D numerical simulations of homogeneous shear flow and isotropic turbulence. The average time taken by perturbations in the energy flux to travel between scales is measured and shown to be additive. Our data suggests that the propagation of disturbances in the energy flux is independent of the forcing and that it defines a `velocity' that determines the energy flux itself. These results support that the cascade is, on average, a scale-local process where energy is continuously transmitted from one scale to the next in ord…
Kolmogorov's theory for turbulence in 1941 is based on a hypothesis that small-scale statistics are uniquely determined by the kinematic viscosity and the mean rate of energy dissipation. Landau remarked that the local rate of energy dissipation should fluctuate in space over large scales and hence should affect small-scale statistics. Experimentally, we confirm the significance of this large-scale fluctuation, which is comparable to the mean rate of energy dissipation at the typical scale for energy-containing eddies. The significance is independent of the Reynolds number and the configuratio…
For several flows of laboratory turbulence, we obtain long records of velocity data. These records are divided into numerous segments. In each segment, we calculate the mean rate of energy dissipation, the mean energy at each scale, and the mean total energy. Their values fluctuate significantly among the segments. The fluctuations are lognormal, if the segment length lies within the range of large scales where the velocity correlations are weak but not yet absent. Since the lognormality is observed regardless of the Reynolds number and the configuration for turbulence production, it is expect…
By analyzing hot-wire velocity data taken in an open channel flow, an unambiguous definition of surface-layer thickness is here provided in terms of the cross-over scale between backward and forward energy fluxes. It is shown that the turbulence in the surface layer does not conform to the classical description of two-dimensional turbulence, since the direct energy cascade persists at scales smaller than the cross-over scale, comparable with the distance from the free-surface. The multifractal analysis of the one-dimensional surrogate of the turbulent kinetic energy dissipation rate in terms o…
It is widely believed that at high Reynolds number (Re) all turbulent flows approach a state of "fully developed turbulence" defined by a unique, Re-independent statistics of the velocity fluctuations. Yet direct measurements of the velocity fluctuations have failed to yield clear-cut empirical evidence of the existence of fully developed turbulence. Here we relate the friction coefficient ($f$) of rough-conduit flows to the statistics of the velocity fluctuations. In light of experimental measurements of $f$, our results yield unequivocal evidence of the existence of fully developed turbulenc…
Understanding force generation in non-equilibrium systems is a significant challenge in statistical physics. We uncover a surprising fluctuation-induced force between two plates immersed in homogeneous isotropic turbulence using Direct Numerical Simulation. The force is a non-monotonic function of plate separation. The mechanism of force generation reveals an intriguing analogy with fluctuation-induced forces: energy in the fluid is localised in regions of high vorticity, or "worms", which have a characteristic length scale. The magnitude of the force depends on the packing of worms inside the…
In this paper, using Pao's conjecture [Y.-H. Pao, Phys. Fluids 11, 1371 (1968)], we derive expressions for the spectra and fluxes of kinetic energy and enstrophy for two-dimensional (2D) forced turbulence that extend beyond the inertial range. In these expressions, the fluxes and the spectra contain additional factors of the exponential form. To validate these model predictions, we perform numerical simulations of 2D turbulence with an external force applied at $k=k_f$ in the intermediate range. The numerical results match with the model predictions, except for the energy and enstrophy fluxes …
In this two--part study, we present the development and analysis of a stochastic theory for characterizing the relative positions of monodisperse, low-inertia particle pairs that are settling rapidly in homogeneous isotropic turbulence. In the limits of small Stokes number and Froude number such that $Fr \ll St_η\ll 1$, closures are developed for the drift and diffusion fluxes in the probability density function (PDF) equation for the pair relative positions. The theory focuses on the relative motion of particle pairs in the dissipation regime of turbulence, i.e., for pair separations smaller …
Non-equilibrium fluctuations of the direct cascade in Surface Quasi Geostrophic turbulence
本文通过高分辨率直接数值模拟研究SQG湍流中表面势能通量的时间涨落，发现能量收支瞬时不平衡会产生谱的次主导修正，并利用多尺度方法与量纲闭合推导出适用于α-湍流的幂律修正理论预测，同时提出可推广的平衡与非平衡贡献分离方法。
This work reports an experimental characterisation of the flow properties in a homogeneous bubble swarm rising at high-Reynolds-numbers within a homogeneous and isotropic turbulent flow. Both the gas volume fraction α and the velocity fluctuations of the carrier flow before bubble injection are varied, respectively, in the ranges 0% < alpha < 0.93% and 2.3 cm/s < urms < 5.5 cm/s. The so-called bubblance parameter is used to compare the ratio of the kinetic energy generated by the bubbles to the one produced by the incident turbulence, and is varied from 0 to 1.3. Conditional measurements of th…
The probability density function (PDF) of velocity fluctuations is studied experimentally for grid turbulence in a systematical manner. At small distances from the grid, where the turbulence is still developing, the PDF is sub-Gaussian. At intermediate distances, where the turbulence is fully developed, the PDF is Gaussian. At large distances, where the turbulence has decayed, the PDF is hyper-Gaussian. The Fourier transforms of the velocity fluctuations always have Gaussian PDFs. At intermediate distances from the grid, the Fourier transforms are statistically independent of each other. This …
Energy flux plays a key role in the analyses of energy-cascading turbulence. In isotropic turbulence, the flux is given by a scalar as a function of the magnitude of the wavenumber. On the other hand, the flux in anisotropic turbulence should be a geometric vector that has a direction as well as the magnitude, and depends not only on the magnitude of the wavenumber but also on its direction. The energy-flux vector in the anisotropic turbulence cannot be uniquely determined in a way used for the isotropic flux. In this work, introducing two ansatzes, net locality and efficiency of the nonlinear…
Model for the structure function constant for index of refraction fluctuations in Rayleigh-Benard turbulence
本文基于均匀各向同性、产生耗散平衡、惯性区存在及单涡旋翻转时间耗散等假设，建立了Rayleigh-Bénard湍流折射率起伏结构函数常数模型，预测其与Rayleigh数无关，并通过伪谱法和有限体积法数值模拟验证了模型。
Theory and computations have established that thermodynamic gradients created by hot spots in reactive gas mixtures can lead to spontaneous detonation initiation. However, the current laminar theory of the temperature-gradient mechanism for detonation initiation is restricted to idealized physical configurations. Thus, it only predicts conditions for the onset of detonations in quiescent gases, where an isolated hot spot is formed on a timescale shorter than the chemical and acoustic timescales of the gas. In this work, we extend the laminar temperature-gradient mechanism into a statistical mo…
Within wall turbulence, there is a sublayer where the mean wall-normal flux of the streamwise momentum is constant and related to the logarithmic wall-normal profile of the mean streamwise velocity. This relation, i.e., the law of the wall, has been used to estimate the mean stress at the wall surface. However, the momentum flux exhibits large temporal fluctuations. To relate them theoretically to those of the streamwise velocity at the same position from the wall, we consider an orthogonal decomposition of the fluctuations on a plane of the streamwise and wall-normal velocities. Since a large…
In recent years, scale-by-scale energy transport in wall turbulence has been intensively studied, and the complex spatial and interscale transfer of turbulent energy has been investigated. As the enhancement of heat transfer is one of the most important aspects of turbulence from an engineering perspective, it is also important to study how turbulent heat fluxes are transported in space and in scale by nonlinear multi-scale interactions in wall turbulence as well as turbulent energy. In the present study, the spectral transport budgets of turbulent heat fluxes are investigated based on direct …
On their roller coaster ride through turbulence, tracer particles sample the fluctuations of the underlying fields in space and time. Quantitatively relating particle and field statistics remains a fundamental challenge in a large variety of turbulent flows. We quantify how tracer particles sample turbulence by expressing their temporal velocity fluctuations in terms of an effective probabilistic sampling of spatial velocity field fluctuations. To corroborate our theory, we investigate an extensive suite of direct numerical simulations of hydrodynamic turbulence covering a Taylor-scale Reynold…
Turbulence exhibits significant velocity fluctuations even if the scale is much larger than the scale of the energy supply. Since any spatial correlation is negligible, these large-scale fluctuations have many degrees of freedom and are thereby analogous to thermal fluctuations studied in the statistical mechanics. By using this analogy, we describe the large-scale fluctuations of turbulence in a formalism that has the same mathematical structure as used for canonical ensembles in the statistical mechanics. The formalism yields a universal law for the energy distribution of the fluctuations, w…
To study subregions of a turbulence velocity field, a long record of velocity data of grid turbulence is divided into smaller segments. For each segment, we calculate statistics such as the mean rate of energy dissipation and the mean energy at each scale. Their values significantly fluctuate, in lognormal distributions at least as a good approximation. Each segment is not under equilibrium between the mean rate of energy dissipation and the mean rate of energy transfer that determines the mean energy. These two rates still correlate among segments when their length exceeds the correlation len…
We analyze velocity fluctuations inside coherent vortices generated as a result of the inverse cascade in the two-dimensional ($2d$) turbulence in a finite box. As we demonstrated in \cite{16KL}, the universal velocity profile, established in \cite{14LBFKL}, corresponds to the passive regime of flow fluctuations. The property enables one to calculate correlation functions of the velocity fluctuations in the universal region. We present results of the calculations that demonstrate a non-trivial scaling of the structure function. In addition the calculations reveal strong anisotropy of the struc…
A decomposition of the energy and helicity fluxes in a turbulent hydrodynamic flow is proposed. The decomposition is based on the projection of the flow to a helical basis that allows to investigate separately the role of interactions among modes of different helicity. The proposed formalism is then applied in large scale numerical simulations of a non-helical and a helical flow, where the decomposed fluxes are explicitly calculated. It is shown that the total energy flux can be split in to three fluxes that independently remain constant in the inertial range. One of these fluxes that correspo…
Mechanism generating reverse buoyancy flux at the small scales of stably stratified turbulence
研究揭示了稳定层化湍流中反向浮力通量的机制，通过分析阶梯结构与悬崖结构的作用，解释了浮力通量的反转及湍流能耗散率的变化。
Patchy Polymeric Scalar Turbulence
研究揭示聚合物湍流在低至中等Schmidt数下混合效率低于牛顿湍流，其标量波动呈现更小的强度和更平滑的边界特征。
Using highly resolved direct numerical simulations we examine the statistical properties of the local energy flux rate $Π_\ell(x)$ towards small scales for three isotropic turbulent magnetohydrodynamic flows, which differ in strength and structure of the magnetic field. We analyse the cascade process both in the kinetic and magnetic energy, disentangling the different flux contributions to the overall energy dynamics. The results show that the probability distribution of the local energy flux develops long tails related to extreme events, similar to the hydrodynamic case. The different terms o…
New Exact Betchov-like Relation for the Helicity Flux in Homogeneous Turbulence
本文将能量通量精确分解方法扩展至均匀湍流中的动能螺旋度传输，推导出类似Betchov关系的新精确关系，揭示了尺度局部和多尺度物理过程对螺旋度平均通量的定量贡献。
In fully developed three dimensional fluid turbulence the fluctuating energy is supplied at large scales, cascades through intermediate scales, and dissipates at small scales. It is the hallmark of turbulence that for intermediate scales, in the so called inertial range, the average energy flux is constant and independent of viscosity [1-3]. One very important question is how this range is altered, when an additional agent that can also transport energy is added to the fluid. Long-chain polymers dissolved at very small concentrations in the fluid are such an agent [4,5]. Based on prior work by…
Homogeneous and isotropic turbulent fields obtained from two DNS databases (with $\mbox{Re}_λ$ equal to 150 and 418) were seeded with point particles that moved with the local fluid velocity to obtain Lagrangian pressure histories. Motivated by cavitation inception modeling, the statistics of events in which such particles undergo low-pressure fluctuations were computed, parameterized by the amplitude of the fluctuations and by their duration. The main results are the average frequencies of these events and the probabilistic distribution of their duration, which are of predictive value. A conn…
The commonly accepted description of transition to turbulence in shear flows requires the presence of an external source of disturbances that get amplified by an essentially linear mechanism up to the point where breakdown to turbulence occurs. Microscopic fluctuations are shown here to provide just the right amount of initial disturbances to match the predictions of linear stability theory.
Turbulent flows are out-of-equilibrium because the energy supply at large scales and its dissipation by viscosity at small scales create a net transfer of energy among all scales. Here, the energy cascade is approximated by a combined contribution of a forward drift and diffusion that recover accepted phenomenological theories of turbulence. The fluctuation theorem (FT) is then shown to describe the scale-wise statistics of forward and backward energy transfer and their connection to irreversibility and entropy production. The ensuing turbulence entropy may be used to formulate an extended tur…
Scaling turbulence in the near-wall region
本文推导出新的速度尺度，使近壁区流向湍流脉动剖面与雷诺数无关，并揭示壁面剪切应力脉动及大涡对近壁湍流分布的关键作用。
Using data from a large-scale three-dimensional simulation of supersonic isothermal turbulence, we have tested the validity of an exact flux relation derived analytically from the Navier--Stokes equation by Falkovich, Fouxon and Oz [2010 New relations for correlation functions in Navier--Stokes turbulence. J. Fluid Mech. 644, 465]. That relation, for compressible barotropic fluids, was derived assuming turbulence generated by a large-scale force. However, compressible turbulence in simulations is usually initialized and maintained by a large-scale acceleration, as in gravity-driven astrophysic…
Two-dimensional statistically stationary isotropic turbulence with an imposed uniform scalar gradient is investigated. Dimensional arguments are presented to predict the inertial range scaling of the turbulent scalar flux spectrum in both the inverse cascade range and the enstrophy cascade range for small and unity Schmidt numbers. The scaling predictions are checked by direct numerical simulations and good agreement is observed.
Measurements of the energy spectrum and of the vortex-density fluctuation spectrum in superfluid turbulence seem to contradict each other. Using a numerical model, we show that at each instance of time the total vortex line density can be decomposed into two parts: one formed by metastable bundles of coherent vortices, and one in which the vortices are randomly oriented. We show that the former is responsible for the observed Kolmogorov energy spectrum, and the latter for the spectrum of the vortex line density fluctuations.
High resolution direct numerical simulations of two-dimensional turbulence in stationary conditions are presented. The development of an energy-enstrophy double cascade is studied and found to be compatible with the classical Kraichnan theory in the limit of extended inertial ranges. The analysis of the joint distribution of energy and enstrophy fluxes in physical space reveals a small value of cross correlation. This result supports many experimental and numerical studies where only one cascade is generated.
The scale locality of energy fluxes for magnetohydrodynamics (MHD) is investigated numerically for stationary states of turbulence. Two types of forces are used to drive turbulence, a kinetic force that acts only on the velocity field and a kinetic-inductive forcing mechanism, which acts on the velocity and magnetic fields alike. The analysis is performed in spectral space, which is decomposed into a series of shells following a power law for the boundaries. The triadic transfers occurring among these shells are computed and the fluxes and locality functions are recovered by partial summation …
This dissertation discusses the intermitency phenomenon in three models of turbulence, employing analytical and numerical techniques in the analysis of stochastic processes and the probability distributions which they induce. The initial chapters present a review of the statistical theory of turbulence and of statistical theory of fields as applied to out of equilibrium physics. Two chapters of the main text investigate the RFD model and the Burgers model through the Martin-Siggia-Rose-Janssen-de Dominicis (MSRJD) functional method. An analysis of the perturbative corrections corresponding to …
Molecular Fluctuations Inhibit Intermittency in Compressible Turbulence
分子波动抑制压缩湍流中的间歇性，改变化了耗散范围内的湍流统计特性。
An ensemble model of turbulence is proposed. The ensemble consists of flow fields in which the flux of an inviscid conserved quantity, such as energy (or enstrophy in two-dimensional flow fields), across the wavenumber $k$ is a constant independent of $k$ in an appropriate range. Two-dimensional flow fields of constant enstrophy flux are sampled randomly by a Monte Carlo method. The energy spectra $E_k$ of the flow fields are consistent with the scaling $E_k \propto k^{-3}(\ln(k/k_\mathrm{b}))^{-1/3}$ where $k_\mathrm{b}$ is the bottom wavenumber of the constant-flux range.
Cosmic rays density fluctuations with turbulence universal spectrum -8/3
基于可压缩湍流解析理论与CR动力学双流体模型，研究获得CR密度涨落的湍流普适标度律-8/3，揭示其起源与CR介质非线性简单波在拉莫尔半径尺度附近破裂相关。
Numerical search for states with constant enstrophy flux over finite time intervals in two-dimensional turbulence
采用蒙特卡洛方法数值搜索二维湍流中有限时间间隔内波数空间具有恒定涡度通量的状态，并检验其能谱等性质与直接数值模拟湍流状态的相似性。
In quasi-static MHD, experiments and numerical simulations reveal that the energy spectrum is steeper than Kolmogorov's $k^{-5/3}$ spectrum. To explain this observation, we construct turbulence models based on variable energy flux, which is caused by the Joule dissipation. In the first model, which is applicable to small interaction parameters, the energy spectrum is a power law, but with a spectral exponent steeper than -5/3. In the other limit of large interaction parameters, the second model predicts an exponential energy spectrum and flux. The model predictions are in good agreement with t…
Experiments and numerical simulations reveal that in the forward cascade regime, the energy spectrum of two-dimensional turbulence with Ekman friction deviates from Kraichnan's prediction of $k^{-3}$ power spectrum. In this letter we explain this observation using an analytic model based on variable enstrophy flux arising due to Ekman friction. We derive an expression for the enstrophy flux which exhibits a logarithmic dependence in the inertial range for the Ekman-friction dominated flows. The energy spectrum obtained using this enstrophy flux shows a power law scaling for large Reynolds numb…
In three-dimensional hydrodynamic turbulence forced at large length scales, a constant energy flux $ Π_u $ flows from large scales to intermediate scales, and then to small scales. It is well known that for multiscale energy injection and dissipation, the energy flux $Π_u$ varies with scales. In this review we describe this principle and show how this general framework is useful for describing a variety of turbulent phenomena. Compared to Kolmogorov's spectrum, the energy spectrum steepens in turbulence involving quasi-static magnetofluid, Ekman friction, stable stratification, magnetohydrodyn…
The nature of the nonlinear interactions in gyrokinetic (GK) turbulence, driven by an ion-temperature gradient instability, is investigated using numerical simulations of single ion species plasma in three-dimensional flux tube geometry. To account for the level of separation existing between scales involved in an energetic interaction, the degree of locality of the free energy scale flux is analyzed employing Kraichnan's infrared (IR) and ultraviolet locality functions. Due to the nontrivial dissipative nature of GK turbulence, an asymptotic level for the locality exponents, indicative of a u…
Both linear growth processes associated with non-normality of the mean flow and nonlinear interaction transferring energy among fluctuations contribute to maintaining turbulence. However, a detailed understanding of the mechanism by which they cooperate in sustaining the turbulent state is lacking. In this report, we examine the role of fluctuation-fluctuation nonlinearity by varying the magnitude of the associated term in the dynamics of Couette flow turbulence to determine how this nonlinear component helps maintain and determine the structure of the turbulent state, and particularly whether…
Experiments and numerical simulations show that the energy spectrum of the magnetohydrodynamic turbulence in the quasi-static limit deviates from Kolmogorov's $k^{-5/3}$ spectrum as the external magnetic field, or equivalently the interaction parameter, is increased. To explain this phenomena, we construct an analytical turbulence model with variable energy flux that arises due to the Lorentz-force induced dissipation. The energy spectra computed using our model for various interaction parameters are in qualitative agreement with earlier experimental and numerical results.
The fluctuations of turbulence intensity in a pipe flow around the critical Reynolds number is difficult to study but important because they are related to turbulent-laminar transitions. We here propose a rare-event sampling method to study such fluctuations in order to measure the time-scale of the transition efficiently. The method is composed of two parts: (i) the measurement of typical fluctuations (the bulk part of an accumulative probability function) and (ii) the measurement of rare fluctuations (the tail part of the probability function) by employing dynamics where a feedback control o…
Turbulence is a paradigm for far-from-equilibrium systems without time reversal symmetry. To capture the nonequilibrium irreversible nature of turbulence and investigate its implications, we develop a potential landscape and flux field theory for turbulent flow and more general nonequilibrium fluid systems governed by stochastic Navier-Stokes equations. We find that equilibrium fluid systems with time reversibility are characterized by a detailed balance constraint that quantifies the detailed balance condition. In nonequilibrium fluid systems with nonequilibrium steady states, detailed balanc…
We report a non-perturbative study of the effect of different type of shear flows on the evolution of vorticity and particle density fluctuations in interchange turbulence. For the same shear strength, the transport of density is less reduced by streamers than by zonal flows, zonal flows leading to oscillation death. In the inviscid limit, vorticity (density) grows (decays) as a power law due to streamer or zonal flow, and exponentially due to the combined effect of zonal flow and streamer with the same sign of shear. Zonal flow and streamer with the opposite sign of shear lead to oscillation …
Fluctuation Relations at Large Scales in Three-Dimensional Hydrodynamic Turbulence
本研究通过大量直接数值模拟验证了三维湍流中大尺度速度模式的涨落-耗散关系和涨落定理，进一步证实大尺度模式遵循平衡动力学，并提供了表征能量注入的新工具。
The energy and flux budget (EFB) closure theory for a passive scalar (non-buoyant and non-inertial particles or gaseous admixtures) is developed for stably stratified turbulence. The physical background of the EFB turbulence closures is based on the budget equations for the turbulent kinetic and potential energies and turbulent fluxes of momentum and buoyancy, as well as the turbulent flux of particles. The EFB turbulence closure is designed for stratified geophysical flows from neutral to very stable stratification and it implies that turbulence is maintained by the velocity shear at any stra…
扫码添加微信好友，提出您的宝贵建议 👇
💡 备注请填写：网站反馈
发表机构由 AI 从论文文本抽取，如发现错误，欢迎反馈修正建议。