On the presence of spectral shortcut in the energy budget of an asymmetric jet–wake flow in a forward-curved centrifugal turbomachine as deduced from SPIV measurements

Viscous dissipation and its contribution to turbulent kinetic energy (TKE) budget are investigated in the asymmetric jet–wake flow of a forward-curved centrifugal turbomachine. Single-plane three-dimensional turbulent data are obtained using stereoscopic particle image velocimetry (SPIV). Viscous dissipation is indirectly estimated from subgrid-scale (SGS) dissipation (SGS energy flux) by filtering velocity field using a top-hat filter. The filter scale should be within the inertial sub-range and this is ensured by spectral analysis of the measured field. Reduction of turbulent energy flux for smaller filter scales plus underestimation of viscous dissipation as compared with other TKE terms both suggest the presence of spectral shortcut. This bypass energy transfer (from intermediate scales towards dissipative scales) works in parallel with direct SGS energy transfer and affects the classical energy cascade. Analysis of TKE budget in the rotor exit region shows significant radial/circumferential variations in the contributing terms. These variations are mainly due to jet–wake–volute interactions, circumferential asymmetry of volute area and expansion of flow toward the fan outlet.     

Spectral energy transfer and dissipation of magnetic energy from fluid to kinetic scales

We investigate the magnetic energy transfer from the fluid to kinetic scales and dissipation processes using three-dimensional fully kinetic particle-in-cell plasma simulations. The nonlinear evolution of a sheet pinch is studied where we show that it exhibits both fluid scale global relaxation and kinetic scale collisionless reconnection at multiple resonant surfaces. The interactions among collisionless tearing modes destroy the original flux surfaces and produce stochastic fields, along with generating sheets and filaments of intensified currents. In addition, the magnetic energy is transferred from the original shear length scale both to the large scales due to the global relaxation and to the smaller, kinetic scales for dissipation. The dissipation is dominated by the thermal or pressure effect in the generalized Ohm's law, and electrons are preferentially accelerated.     

Phenomenology of two-dimensional stably stratified turbulence under large-scale forcing

In this paper, we characterise the scaling of energy spectra, and the interscale transfer of energy and enstrophy, for strongly, moderately and weakly stably stratified two-dimensional (2D) turbulence, restricted in a vertical plane, under large-scale random forcing. In the strongly stratified case, a large-scale vertically sheared horizontal flow (VSHF) coexists with small scale turbulence. The VSHF consists of internal gravity waves and the turbulent flow has a kinetic energy (KE) spectrum that follows an approximate k^?3 scaling with zero KE flux and a robust positive enstrophy flux. The spectrum of the turbulent potential energy (PE) also approximately follows a k^?3 power-law and its flux is directed to small scales. For moderate stratification, there is no VSHF and the KE of the turbulent flow exhibits Bolgiano–Obukhov scaling that transitions from a shallow k^?11/5 form at large scales, to a steeper approximate k^?3 scaling at small scales. The entire range of scales shows a strong forward enstrophy flux, and interestingly, large (small) scales show an inverse (forward) KE flux. The PE flux in this regime is directed to small scales, and the PE spectrum is characterised by an approximate k^?1.64 scaling. Finally, for weak stratification, KE is transferred upscale and its spectrum closely follows a k^?2.5 scaling, while PE exhibits a forward transfer and its spectrum shows an approximate k^?1.6 power-law. For all stratification strengths, the total energy always flows from large to small scales and almost all the spectral indicies are well explained by accounting for the scale-dependent nature of the corresponding flux.     

Lagrangian view of time irreversibility of fluid turbulence

A turbulent flow is maintained by an external supply of kinetic energy, which is eventually dissipated into heat at steep velocity gradients. The scale at which energy is supplied greatly differs from the scale at which energy is dissipated, the more so as the turbulent intensity(the Reynolds number) is larger. The resulting energy flux over the range of scales, intermediate between energy injection and dissipation, acts as a source of time irreversibility. As it is now possible to follow accurately fluid particles in a turbulent flow field, both from laboratory experiments and from numerical simulations, a natural question arises: how do we detect time irreversibility from these Lagrangian data? Here we discuss recent results concerning this problem. For Lagrangian statistics involving more than one fluid particle, the distance between fluid particles introduces an intrinsic length scale into the problem. The evolution of quantities dependent on the relative motion between these fluid particles, including the kinetic energy in the relative motion, or the configuration of an initially isotropic structure can be related to the equal-time correlation functions of the velocity field, and is therefore sensitive to the energy flux through scales, hence to the irreversibility of the flow. In contrast, for singleparticle Lagrangian statistics, the most often studied velocity structure functions cannot distinguish the "arrow of time". Recent observations from experimental and numerical simulation data, however, show that the change of kinetic energy following the particle motion, is sensitive to time-reversal. We end the survey with a brief discussion of the implication of this line of work.     

Compressible turbulence: the cascade and its locality

We prove that interscale transfer of kinetic energy in compressible turbulence is dominated by local interactions. In particular, our results preclude direct transfer of kinetic energy from large-scales to dissipation scales, such as into shocks, in high Reynolds number turbulence as is commonly believed. Our assumptions on the scaling of structure functions are weak and enjoy compelling empirical support. Under a stronger assumption on pressure dilatation cospectrum, we show that mean kinetic and internal energy budgets statistically decouple beyond a transitional conversion range. Our analysis establishes the existence of an ensuing inertial range over which mean subgrid scale kinetic energy flux becomes constant, independent of scale. Over this inertial range, mean kinetic energy cascades locally and in a conservative fashion despite not being an invariant.     

Spectral energy balance in dry convective boundary layers

Three-dimensional large-eddy simulations (LES) of the convective boundary layer over a domain of approximately 6 km are performed with the UCLA LES model. Simulations are forced with a constant surface heat flux and prescribed subsidence, and are run to equilibrium. Sub-grid scale fluxes are parameterised with the Smagorinsky–Lilly scheme. A range of grid spacings from 40 down to 5 m are employed. Kinetic energy spectra and the various terms in the kinetic energy spectral budget – heat flux, nonlinear transfer, pressure, and dissipation – are computed using two-dimensional discrete Fourier transforms at every vertical level. Despite the fact that isotropic grid spacings of down to 5 m (grid sizes of 1152²×400) were used, an inertial range with a ?5/3 spectrum is not obtained. Rather, shallower energy spectral slopes that are closer to ?4/3 are found. The shallower spectra are shown to possibly result from the injection of kinetic energy over a wide range of scales via a very broad heat flux spectrum. Only with the highest resolution (Δx = 5 m) does the total heat flux begin to converge and the possibility of local isotropy emerge at small scales. Dependence on surface heat flux and domain size is considered. Preliminary sub-grid scale sensitivity results are obtained through comparison with the turbulent kinetic energy sub-grid scale model.     

Insights into the Second Law of Thermodynamics from Anisotropic Gas-Surface Interactions

Thermodynamic implications of anisotropic gas-surface interactions in a closed molecular flow cavity are examined. Anisotropy at the microscopic scale, such as might be caused by reduced-dimensionality surfaces, is shown to lead to reversibility at the macroscopic scale. The possibility of a self-sustaining nonequilibrium stationary state induced by surface anisotropy is demonstrated that simultaneously satisfies flux balance, conservation of momentum, and conservation of energy. Conversely, it is also shown that the second law of thermodynamics prohibits anisotropic gas-surface interactions in “equilibrium”, even for reduced dimensionality surfaces. This is particularly startling because reduced dimensionality surfaces are known to exhibit a plethora of anisotropic properties. That gas-surface interactions would be excluded from these anisotropic properties is completely counterintuitive from a causality perspective. These results provide intriguing insights into the second law of thermodynamics and its relation to gas-surface interaction physics. Sandia National Laboratories is the author’s employer, but is not officially affiliated with this work.     

Lagrangian Particle Approach to Large Eddy Simulations of Hydrodynamic Turbulence

The flux of energy from large to small scales in hydrodynamic turbulence controls the dissipation of energy at a given scale in the fluid. An accurate parametrization of this flux is a prerequisite in order to devise reliable methods to simulate turbulent flows without resolving all the scales of motion. This problem is discussed in the context of a particle method based on the Smooth Particles Hydrodynamics algorithm. Motivated by the von Karman–Howarth–Kolmogorov exact relation for the energy flux, and by Lagrangian dynamics considerations we postulate an energy transfer term which is quadratic in the velocity and formally time reversal invariant. The numerical simulation of the model however is observed to spontaneously break the time reversal symmetry, demonstrating that the proposed term acts on average as the desired eddy damping.     

可压缩湍流研究进展

高马赫数可压缩湍流的运动是一个多尺度多过程的物理现象。采用了多过程分解的方法,将可压缩湍流分解为剪切和胀压过程,分析其统计行为和动力学行为。发展了一种新的紧致差分和WENO格式相结合的混合型数值格式,准确模拟了可压缩湍流场;研究了其多尺度多过程行为和对粒子的输运影响;研究了激波结构对湍流场的影响;在高雷诺数可压缩湍流中,证明存在惯性区,其中流运动和压力做功引起的动能流通量都是常数;证明可压缩湍流中存在从大尺度到小尺度的动能级串过程;证明动能流通量的剪切部分和胀压部分在惯性区都为常数;分析亚格子应力项和亚格子质量流动项对动能级串的影响。     

Mesoscopic biology

In this paper we present a qualitative outlook of mesoscopic biology where the typical length scale is of the order of nanometers and the energy scales comparable to thermal energy. Novel biomolecular machines, governed by coded information at the level of DNA and proteins, operate at these length scales in biological systems. In recent years advances in technology have led to the study of some of the design principles of these machines; in particular at the level of an individual molecule. For example, the forces that operate in molecular interactions, the stochasticity involved in these interactions and their spatio-temporal dynamics are beginning to be explored. Understanding such design principles is opening new possibilities in mesoscopic physics with potential applications.     

Statistics of particle pair relative velocity in the homogeneous shear flow

Small scale clustering of inertial particles and relative velocity of particle pairs have been fully characterized for statistically steady homogeneous isotropic flows. Depending on the particle Stokes relaxation time, the spatial distribution of the disperse phase results in a multi-scale manifold characterized by local particle concentration and voids and, because of finite inertia, the two nearby particles have high probability to exhibit large relative velocities. Both effects might explain the speed-up of particle collision rate in turbulent flows. Recently it has been shown that the large scale geometry of the flow plays a crucial role in organizing small scale particle clusters. For instance, a mean shear preferentially orients particle patterns. In this case, depending on the Stokes time, anisotropic clustering may occur even in the inertial range of scales where the turbulent fluctuations which drive the particles have already recovered isotropy. Here we consider the statistics of particle pair relative velocity in the homogeneous shear flow, the prototypical flow which manifests anisotropic clustering at small scales. We show that the mean shear, by imprinting anisotropy on the large scale velocity fluctuations, dramatically affects the particle relative velocity distribution even in the range of small scales where the anisotropic mechanisms of turbulent kinetic energy production are sub-dominant with respect to the inertial energy transfer which drives the carrier fluid velocity towards isotropy. We find that the particles’ populations which manifest strong anisotropy in their relative velocities are the same which exhibit small scale clustering. In contrast to any Kolmogorov-like picture of turbulent transport these phenomena may persist even below the smallest dissipative scales where the residual level of anisotropy may eventually blow-up. The observed anisotropy of particle relative velocity and spatial configuration is suggested to influence the directionality of the collision probability, as inferred on the basis of the so-called “ghost collision” model.     

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由色散方程和流体方程推导得到了横等离激元和对等离子体相互作用的非线性控制方程,利用场论的方法构建非线性控制方程的拉格朗日密度函数并求得相互作用过程中守恒的等离激元数和总能量。通过标度变换发现横等离激元由于调制不稳定性将坍塌形成小尺度的局域结构。在坍塌过程中横等离激元产生的有质动力随场强的增强而增强。由于有质动力对粒子的排斥,对等离子体中将产生小尺度的密度空穴。     

Jet noise prediction using different turbulent scales

The turbulent energy dissipation rate time-scale and length-scale has been routinely used for the prediction of noise from turbulent flows, particularly jet streams. However, this is not the only possible choice. In general, scales evolving in a turbulent medium are threefold. First, those associated with the mean flow; second, those attributed to the turbulence and the mean flow interactions; and third, scales related to the turbulence-turbulence interactions. In this paper, special attention will be paid to further study of the underlying physics of aerodynamic noise by examining various time-scales. To do so, three time scales, namely, dissipation, production, and strain rate time scales, are defined and used in the source modelling to emphasis the effect of the turbulence structures at different jet regions on the jet noise production mechanism. The required mean value and turbulence parameters are obtained using a modified k − ∈ turbulence model, and Lighthill’s Acoustic Analogy is used for the prediction of the emanated noise. The text was submitted by the authors in English.     

等离子体湍流能量传输的尺度相关性

对于空间环境中近乎无碰撞的等离子体,可采用Vlasov方程进行理论描述,基于Vlasov方程,讨论了等离子体湍流能量传输和耗散的过程:由亚格子应力引起的尺度间的能量传输,电场做功,压强张量做功（压强张量与速度梯度张量的相互作用）.通过混合Vlasov-Maxwell（HVM）数值模拟,进一步研究了能量传输通道之间的联系与区别.不同能量传输通道尽管在不同尺度起主要作用,但其空间的分布非常相似,即各能量传输通道之间存在一定的空间相关.结合近年数值模拟和卫星观测的结果,可以大致概括等离子体湍流从磁流体动力学（magnetohydrodynamic,MHD）尺度到动理学尺度的能量传输过程.      

Energy Cascades and Flux Locality in Physical Scales of the 3D Navier-Stokes Equations

Rigorous estimates for the total – (kinetic) energy plus pressure – flux in \mathbbR³{\mathbb{R}^3} are obtained from the three dimensional Navier-Stokes equations. The bounds are used to establish a condition – involving Taylor length scale and the size of the domain – sufficient for existence of the inertial range and the energy cascade in decaying turbulence (zero driving force, non-increasing global energy). Several manifestations of the locality of the flux under this condition are obtained. All the scales involved are actual physical scales in \mathbbR³{\mathbb{R}^3} and no regularity or homogeneity/scaling assumptions are made.     

Roughness of stylolites: implications of 3D high resolution topography measurements

Stylolites are natural pressure-dissolution surfaces in sedimentary rocks. We present 3D high resolution measurements at laboratory scales of their complex roughness. The topography is shown to be described by a self-affine scaling invariance. At large scales, the Hurst exponent is zeta(1) approximately 0.5 and very different from that at small scales where zeta(2) approximately 1.2. A crossover length scale at around L(c)=1 mm is well characterized. Measurements are consistent with a Langevin equation that describes the growth of a stylolitic interface as a competition between stabilizing long range elastic interactions at large scales or local surface tension effects at small scales and a destabilizing quenched material disorder.     

Spectrum of magnetohydrodynamic turbulence

We propose a phenomenological theory of strong incompressible magnetohydrodynamic turbulence in the presence of a strong large-scale external magnetic field. We argue that in the inertial range of scales, magnetic-field and velocity-field fluctuations tend to align the directions of their polarizations. However, the perfect alignment cannot be reached; it is precluded by the presence of a constant energy flux over scales. As a consequence, the directions of shear-Alfvén fluid and magnetic-field fluctuations at each scale lambda become effectively aligned within the angle phi(lambda) proportional to lambda (1/4), which leads to scale-dependent depletion of the nonlinear interaction and to the field-perpendicular energy spectrum E(k(perpendicular)) proportional to k(perpendicular)(-3/2). Our results may be universal, i.e., independent of the external magnetic field, since small-scale fluctuations locally experience a strong field produced by large-scale eddies.     

Spin-1 chain doped with mobile S = 1/2 fermions

We investigate the doping of a two-orbital chain with mobile S = 1/2 fermions as a valid model for Y2-xCaxBaNiO5. The S = 1 spins are stabilized by strong, ferromagnetic Hund's rule couplings. We calculate correlation functions and thermodynamic quantities by density matrix renormalization group methods and find a new hierarchy of energy scales in the spin sector upon doping. Gapless spin excitations are generated at a lower energy scale by interactions among itinerant polarons created by each hole and coexist with the larger scale of the gapful spin-liquid background of the S = 1 chain accompanied by a finite string order parameter.     

Energy fluxes in helical magnetohydrodynamics and dynamo action

Renormalized viscosity, renormalized resistivity, and various energy fluxes are calculated for helical magnetohydrodynamics using perturbative field theory. The calculation is of firstorder in perturbation. Kinetic and magnetic helicities do not affect the renormalized parameters, but they induce an inverse cascade of magnetic energy. The sources for the large-scale magnetic field have been shown to be (1) energy flux from large-scale velocity field to large-scale magnetic field arising due to non-helical interactions and (2) inverse energy flux of magnetic energy caused by helical interactions. Based on our flux results, a primitive model for galactic dynamo has been constructed. Our calculations yield dynamo time-scale for a typical galaxy to be of the order of 10⁸ years. Our field-theoretic calculations also reveal that the flux of magnetic helicity is backward, consistent with the earlier observations based on absolute equilibrium theory.