Fractional Brownian Motions and Enhanced Diffusion in a Unidirectional Wave-Like Turbulence

We study transport in random undirectional wave-like velocity fields with nonlinear dispersion relations. For this simple model, we have several interesting findings: (1) In the absence of molecular diffusion the entire family of fractional Brownian motions (FBMs), persistent or anti-persistent, can arise in the scaling limit. (2) The infrared cutoff may alter the scaling limit depending on whether the cutoff exceeds certain critical value or not. (3) Small, but nonzero, molecular diffusion can drastically change the scaling limit. As a result, some regimes stay intact; some (persistent) FBM regimes become non-Gaussian and some other FBM regimes become Brownian motions with enhanced diffusion coefficients. Moreover, in the particular regime where the scaling limit is a Brownian motion in the absence of molecular diffusion, the vanishing molecular diffusion limit of the enhanced diffusion coefficient is strictly larger than the diffusion coefficient with zero molecular diffusion. This is the first such example that we are aware of to demonstrate rigorously a nonperturbative effect of vanishing molecular diffusion on turbulent diffusion coefficient.     

Turbulence spectra generated by singularities

The problem of turbulence spectra generated by the singularities located on lines and planes is considered. It is shown that the frequency spectrum of fluid-surface displacements due to whitecaps (linear singularities) is scaled like a weakly turbulent Zakharov-Filonenko spectrum. The corresponding wave-vector spectrum may be highly anisotropic with a decrease in maximum, as in the Phillips spectrum. However, in the isotropic situation, the spectrum differs markedly from the Phillips form. For a highly anisotropic two-dimensional turbulence, the vorticity jumps can generate the Kraichnan power-law distribution in the region of maximal angular peak. For the isotropic distribution, the turbulence spectrum coincides with the Saffman spectrum. For the shock-generated acoustic turbulence, the spectrum has the form of the Kadomtsev-Petviashvili spectrum Eω～ ω^?2 for all spatial dimensionalities.     

Predictive Turbulence Modeling by Variational Closure

We show that a variational implementation of probability density function (PDF) closures has the potential to make predictions of general turbulence mean statistics for which a priori knowledge of the incorrectness is possible. This possibility exists because of realizability conditions on effective potential functions for general turbulence statistics. These potentials measure the cost for fluctuations to occur away from the ensemble-mean value in empirical time-averages of the given variable, and their existence is a consequence of a refined ergodic hypothesis for the governing dynamical system (Navier–Stokes dynamics). Approximations of the effective potentials can be calculated within PDF closures by an efficient Rayleigh–Ritz algorithm. The failure of realizability within a closure for the approximate potential of any chosen statistic implies a priori that the closure prediction for that statistic is not converged. The systematic use of these novel realizability conditions within PDF closures is shown in a simple 3-mode system of Lorenz to result in a statistically improved predictive ability. In certain cases the variational method allows an a priori optimum choice of free parameters in the closure to be made.     

Sensing Atmospheric Turbulence by Laser Radiation

Atmospheric turbulence sensing by lateral fluctuations of thin beams is described. Practical use of correlation functions of lateral fluctuations to investigate the refractive index spectrum and its parameters, inner and outer scale and structure constant, is presented. A “maximum” method is also shown to derive the inner scale independently of the other parameters, without either knowing much of the turbulence or solving an inverse problem.Presented at the International Commission for Optics Topical Meeting, Kyoto, 1994.     

Turbulence spectra

The scaling invariance of the Navier-Stokes equations in the limit of infinite Reynolds number is used to derive laws for the inertial range of the turbulence spectrum. Whether the flow is homogeneous or not, the spectrum is chosen to be that given by a well-chosen biorthogonal decomposition. If the flow is hoogeneous, this spectrum coincides with the classical Fourier (energy) spectrum which exhibits Kolmogorov's k^–5/3 power law if the scaling exponent is assumed to be 1/3. In the more general case where the homogeneity assumption is relaxed, the spectrum is discrete and decays exponentially fast under the assumption that the flow is invariant (in a deterministic or statistical sense) under only one subgroup of the scaling coefficient of one scaling group of the equations (corresponding to one value of the scaling exponent). If the flow is invariant under two subgroups of scaling coefficients and, the spectrum becomes maximal, equal toR ₊. Finally, when a full symmetry, namely an invariance under a whole group, is assumed and the spectrum becomes continuous, the decaying law for the spectral density is derived and found to be independent of the specific value ofh These ideas are then applied to locally self-similar flows with multiple dilation centers (localized in space and time) and multiple scaling exponents, extending the concept of multifractals to space and time.     

Turbulence noise

We show that the large-eddy motions in turbulent fluid flow obey a modified hydrodynamic equation with a stochastic turbulent stress whose distribution is a causal functional of the large-scale velocity field itself. We do so by means of an exact procedure of statistical filtering of the Navier-Stokes equations, which formally solves the closure problem, and we discuss the relation of our analysis with the decimation theory of Kraichnan. We show that the statistical filtering procedure can be formulated using field-theoretic path-integral methods within the Martin-Siggia-Rose (MSR) formalism for classical statistical dynamics. We also establish within the MSR formalism a least-effective-action principle for mean turbulent velocity profiles, which generalizes Onsager's principle of least dissipation. This minimum principle is a consequence of a simple realizability inequality and therefore holds also in any realizable closure. Symanzik's theorem in field theory—which characterizes the static effective action as the minimum expected value of the quantum Hamiltonian over all state vectors with prescribed expectations of fields—is extended to MSR theory with non-Hermitian Hamiltonian. This allows stationary mean velocity profiles and other turbulence statistics to be calculated variationally by a Rayleigh-Ritz procedure. Finally, we develop approximations of the exact Langevin equations for large eddies, e.g., a random-coupling DIA model, which yield new stochastic LES models. These are compared with stochastic subgrid modeling schemes proposed by Rose, Chasnov, Leith, and others, and various applications are discussed.     

Turbulence in noninteger dimensions by fractal Fourier decimation

Fractal decimation reduces the effective dimensionality D of a flow by keeping only a (randomly chosen) set of Fourier modes whose number in a ball of radius k is proportional to k(D) for large k. At the critical dimension D(c)=4/3 there is an equilibrium Gibbs state with a k(-5/3) spectrum, as in V. L'vov et al., Phys. Rev. Lett. 89, 064501 (2002). Spectral simulations of fractally decimated two-dimensional turbulence show that the inverse cascade persists below D=2 with a rapidly rising Kolmogorov constant, likely to diverge as (D-4/3)(-2/3).     

激光雷达湍流大气探测

基于湍流对激光束的扩散和漂移效应,提出了一种采用激光雷达观测湍流强度的方法。湍流对光束产生扩散和飘移作用,使激光光束偏离激光雷达接收视场,造成后向散射光能量损失。对比常规散射回波信号与畸变回波信号的差别可以测量湍流强度。实验表明该方法与其他方法的测量结果具有一致性,证明了该方法的有效性。     

Trapped Electron Turbulence

The effect of trapped electron turbulence on the dynamics of a typical unstable mode is investigated. We establish that its principal effects are turbulence-induced additional collision frequencies for the trapped electrons and transit ions both of which are stabilizing. The resulting nonlinearly saturated fluctuation level is found to be considerably smaller than other estimates. The corresponding estimates of anomalous particle and thermal diffusion are also smaller than previous results.     

Characteristics of Turbulence Induced by Mechanical Waves in a Tank

Journal of Experimental and Theoretical Physics - Three components of current velocity ui(i = x, y, z) induced by mechanical waves generated by a wave maker are measured in a wind-wave tank for...     

地物散射和大气湍流导致的激光闪烁统计

通过分析大气湍流和地物散射对传输激光束的调制机理，运用双随机统计理论研究了空－地－空传输路径空载探测器接收到光闪烁统计问题。闪烁统计由大气湍流和地物（岩石，海洋和森林等）散射的联合效应给出，分析中采用最速下降法处理概率积分，获得了与岩石，海洋和森林二大类地物散射体对应的闪概率密度函数，广义Ｃｈｉ－Ｓｑｕａｒｅｄ地面散射与大气湍流综合调制效应明显地压缩了概率分布的宽度并使分布函数的峰值移向归一化强度     

Turbulence without strange attractor

It is shown that pipe-flow turbulence consists of transients. The fractal dimensions of the dynamical process are thus all zero. Nevertheless, this is compatible with Grassberger-Procaccia analyses suggesting the existence of a high-dimensional strange attractor. The usefulness of the Grassberger-Procaccia method to detect the aging of transients is demonstrated.     

Diffusion of electrons by coherent wavepackets

The momentum transfer and velocity diffusion of electrons periodically interacting with a coherent longitudinal wavepacket is considered. Applying the resonance overlap criterion, we establish the threshold for intrinsic stochasticity and the width of the stochastic region Δv_stoch in velocity space. Direct numerical integration of the single-particle dynamics and an approximate discrete mapping are used to corroborate the resonance overlap results and to find the short- and long-term momentum transfer and diffusion in the field. After the onset of stochasticity, we find a net induced current j ≈ Δv_stoch and in the weak-field regime (autocorrelation time ? bounce time) an initial rate of change of the variance 〈πv²〉 /2t equal to the quasilinear-theory diffusion coefficient. In the strong-field regime momentum transfer and stochasticity persist owing to non-adiabatic transitions between trapped and untrapped states as the electron traverses the wavepacket. The diffusion coefficient substantially deviates from the quasilinear (≈E²) as well as from resonance broadening ($\text{≈E}{}^{\mathrm{<mtext>3</mtext><mtext>2</mtext>}}$) scaling, while the scattering in velocity space tends to lose the local, diffusive nature characteristic of weak fields.     

Cross-Field Diffusion by Charge Changing Processes

The particle transport induced by ionization, recombination and charge exchange processes in magnetically confined plasmas is analyzed. For ions with charge numbers Z ≧ 2 a random walk is caused by the fluttering of the gyro-radius as a result of successive recombination and ionization events. The corresponding diffusion coefficient, however, is very small and may be neglected even in the case of high-energy alpha particles being produced in fusion plasmas. Single and neutral particles are subjected to joint transport across the magnetic field due to their unimpeded motion during the short atomic phases. It is found that this mechanism is more important than classical transport over a wide temperature and density range. The corresponding diffusion coefficient D₁ = f(Te)Ti/mine is independent of the magnetic field strength and shows an electron temperature dependence which can be expressed in terms of the rate coefficients for ionization, recombination and charge exchange. The latter effect leads to a strong reduction of the diffusion process in hydrogen plasmas. Diffusion coefficients comparable with anomalous values of about 1m²/s are therefore reached only for cool (divertor) plasmas with T < 5eV.     

Turbulence Driven Tearing Modes

The effect of a turbulent background of density, electrostatic, and magnetic fluctuations on the growth of tearing modes is considered assuming three-wave interaction. It is found that, depending on the background conditions, the turbulence can cause anomalous electron resistivity or viscosity, leading to enhanced growth rate.