Cascade-like and scaling behavior of wind velocity increments in the atmospheric surface layer

By using a large amount of data collected in the atmospheric surface layer, we analyze the probability density functions (PDFs), the probability of return and the moments of wind velocity increments. Results show that the PDFs change from the non-Gaussian long-tailed distributions to Gaussian with the increase of time scales. This is similar to what has been observed and interpreted as an indication of cascade in the fully developed homogeneous and isotropic turbulence. Besides, both the probability of return and the moments are found to be scaling with time scales. We then compare above results with the truncated Lévy flights and the log-normal PDF model. It is found that although both models show the cascade-like behavior in the PDFs and the scaling behavior in the probability of return and the moments under some conditions, they are not good enough for quantitatively describing the random process of wind velocity increments.     

Fractality feature in incompressible three-dimensional magnetohydrodynamic turbulence

Direct Numerical Simulation (DNS) of decaying isotropic 3D magnetohydrodynamic (MHD) turbulence based on the 10243-modes in a periodic box is used to study the statistical properties of turbulence. In this paper, the presence of intermittency in MHD turbulence is investigated through the analysis of the Probability Distribution Function (PDF) for Elsässer fields and total energy fluctuations. We observe that the PDFs of the Elsässer fields fluctuations display a strong non-Gaussian behavior at small scale, which can be ascribed to multifractality feature, while the PDFs of the total energy fluctuations have the same shape over all observed scales and are monofractal. The PDFs have stretched exponential tail and satisfy the function P(|δX|) ～ exp(?A|δX| ^μ ). Numerically, we extract the exponent μ and find that it is constant for monofractal behavior as the length scale varies. To check the notion of self-similarity in the respective fluctuation, we apply the compensated structure functions.     

Probability distribution functions for a single-particle vibrating in one dimension: experimental study and theoretical analysis

We consider the form of the rebound velocity, ν₀, particle velocity, ν, and height, h, probability density functions (PDFs) for the one-dimensional motion of a single particle on a sinusoidally oscillating base. The motion is considered in the limit of high excitation (vibration frequency ⪢ collision rate). Experimentally, we find that these PDFs are well-approximated by P_ν0(ν₀) ∞ ν₀ exp(− αν₀²), a Gaussian P_ν(ν) ∞ exp(− αν²) and a Boltzmann-type function P_h(h) ∞ exp(− 2αgh), where α is a constant and g is the acceleration due to gravity. We develop an analytical model which accurately predicts the general form for the rebound velocity PDF; the other two PDFs are then analytically shown to follow as a consequence. Scaling laws for the particle granular temperature with peak base velocity and particle-base restitution coefficient, determined from previous work, can also be predicted from the PDF. A fine scale “spiky” structure in the rebound velocity PDF is found, using numerical simulations, to be a consequence of resonance phenomena between the particle and vibrating base. Good agreement between scaling laws from the theory and simulation is found but insufficient data is obtainable to derive accuracy exponents experimentally.     

Extreme waves statistics for the Ablowitz-Ladik system

We examine statistics of waves for the problem of modulation instability development in the framework of discrete integrable Ablowitz-Ladik (AL) system. Modulation instability depends on one free parameter h that has the meaning of the coupling between the nodes on the lattice. For strong coupling h ? 1, the probability density functions (PDFs) for waves amplitudes coincide with that for the continuous classical nonlinear Schrödinger equation; the PDFs for both systems are very close to Rayleigh ones. When the coupling is weak h ～ 1, there appear highly localized waves with very large amplitudes, that drastically change the PDFs to significantly non-Rayleigh ones, with so-called “fat tails” when the probability of a large wave occurrence is by several orders of magnitude higher than that predicted by the linear theory. Evolution of amplitudes for such rogue waves with time is similar to that of the Peregrine solution for the classical nonlinear Schrödinger equation.     

Joint-scalar transported PDF modeling of soot formation and oxidation

The ability of the transported probability density function (PDF) approach to reproduce the evolution of mean, rms fluctuations, and conditional PDFs of soot is explored in the context of two turbulent ethylene diffusion flames at Reynolds numbers of 11,800 and 15,600. The chemical similarity between surface reactions and PAH formation is explored on the basis of a second ring PAH analogy, and soot oxidation is accounted for through reactions with O, OH, and O₂. The method of moments is used to account for coagulation and agglomeration in the coalescent and fractal aggregate limits. The soot model is coupled with a transported PDF approach closed at the joint-scalar level to directly account for interactions between turbulence, and the solid and gas phase chemistry. The latter is represented by a systematically reduced reaction mechanism for ethylene featuring 144 reactions, 15 solved and 14 steady-state species. Radiation from soot and gas phase species is accounted for through the RADCAL method and the inclusion of enthalpy into the joint-scalar PDF. Predicted temperature and soot statistics compare well with experimental data indicating the practical potential of the approach and the importance of turbulence-chemistry interactions in the context of soot formation and burnout.     

Asymptotics of unit Burger number rotating and stratified flows for small aspect ratio

Rotating and stably stratified Boussinesq flow is investigated for Burger number unity in domain aspect ratio (height/horizontal length) δ<1 and δ=1. To achieve Burger number unity, the non-dimensional rotation and stratification frequencies (Rossby and Froude numbers, respectively) are both set equal to a second small parameter ?<1. Non-dimensionalization of potential vorticity distinguishes contributions proportional to (?δ)⁻¹, δ⁻¹ and O(1). The (?δ)⁻¹ terms are the linear terms associated with the pseudo-potential vorticity of the quasi-geostrophic limit. For fixed δ=1/4 and a series of decreasing ?, numerical simulations are used to assess the importance of the δ⁻¹ contribution of potential vorticity to the potential enstrophy. The change in the energy spectral scalings is studied as ? is decreased. For intermediate values of ?, as the flow transitions to the (δ?)⁻¹ regime in potential vorticity, both the wave and vortical components of the energy spectrum undergo changes in their scaling behavior. For sufficiently small ?, the (δ?)⁻¹ contributions dominate the potential vorticity, and the vortical mode spectrum recovers k⁻³ quasi-geostrophic scaling. However, the wave mode spectrum shows scaling that is very different from the well-known k⁻¹ scaling observed for the same asymptotics at δ=1. Visualization of the wave component of the horizontal velocity at δ=1/4 reveals a tendency toward a layered structure while there is no evidence of layering in the δ=1 case. The investigation makes progress toward quantifying the effects of aspect ratio δ on the ?→0 asymptotics for the wave component of unit Burger number flows. At the lowest value of ?=0.002, it is shown that the horizontal kinetic energy spectral scalings are consistent with phenomenology that explains how linear potential vorticity constrains energy in the limit ?→0 for fixed δ.     

Bit error rate analysis with real-time pointing errors correction in free space optical communication systems

Pointing errors caused by the atmospheric turbulence will degrade the performance of free space optical (FSO) communication systems, especially the bit error rate (BER). In this paper, we innovatively analyze the relationship between BER and pointing errors by the probability density functions (PDFs) and intensity displacement in focal plane under the On-Off Keying (OOK) modulation conditions. The closed-loop experimental system is set up in laboratory, where the fast steering mirror (FSM) is real-time controlled by embedded controller with the parallel processing technology and the atmospheric turbulence is simulated by a turbulence simulation box. The results of repeated experiments show that the method of pointing errors correction we proposed is efficient under the conditions of atmospheric turbulence. By utilizing our method, the BER can decrease from nearly 10⁻³ to nearly or even below 10⁻⁹, thus improving the performance of FSO communication systems significantly.     

Space use by foragers consuming renewable resources

Through the analysis of unbiased random walks on fractal trees and continuous time random walks, we show that even if a process is characterized by a mean square displacement (MSD) growing linearly with time (standard behaviour) its diffusion properties can be not trivial. In particular, we show that the following scenarios are consistent with a linear increase of MSD with time: (i) the high-order moments, ?x(t) ^q ? for q > 2 and the probability density of the process exhibit multiscaling; (ii) the random walk on certain fractal graphs, with non integer spectral dimension, can display a fully standard diffusion; (iii) positive order moments satisfying standard scaling does not imply an exact scaling property of the probability density.     

Computing the Scaling Exponents in Fluid Turbulence from First Principles: Demonstration of Multiscaling

We develop a consistent closure procedure for the calculation of the scaling exponents ζ _n of the nth-order correlation functions in fully developed hydro-dynamic turbulence, starting from first principles. The closure procedure is constructed to respect the fundamental rescaling symmetry of the Euler equation. The starting point of the procedure is an infinite hierarchy of coupled equations that are obeyed identically with respect to scaling for any set of scaling exponents ζ _n . This hierarchy was discussed in detail in a recent publication by V. S. L'vov and I. Procaccia. The scaling exponents in this set of equations cannot be found from power counting. In this paper we present in detail the lowest non-trivial closure of this infinite set of equations, and prove that this closure leads to the determination of the scaling exponents from solvability conditions. The equations under consideration after this closure are nonlinear integro-differential equations, reflecting the nonlinearity of the original Navier–Stokes equations. Nevertheless they have a very special structure such that the determination of the scaling exponents requires a procedure that is very similar to the solution of linear homogeneous equations, in which amplitudes are determined by fitting to the boundary conditions in the space of scales. The renormalization scale that is necessary for any anomalous scaling appears at this point. The Hölder inequalities on the scaling exponents select the renormalization scale as the outer scale of turbulence L. We demonstrate that the solvability condition of our equations leads to non-Kolmogorov values of the scaling exponents ζ _n . Finally, we show that this solutions is a first approximation in a systematic series of improving approximations for the calculation of the anomalous exponents in turbulence.     

Gottfried sum rule from maximum entropy method quark distributions with DGLAP evolution and with DGLAP evolution with GLR-MQ-ZRS corrections

A new method to test the valence quark distribution of nucleons obtained from the maximum entropy method using the Gottfried sum rule by performing the DGLAP equations with GLR-MQ-ZRS corrections and the original leading-order/next-to-leading-order(LO/NLO) DGLAP equations is outlined. The test relies on knowledge of the unpolarized electron–proton structure function F_2~(ep) and the electron–neutron structure function F_2~(en) and the assumption that Bjorken scaling is satisfied. In this work, the original Gottfried summation value obtained by the integrals of the structure function at different Q~2 is in accordance with the theoretical value of 1/3 under the premise of light-quark flavor symmetry of the nucleon sea, whether it results from dynamical evolution equations or from global quantum chromodynamics fits of PDFs. Finally, we present the summation value of the LO/NLO DGLAP global fits of PDFs under the premise of light-quark flavor asymmetry of the nucleon sea. According to analysis of the original Gottfried summation value with two evolution equations at different Q~2, we find that the valence quark distributions of nucleons obtained by using the maximum entropy method are effective and reliable.     

Statistical properties of visibility graph of energy dissipation rates in three-dimensional fully developed turbulence

We study the statistical properties of complex networks constructed from time series of energy dissipation rates in three-dimensional fully developed turbulence using the visibility algorithm. The degree distribution is found to have a power-law tail with the tail exponent α=3.0. The exponential relation between the number of the boxes N_B and the box size l_B based on the edge-covering box-counting method illustrates that the network is not self-similar, which is also confirmed by the hub-hub attraction according to the visibility algorithm. In addition, it is found that the skeleton of the visibility network exhibits excellent allometric scaling with the scaling exponent η=1.163±0.005.     

Collisionless magnetohydrodynamic turbulence in two dimensions

In this paper we give a formulation of two-dimensional (2D) collisionless magnetohydrodynamic (MHD) turbulence that includes the effects of both electron inertia and electron pressure (or parallel electron compressibility) and is applicable to strongly magnetized collisionless plasmas. We place particular emphasis on the departures from the 2D classical MHD turbulence results produced by the collisionless MHD effects. We investigate the fractal/multi-fractal aspects of spatial intermittency. The fractal model for intermittent collisionless MHD turbulence appears to be able to describe the observed k⁻¹ spectrum in the solar wind. Multi-fractal scaling behaviors in the inertial range are first deduced, and are then extrapolated down to the dissipative microscales. We then consider a parabolic-profile model for the singularity spectrum f (α), as an explicit example of a multi-fractal scenario. These considerations provide considerable insights into the basic mechanisms underlying spatial intermittency in 2D fully developed collisionless MHD turbulence.     

Anomalous Scaling of Structure Functions and Dynamic Constraints on Turbulence Simulations

The connection between anomalous scaling of structure functions (intermittency) and numerical methods for turbulence simulations is discussed. It is argued that the computational work for direct numerical simulations (DNS) of fully developed turbulence increases as Re ⁴, and not as Re ³ expected from Kolmogorov’s theory, where Re is a large-scale Reynolds number. Various relations for the moments of acceleration and velocity derivatives are derived. An infinite set of exact constraints on dynamically consistent subgrid models for Large Eddy Simulations (LES) is derived from the Navier–Stokes equations, and some problems of principle associated with existing LES models are highlighted     

Über die Anwendung von Greenfunktionen zur Beschreibung von Paarungseffekten bei deformierten Atomkernen

The theory of nuclear pairing correlations, recently developed byMigdal, introduces only one constant, which should be nearly the same for all nuclei. This Green's function method is compared with the well known BCS-theory. The constant is fitted and the problem has been solved by numerical methods. We found that the constant varies likeA ^?1/2. The individual magnitude of the pairing energy depends strongly on the single particle level density which determines the value of the renormalized coupling constant of the pairinteraction. This enables us to reproduce the deviations of the pairing energy from the curveδ _n =11,2A ^?1/2. The results are independent from the choice of the cut-off level.     

Reconnection dynamics for quantized vortices

By analyzing trajectories of solid hydrogen tracers in superfluid ⁴He, we identify tens of thousands of individual reconnection events between quantized vortices. We characterize the dynamics by the minimum separation distance δ(t) between the two reconnecting vortices both before and after the events. Applying dimensional arguments, this separation has been predicted to behave asymptotically as δ(t)≈A(κ|t−t₀|)^1/2, where κ=h/m is the quantum of circulation. The major finding of the experiments and their analysis is strong support for this asymptotic form with κ as the dominant controlling feature, although there are significant event to event fluctuations. At the three-parameter level the dynamics may be about equally well-fit by two modified expressions: (a) an arbitrary power-law expression of the form δ(t)=B|t−t₀|^α and (b) a correction-factor expression δ(t)=A(κ|t−t₀|)^1/2(1+c|t−t₀|). The measured frequency distribution of α is peaked at the predicted value α=0.5, although the half-height values are α=0.35 and 0.80 and there is marked variation in all fitted quantities. Accepting (b) the amplitude A has mean values of 1.24±0.01 and half height values of 0.8 and 1.6 while the c distribution is peaked close to c=0 with a half-height range of −0.9 s⁻¹ to 1.5 s⁻¹. In light of possible physical interpretations we regard the correction-factor expression (b), which attributes the observed deviations from the predicted asymptotic form to fluctuations in the local environment and in boundary conditions, as best describing our experimental data. The observed dynamics appear statistically time-reversible, which suggests that an effective equilibrium has been established in quantum turbulence on the time scales (≤0.25 s) investigated. We discuss the impact of reconnection on velocity statistics in quantum turbulence and, as regards classical turbulence, we argue that forms analogous to (b) could well provide an alternative interpretation of the observed deviations from Kolmogorov scaling exponents of the longitudinal structure functions.     

Capillary turbulence at the surface of liquid hydrogen

The results of studying the nonlinear capillary waves at a charged surface of liquid hydrogen are reported. Spectral density is experimentally determined for the surface elevations excited by spectrally narrow low-frequency pumping. It is shown that the spectral density in the range 100 Hz–5 kHz obeys the power-law dependence constω^m (scaling). The m exponent is close to ?3, indicating that the capillary turbulence regime is established.     

Lagrangian structure functions in hydrodynamic turbulence

Based on a solution of the Navier-Stokes equations for the inertial range of fully developed turbulence, a statistical theory is developed to determine the Lagrangian structure functions K _n (τ). Over times τ shorter than the large-scale correlation time τ_c, they obey scaling relations of the form K _n (τ) ∞ \(\tau ^{\zeta _n } \). Analytical expressions are derived for ζ _n . A detailed comparison between the theory and the experimental results presented in [1] demonstrates complete quantitative agreement. A new concept is introduced in turbulence theory: the correlation R _n (τ) between tracer-particle positions on a Lagrangian trajectory. It is shown that the position correlation functions R _n exhibit universal scaling behavior for n > 3.     

Finite-rate chemistry effects in turbulent opposed flows: comparison of Raman/Rayleigh measurements and Monte Carlo PDF simulations

This study reports results from experimental and numerical investigations of a partially premixed turbulent opposed methane/air jet flame. Experimentally determined properties of the scalar and the flow field are compared to the results from a Monte Carlo simulation. One-dimensional spatially resolved Raman/Rayleigh scattering serves to quantify the mean species concentrations and temperature, whereas laser Doppler velocimetry is used to measure axial and radial velocity components. The simulation is simplified by using a one-dimensional formulation. It includes a Reynolds-stress turbulence model and a Monte Carlo simulation of the joint scalar probability density function (PDF). A non-uniform Monte Carlo particle distribution is used to minimize stochastic errors. The flame is operated close to extinction with strong interactions between turbulence and chemistry. Comparisons between experimental and numerical results reveal a good agreement of mixture fraction profiles along the centreline. However, species scatter plots and mixture fraction PDFs show discrepancies between experiment and simulation. Numerical simulations over-predict the extinction limits and therefore under-predict the intermittent nature of turbulence and mixing of the scalars.     

Domain Number Distribution in the Nonequilibrium Ising Model

We study domain distributions in the one-dimensional Ising model subject to zero-temperature Glauber and Kawasaki dynamics. The survival probability of a domain, S(t)～t ^?ψ, and an unreacted domain, Q ₁(t)～t ^?δ, are characterized by two independent nontrivial exponents. We develop an independent interval approximation that provides close estimates for many characteristics of the domain length and number distributions including the scaling exponents.     

Spreading of spatially partially coherent polychromatic beams in atmospheric turbulence

Taking the polychromatic Gaussian Schell-model (GSM) beam as a typical example of spatially partially coherent polychromatic beams, the spreading of polychromatic GSM beams in atmospheric turbulence is studied. The mean-squared width of polychromatic GSM beams in turbulence is derived by using the effective source and the strong fluctuation models. It is shown that the same result is obtained using both the models. The diffraction, atmospheric turbulence and beam polychroism result in a spreading of polychromatic GSM beams. If the scaling law fails, the spreading of polychromatic GSM beams increases with increasing bandwidth Γ, but the influence of Γ on the spreading of polychromatic GSM beams becomes small as the structure constant C_n² of the refractive index and spatial correlation parameter α increase. The spreading of polychromatic GSM beams increases as C_n² increases and α decreases. Spatially partially coherent polychromatic beams are less sensitive to the effects of atmospheric turbulence than spatially fully coherent polychromatic beams.