PROBABILITY DISTRIBUTION FUNCTION OF NEAR-WALL TURBULENT VELOCITY FLUCTUATIONS

By large eddy simulation （LES）, turbulent databases of channel flows at different Reynolds numbers were established. Then, the probability distribution functions of the streamwise and wall-normal velocity fluctuations were obtained and compared with the corresponding normal distributions. By hypothesis test, the deviation from the normal distribution was analyzed quantitatively. The skewness and flatness factors were also calculated. And the variations of these two factors in the viscous sublayer, buffer layer and log-law layer were discussed. Still illustrated were the relations between the probability distribution functions and the burst events-sweep of high-speed fluids and ejection of low-speed fluidsIin the viscous sub-layer, buffer layer and loglaw layer. Finally the variations of the probability distribution functions with Reynolds number were examined.

Probability Distribution Function of a Forced Passive Tracer in the Lower Stratosphere

The probability distribution function （PDF） of a passive tracer, forced by a ＂mean gradient＂, is studied. First, we take two theoretical approaches, the Lagrangian and the conditional closure formalisms, to study the PDFs of such an externally forced passive tracer. Then, we carry out numerical simulations for an idealized random flow on a sphere and for European Center for Medium-Range Weather Forecasts （ECMWF） stratospheric winds to test whether the mean-gradient model can be applied to studying stratospheric tracer mixing in midlatitude surf zones, in which a weak and poleward zonal-mean gradient is maintained by tracer leakage through polar and tropical mixing barriers, and whether the PDFs of tracer fluctuations in midlatitudes are consistent with the theoretical predictions. The numerical simulations show that when diffusive dissipation is balanced by the mean-gradient forcing, the PDF in the random flow and the Southern-Hemisphere PDFs in ECMWF winds show time-invariant exponential tails, consistent with theoretical predictions. In the Northern Hemisphere, the PDFs exhibit non-Gaussian tails. However, the PDF tails are not consistent with theoretical expectations. The long-term behavior of the PDF tails of the forced tracer is compared to that of a decaying tracer. It is found that the PDF tails of the decaying tracer are time-dependent, and evolve toward flatter than exponential.

Joint probability distribution of winds and waves from wave simulation of 20 years (1989-2008) in Bohai Bay

The joint probability distribution of wind speed and significant wave height in the Bohai Bay was investigated by comparing the Gurnbel logistic model, the Gumbel-Hougaard （GH） copula function, and the Clayton copula function. Twenty years of wind data from 1989 to 2008 were collected from the European Centre for Medium-Range Weather Forecasts （ECMWF） database and the blended wind data of the Quick Scatterometer （QSCAT） satellite data set and re-analysis data from the United States National Centers for Environmental Prediction （NCEP）. Several typhoons were taken into account and merged with the background wind fields from the ECMWF or QSCAT/NCEP database. The 20-year data of significant wave height were calculated with the unstructured-grid version of the third-generation wind wave model Simulating WAves Nearshore （SWAN） under extreme wind process conditions. The Gumbel distribution was used for univariate and marginal distributions. The distribution parameters were estimated with the method of L-moments. Based on the marginal distributions, the joint probability distributions, the associated return periods, and the conditional probability distributions were obtained. The GH copula function was found to be optimal according to the ordinary least squares （OLS） test. The results show that wind waves are the prevailing type of wave in the Bohai Bay.

Single point velocity distributions in homogeneous isotropic turbulence

The starting point for this paper lies in the results obtained by Tatsumi （2004） for isotropic turbulence with the self-preserving hypothesis. A careful consideration of the mathematical structure of the one-point velocity distribution function equation obtained by Tatsumi （2004） leads to an exact ＂analysis of all possible cases and to all admissible solutions of the problem. This paper revisits this interesting problem from a new point of view, and obtains a new complete set of solutions. Based on these exact solutions, some physically significant consequences of recent advances in the theory of homogenous statistical solution of the Navier-Stokes equations are presented. The comparison with former theory was also made. The origin of non-Caussian character could be deduced from the above exact solutions.

Establishment Method of a Mixture Model and Its Practical Application for Transmission Gears in an Engineering Vehicle

Highly versatile machines, such as wheel loaders, forklifts, and mining haulers, are subject to many kinds of working conditions, as well as indefinite factors that lead to the complexity of the load. The load probability distribution function （PDF） of transmission gears has many distributions centers; thus, its PDF cannot be well represented by just a single-peak function. For the purpose of representing the distribution characteristics of the complicated phenomenon accurately, this paper proposes a novel method to establish a mixture model. Based on linear regression models and correlation coefficients, the proposed method can be used to automatically select the best-fitting function in the mixture model. Coefficient of determination, the mean square error, and the maximum deviation are chosen and then used as judging criteria to describe the fitting precision between the theoretical distribution and the corresponding histogram of the available load data. The applicability of this modeling method is illustrated by the field testing data of a wheel loader. Meanwhile, the load spectra based on the mixture model are compiled. The comparison results show that the mixture model is more suitable for the description of the load-distribution characteristics. The proposed research improves the flexibility and intelligence of modeling, reduces the statistical error and enhances the fitting accuracy, and the load spectra complied by this method can better reflect the actual load characteristic of the gear component.

Coverage of communication-based sensor nodes deployed location and energy efficient clustering algorithm in WSN

An effective algorithm based on signal coverage of effective communication and local energy-consumption saving strategy is proposed for the application in wireless sensor networks.This algorithm consists of two sub-algorithms.One is the multi-hop partition subspaces clustering algorithm for ensuring local energybalanced consumption ascribed to the deployment from another algorithm of distributed locating deployment based on efficient communication coverage probability（DLD-ECCP）.DLD-ECCP makes use of the characteristics of Markov chain and probabilistic optimization to obtain the optimum topology and number of sensor nodes.Through simulation,the relative data demonstrate the advantages of the proposed approaches on saving hardware resources and energy consumption of networks.

Time-Delayed Feedback Control in a Single-Mode Laser System

The effects of time-delayed feedback control in a single-mode laser system is investigated.Using the smalltime delay approximation,the analytic expression of the stationary probability distribution function of the laser field isobtained.The mean,normalized variance and skewness of the steady-state laser intensity are calculated.It is found thatthe time-delayed feedback control can suppress the intensity fluctuation of the laser system.The numerical simulationsare in good agreement with the approximate analytic results.

Wave Energy Estimation by Using A Statistical Analysis and Wave Buoy Data near the Southern Caspian Sea

Statistical analysis was done on simultaneous wave and wind using data recorded by discus-shape wave buoy. The area is located in the southern Caspian Sea near the Anzali Port. Recorded wave data were obtained through directional spectrum wave analysis. Recorded wind direction and wind speed were obtained through the related time series as well. For 12-month measurements（May 25 2007-2008）, statistical calculations were done to specify the value of nonlinear auto-correlation of wave and wind using the probability distribution function of wave characteristics and statistical analysis in various time periods. The paper also presents and analyzes the amount of wave energy for the area mentioned on the basis of available database. Analyses showed a suitable comparison between the amounts of wave energy in different seasons. As a result, the best period for the largest amount of wave energy was known. Results showed that in the research period, the mean wave and wind auto correlation were about three hours. Among the probability distribution functions, i.e Weibull, Normal, Lognormal and Rayleigh, ＂Weibull＂ had the best consistency with experimental distribution function shown in different diagrams for each season. Results also showed that the mean wave energy in the research period was about 49.88 k W/m and the maximum density of wave energy was found in February and March, 2010.

Enhancement of density divergence in an insect outbreak model driven by colored noise

The steady states and the transient properties of an insect outbreak model driven by Gaussian colored noise are studied in this paper. According to the Fokker-Planck equation in the unified colored-noise approximation, we analyse the stationary probability distribution and the mean first-passage time of this model. By numerical analysis, the effects of the self-correlation time of insect birth rate and predation rate respectively reveal a manifest population divergence on the insect density. The decrease of the mean first-passage time indicates an enhancement dynamic on the density divergency with colored noise of a large self-correlation time based on the insect outbreak model.

An Experimental Study on the Void Fraction for Gas-Liquid Two-Phase Flows in a Horizontal Pipe

The flow patterns and the void fraction related to a gas-liquid two-phase flow in a small channel are experimentally studied.The test channel is a transparent quartz glass circular channel with an inner diameter of 6.68 mm.The working fluids are air and water and their superficial velocities range from 0.014 to 8.127 m/s and from 0.0238 to 0.556 m/s,respectively.The void fraction is determined using the flow pattern images captured by a high-speed camera,while quick closing valves are used for verification.Four flow patterns are analyzed in experiments:slug flow,bubbly flow,annular flow and stratified flow.For intermittent flows(bubbly flow and slug flow),the cross-sectional void fraction is in a borderline condition while its probability distribution function(PDF)image displays a bimodal structure.For continuous flows(annular flow and stratified flow)the cross-sectional void fraction behaves as a fluctuating continuous curve while the(PDF)image displays a single peak structure.The volumetric void fraction data are also compared with available predictive formulas,and the results show that the agreement is very good.An effort is also provided to improve the so-called Gregory and Scott model using the available data.

Extreme Values of Wind Speed over the Kara Sea Based on the ERA5 Dataset

Extreme values of wind speed were studied based on the highly detailed ERA5 dataset covering the central part of the Kara Sea. Cases in which the ice coverage of the cells exceeded 15% were filtered. Our study shows that the wind speed extrema obtained from station observations, as well as from modelling results in the framework of mesoscale models, can be divided into two groups according to their probability distribution laws. One group is specifically designated as black swans, with the other referred to as dragons (or dragon-kings). In this study we determined that the data of ERA5 accurately described the swans, but did not fully reproduce extrema related to the dragons;these extrema were identified only in half of ERA5 grid points. Weibull probability distribution function (PDF) parameters were identified in only a quarter of the pixels. The parameters were connected almost deterministically. This converted the Weibull function into a one-parameter dependence. It was not clear whether this uniqueness was a consequence of the features of the calculation algorithm used in ERA5, or whether it was a consequence of a relatively small area being considered, which had the same wind regime. Extremes of wind speed arise as mesoscale features and are associated with hydrodynamic features of the wind flow. If the flow was non-geostrophic and if its trajectory had a substantial curvature, then the extreme velocities were distributed according to a rule similar to the Weibull law.

Dynamic Stability and Fuzzy Reliability Analysis of Toppling Perilous Rock Under Seismic Excitation

To predict the occurrence of the collapse disaster in toppling perilous rock under the action of bidirectional earthquakes,the dynamic stability and fuzzy reliability calculation method of toppling perilous rock under the action of bidirectional earthquakes is proposed.First,the mass viscoelasticity model is used to simulate two main control surfaces of toppling perilous rock,the seismic dynamic response model and motion equation of toppling perilous rock are established based on the D'Alembert principle,and the Newmark-β method is used to solve the dynamic motion equation.Then,the instability event of toppling perilous rock is considered a fuzzy event,the membership function expression of the stability coefficient of toppling perilous rock is determined based on the fuzzy failure criterion,the calculation equations of the toppling perilous rock dynamic stability coefficient and fuzzy reliability are established,and the fuzzy reliability evaluation method based on the probability distribution of reliability is proposed.Finally,the influence of different superposition modes of seismic excitation on the fuzzy reliability of toppling perilous rock is analyzed.The calculation results of toppling perilous rock in the engineering case show that the fuzzy reliability calculated after considering the fuzzy failure criterion is reduced by 10.73% to 25.66% compared with the classical reliability.Considering the bidirectional seismic excitation,the fuzzy reliability of toppling perilous rock is reduced by 5.46% to 14.89%.Compared with using the acceleration peak time encounter mode to superpose the seismic excitation,the fuzzy reliability of toppling perilous rock is reduced by 3.4% when the maximum action effect time encounter mode is adopted.

ON THE PDF MODELS FOR ATMOSPHERIC DIFFUSION IN BOUNDARY LAYER

In this paper, taking its turbulent exchange coefficient as a function of the Lagrangian time scale and standard variance of the turbulence in atmosphere, the atmospheric dispersion PDF models are obtained on the basis of atmospheric diffusion K-theory. In the model the statistics of wind speed are directly used as its parameters instead of classic dispersion parameters. The bi- Gaussian PDF is derived in convective boundary layer (CBL), from the statistics of vertical velocity in both of the downdraft and updraft regions that are investigated theoretically in the other part of this paper. Giving the driven parameters of the CBL (including the convective velocity scale w* and the mixing depth h_i) and the time-averaged wind speed at release level, the PDF model is able to simulate the distribution of concentration released at any levels in the CBL. The PDF's simulations are fairly consistent with the measurements in CONDORS experiment or the results brought out by some numerical simulations.

Regional moment-independent sensitivity analysis with its applications in engineering

Traditional Global Sensitivity Analysis（GSA） focuses on ranking inputs according to their contributions to the output uncertainty.However,information about how the specific regions inside an input affect the output is beyond the traditional GSA techniques.To fully address this issue,in this work,two regional moment-independent importance measures,Regional Importance Measure based on Probability Density Function（RIMPDF） and Regional Importance Measure based on Cumulative Distribution Function（RIMCDF）,are introduced to find out the contributions of specific regions of an input to the whole output distribution.The two regional importance measures prove to be reasonable supplements of the traditional GSA techniques.The ideas of RIMPDF and RIMCDF are applied in two engineering examples to demonstrate that the regional moment-independent importance analysis can add more information concerning the contributions of model inputs.

Modified Moment-based Image Watermarking Method Robust to Cropping Attack

Developing a watermarking method that is robust to cropping attack is a challenging task in image watermarking. The moment-based watermarking schemes show good robustness to common signal processing attacks and some geometric attacks but are sensitive to cropping attack. In this paper, we modify the moment-based approach to deal with cropping attack. Firstly, we find the probability density function （PDF） of the pixel value distribution from the original image. Secondly, we reshape and normalize the pdf of the pixel value distribution （PPVD） to form a two dimensional image. Then, the moment invariants are calculated from the PPVD image. Since PPVD is insensitive to cropping, the proposed method is robust to cropping attack. Besides, it also has high robustness against other common attacks. Theoretical analysis and experimental results demonstrate the effectiveness of the proposed method.