FUZZY CLUSTER ANALYSIS OF TURBULENT SCALES

Turbulent motion could be regarded as the superposition of fluctuations with different scales. It's of great theoretical and practical importance to determine the classification of turbulent scales quantitatively to the better description of vortex motions with different scales, and to the research of the interaction among different sclaes of vortex and the construction of better turbulent models. The mathematical method, which carries out the classification on a certain requirement, is called cluster analysis. In this paper, fuzzy cluster analysis method is used to study the classification of turbulent scales quantitatively in smooth and rough wall boundary conditions. Furthermore, the properties and interactions among all kinds of flow structures are also studied. The results are helpful to gain some insight into the properties and interactions of all kinds of turbulent scales in wall turbulent shear flow.

Universal hierarchical symmetry for turbulence and general multi-scale fluctuation systems

Scaling is an important measure of multi-scale fluctuation systems. Turbulence as the most remarkable multi-scale system possesses scaling over a wide range of scales. She-Leveque （SL） hierarchical symmetry, since its publication in 1994, has received wide attention. A number of experimental, numerical and theoretical work have been devoted to its verification, extension, and modification. Application to the understanding of magnetohydrodynamic turbulence, motions of cosmic baryon fluids, cosmological supersonic turbulence, natural image, spiral turbulent patterns, DNA anomalous composition, human heart variability are just a few among the most successful examples. A number of modified scaling laws have been derived in the framework of the hierarchical symmetry, and the SL model parameters are found to reveal both the organizational order of the whole system and the properties of the most significant fluctuation structures. A partial set of work related to these studies are reviewed. Particular emphasis is placed on the nature of the hierarchical symmetry. It is suggested that the SL hierarchical symmetry is a new form of the self-organization principle for multi-scale fluctuation systems, and can be employed as a standard analysis tool in the general multi-scale methodology. It is further suggested that the SL hierarchical symmetry implies the existence of a turbulence ensemble. It is speculated that the search for defining the turbulence ensemble might open a new way for deriving statistical closure equations for turbulence and other multi-scale fluctuation systems.

Study on Horizontal Relative Diffusion in theTroposphere and Lower Stratosphere

The behaviour of relative diffusion theory and Gifford’s random-force theory for long-range atmospheric diffusion is examined. When a puff scale is smaller than the Lagrangian length scale, √2KTL, an accelerative relative diffusion region exists, i.e., σy∝ t 3/2. While the puff diffusion enters a two-dimensional turbulence region, in which the diffusion scale is larger than 500 km, or time scale is larger than 1 day, divergence and convergence are main cause of horizontal diffusion. Between the two above-mentioned regimes, diffusion deviation is given by σy = √2KT. The large-scale horizontal relative diffusion parameters were obtained by analyzing the data of radioactive cloud width collected in air nuclear tests. Key words Tropospheric and lower stratospheric diffusion - Relative diffusion - Large scale turbulence - Nuclear explosion clouds This work is sponsored by the National Natural Science Foundation of China under Grant No. 49505064.The author would like to thank Prof. Chen Jiayi Department of Geophysics of Peking University and Dr. Cai Xiaoming School of Geography and Environmental Sciences of Birmingham University for their helpful discussions.

Corrections to the scaling of the second-order structure function in isotropic turbulence

The approach of Obukhov assuming a constant skewness was used to obtain analytical corrections to the scaling of the second order structure function, starting from Kolmogorov＇s 4/5 law. These corrections can be used in model applications in which explicit expressions, rather than numerical solutions are needed. The comparison with an interpolation formula proposed by Batchelor, showed that the latter gives surprisingly precise results. The modification of the same method to obtain analytical corrections to the scaling law, taking into account the possible corrections induced by intermittency, is also proposed.

Structural subgrid-scale modeling for large-eddy simulation: A review

Accurately modeling nonlinear interactions in turbulence is one of the key challenges for large-eddy simulation（LES） of turbulence. In this article, we review recent studies on structural subgrid scale modeling, focusing on evaluating how well these models predict the effects of small scales. The article discusses a priori and a posteriori test results. Other nonlinear models are briefly discussed, and future prospects are noted.

The Effects of Turbulence Intensity and Tip Speed Ratio on the Coherent Structure of Horizontal-Axis Wind Turbine Wake:A Wind Tunnel Experiment

The evolution laws of the large-eddy coherent structure of the wind turbine wake have been evaluated via wind tunnel experiments under uniform and turbulent inflow conditions.The spatial correlation coefficients,the turbulence integral scales and power spectrum are obtained at different tip speed ratios(TSRs)based on the time-resolved particle image velocity(TR-PIV)technique.The results indicate that the large-eddy coherent structures are more likely to dissipate with an increase in turbulence intensity and TSR.Furthermore,the spatial correlation of the longitudinal pulsation velocity is greater than its axial counterpart,resulting into a wake turbulence dominated by the longitudinal pulsation.With an increase of turbulence intensity,the integral scale of the axial turbulence increases,meanwhile,its longitudinal counterpart decreases.Owing to an increase in TSR,the integral scale of axial turbulence decreases,whereas,that of the longitudinal turbulence increases.By analyzing the wake power spectrum,it is found that the turbulent pulsation kinetic energy of the wake structure is mainly concentrated in the low-frequency vortex region.The dissipation rate of turbulent kinetic energy increases with an increase of turbulence intensity and the turbulence is transported and dissipated on a smaller scale vortex,thus promoting the recovery of wake.

A Closure for Isotropic Turbulence Based on Extended Scale Similarity Theory in Physical Space

The closure of a turbulence field is a longstanding fundamental problem, while most closure models are introduced in spectral space. Inspired by Chou＇s quasi-normal closure method in spectral space, we propose an analytical closure model for isotropic turbulence based on the extended scale similarity theory of the velocity structure function in physical space. The assumptions and certain approximations are justified with direct numerical simulation. The asymptotic scaling properties are reproduced by this new closure method, in comparison to the classical Batchelor model.

Enhancing PIV image and fractal descriptor for velocity and shear stresses propagation around a circular pier

In this study,the fractal dimensions of velocity fluctuations and the Reynolds shear stresses propagation for flow around a circular bridge pier are presented.In the study reported herein,the fractal dimension of velocity fluctuations（u′,v′,w′） and the Reynolds shear stresses（u′v′ and u′w′） of flow around a bridge pier were computed using a Fractal Interpolation Function（FIF） algorithm.The velocity fluctuations of flow along a horizontal plane above the bed were measured using Acoustic Doppler Velocity meter（ADV）and Particle Image Velocimetry（P1V）.The PIV is a powerful technique which enables us to attain high resolution spatial and temporal information of turbulent flow using instantaneous time snapshots.In this study,PIV was used for detection of high resolution fractal scaling around a bridge pier.The results showed that the fractal dimension of flow fluctuated significantly in the longitudinal and transverse directions in the vicinity of the pier.It was also found that the fractal dimension of velocity fluctuations and shear stresses increased rapidly at vicinity of pier at downstream whereas it remained approximately unchanged far downstream of the pier.The higher value of fractal dimension was found at a distance equal to one times of the pier diameter in the back of the pier.Furthermore,the average fractal dimension for the streamwise and transverse velocity fluctuations decreased from the centreline to the side wall of the flume.Finally,the results from ADV measurement were consistent with the result from PIV,therefore,the ADV enables to detect turbulent characteristics of flow around a circular bridge pier.

ON SIMILARITY AND THE TURBULENT STRUCTURE IN THE STABLE BOUNDARY LAYER

In the stably stratified boundary layer,the vertical flux profiles for momentum and heat can be obtained from an atmospheric boundary layer model which includes parameterization of the long-wave radiation,In addi- tion,the Monin-Obukhov similarity theory can be extended to the whole boundary layer by using the local tur- bulent scales L(z),U_*(z)and 0_*(z)in place of surface layer scales.The similarity predictions are in good agreement with observational data.

AN ESTIMATE OF THE EFFECTS OF LARGE SCALE STRUCTURES ON THE TURBULENT TRANSPORT PROCESSES NEAR WALL

Based on the three-term decomposition model for turbulent flows, the fundamental equations for quasi-periodic motions are obtained, and the approximate analytical solutions of these second-order nonlinear partial differential equations are derived by using the match method. The effects on the mo- mentum, heat and mass transport processes in the wall turbulent flows can be estimated approximately.

Wind Gust and Turbulence Statistics of Typhoons in South China

The wind data of four typhoons were obtained and analyzed. The wind speeds were measured by sonic anemometers at four observation sites in Guangdong and Hainan provinces. Detailed analysis of the wind data was conducted to investigate the turbulence characteristics of the typhoons. Characteristics of the gust factor and the turbulence integral scale of the typhoons were concluded with high confidence. The relationships among the gust factor, gust duration time, mean wind speed, roughness length, and turbulence intensity were described. The turbulence integral scale was found to be closely related to the segment length and turbulence intensity.

Wind characteristics near the ground during typhoon Meari

Wind speed and direction data during typhoon Meari were obtained from eight anemometers installed at heights of 10, 20, 30, and 40 m on a 40-m tower built in the Pudong area of Shanghai. Wind-turbulence characteristics, including wind-speed profile, turbulence integral scale, power spectra, correlations, and coherences were analyzed. Wind-speed profiles varied with time during the passage of Meari. Measured wind-speed profiles could be expressed well by both a power law and a log law. Turbulence integral scales for u, v, and w components all increased with wind speed. The ratios of the turbulence scales among the turbulence components averaged for all 10-min data were 1：0.69：0.08 at 10 m, 1：0.61：0.09 at 20 m, and 1：0.65：0.13 at 40 m. The turbulence integral scales for the u and v components increased with average gust time, but the turbulence integral scale for the w component remained almost constant when the gust duration was greater than 10 min. The decay factor of the coherence function increased slightly with wind speed, with average values for longitudinal and lateral dimensions of 14.3 and 11.3, respectively. The slope rates of the turbulence spectra in the inertial range were less than -5/3 at first, but gradually satisfied the Kolmogorov 5/3 law. The longitudinal wind-power fluctuation spectrum roughly fitted the von Karman spectrum, but slight deviations occurred in the high-frequency band for lateral and vertical wind-power fluctuation spectra.

Scale adaptive simulation of vortex structures past a square cylinder

The scale adaptive simulation（SAS） turbulence model is evaluated on a turbulent flow past a square cylinder using the open-source CFD package OpenF OAM 2.3.0. Two and three-dimensional simulations are performed to determine global quantities like drag and lift coefficients and Strouhal number in addition to mean and fluctuating velocity profiles in the recirculation and wake regions. SAS model is evaluated against the Shear Stress Transport k-ω（SST） model and also compared with previously reported results based on DES, LES and DNS turbulence approaches. Results show that global quantities along with mean velocity profiles are well-captured by 2-D SAS model. The 3-D SAS model also succeeded in providing comparable results with recently published DES study on Reynolds shear stress and velocity fluctuation components using about 12 times lower computational cost. It is shown that large values of the SAS model constant result in too dissipative behavior, so that proper calibration of the SAS model constant for different turbulent flows is vital.

OBSERVATION AND ANALYSIS ON CHARACTERISTIC OF NATURAL RIVERS

Based on the previous study on turbulent structure, field experiments on fluctuation velocity were carried out in section Huanglingmiao of main stream of Yangtze River with a 3-D Doppler velocimeter. And a number of data such as velocity of different discharge and different vertical line were obtained. According to the field experiment data, period, frequency, period function and probability density function of large-scale coherent structure in natural river were prescribed by means of quantitative analysis. And the problem about distribution of time average velocity, turbulent intensity and Reynolds stress along depth were further analyzed and calculated. The results in this paper will deepen the understand of large-scale turbulent structure in natural river and so make the base for applying“turbulence theory” to water conservancy, hydroelectric, environment engineering and so on.

Effect of solid mass flux on anisotropic gas-solid flow in risers determined with an LES-SOM model

Within the framework of the two-fluid approach, gas was treated with a large-eddy simulation and a sub-grid-scale （SGS） turbulent kinetic energy model while particles were treated with a second-order- moment method to describe the anisotropy of the fluctuating velocity. A modified 5imonin model was derived for the gas-solid interphase fluctuating energy transfer. The anisotropic gas-solid flow in a cir- culating fluidized bed was investigated. Predictions were in good agreement with experimental data. The distributions of the second-order moment of particles and SGS-turbulent kinetic energy of gas were simulated at different solid mass fluxes. The effects of the solid mass flux on the particle second-order moment, particle anisotropic behavior, gas SGS-turbulent kinetic energy and gas SGS energy dissipation were analyzed for the circulating fluidized bed.