引用：刘磊，胡非，吕瑞，2018，《大气边界层湍流风速脉动的多尺度统计特征及其统计模拟：回顾与展望》，首届中国空气动力学大会论文摘要集（上），文章编号：CARS-01-2018-010 博文发表时略有修改。 1 引言 大气边界层湍流风速脉动是具有高雷诺数的多尺度流体运动。如果从 Navier-Stokes 方程出发，直接模拟大气边界层湍流，以现今常用的计算机运算速度，需要耗费巨量的机时，无法满足边界层研究和工程应用上的需求。为了提高湍流的模拟效率，人们提出了各种替代模拟方案，例如雷诺平均模拟以及大涡模拟。替代方案大大提高了湍流的模拟效率，但在模拟具有复杂下垫面的边界层湍流时，仍需要花费大量的机时，还是无法满足风工程应用中的时效性要求。为此，基于湍流风速脉动统计特征分析的统计模拟方法，以其运算简便、快捷和有效，在工程领域得到广泛应用。本文将对国内外大气边界层湍流风速脉动多尺度统计特征及其统计模拟方面的主要工作进行梳理，其中穿插介绍了作者近年来的研究工作。最后，本文对该领域可能的发展方向和亟待解决的问题进行了总结。 2 大气边界层湍流风速脉动的多尺度统计特征 在各向同性湍流理论的研究中，不同尺度湍涡的运动通常用空间两点的速度差来表示，湍涡的特征尺度即是空间两点的距离。其他的“尺度”定义方式，例如基于傅里叶变换、小波变换或希尔伯特 - 黄变换等的尺度分离方式，并不影响主要结论。在大气边界层湍流的观测中，较为容易获取的是单点风速时间序列。在泰勒假设成立的情况下，不同时刻风速增量和空间两点速度差的描述方式是等价的。因此，大气湍流研究中多分析的是不同时刻的风速增量。风速增量的研究除了具有理论和建模的意义外，也具有实际的工程意义，例如来流横向方向的风速增量会对结构带来额外的转矩 。 2.1 小尺度间歇性 实验室湍流观测表明，当空间中两点之间的距离逐渐变小时，湍流在这两点速度差值的极值出现的概率逐渐增加，表现为明显的间歇性特征，这种特征称为湍流小尺度间歇性特征 。图 1 是一段 5 分钟相邻风速增量的时间序列，表现出明显的小尺度间歇性特征。湍流小尺度间歇性特征可以通过概率密度函数进行定量的研究。由于极值事件出现的概率增加，小尺度湍流概率密度函数的尾分布比高斯分布长，而大尺度湍流没有间歇性特征，仍然近似满足高斯分布 。许多湍流唯像模型可用来拟合湍流的多尺度概率密度函数，例如对数正态分布模型 和对数泊松模型 等。如果在湍流随机映射模型的框架下，这些概率密度函数又可以统一成为一种称为对数无穷可分分布的数学形式 。 图 1 风速增量的小尺度间歇性特征。风速观测频率 100Hz ，风速增量时间间隔 .0.05s 研究表明，虽然大气湍流不具有各向同性的特征，但其概率密度函数随尺度的变化与实验室湍流相似，也是小尺度为非高斯长尾分布，大尺度近似为高斯分布 。作者曾分析过台风和沙尘暴等极端天气条件下的湍流特征，发现其小尺度的间歇性特征与普通天气下的特征相似 。大气湍流脉动的概率密度函数一般认为满足对数正态分布 。然而，作者通过数据分析发现，尽管对数正态分布可以很好地拟合数据，但在拟合高阶矩和回归概率方面存在不协调的结果，表明该模型仍然有需要改进的地方 。与实验室湍流不同，大气湍流小尺度间歇性与大尺度涡旋特征有关，并不是普适的。大气湍流的间歇性主要有两方面来源：稳定边界层间歇性失稳结构 和对流边界层热泡 。作者曾根据大气湍流脉动的概率密度函数特征，提出了一种提取湍流间歇性信号的方法，并详细研究了稳定和对流边界层中间歇性信号的统计特征及其参数化形式 。 2.2 多重分形 分形是上世纪 70 年代 Mandelbrot 提出的概念，它揭示了自然界看似复杂无规则的几何体中普遍存在简单的自相似特征 。分形分为单分形和多重分形。对随机过程而言，前者可用来描述随机过程曲线的自相似特征，后者可用来描述随机过程增量的自相似特征。单分形和多分形不是互斥的，两者从不同角度描述了随机过程的自相似特征，前者本质上反映了随机过程的二阶矩特征，后者本质上反映了随机过程的多阶矩特征。 实验室湍流的观测和理论分析发现，惯性区各向同性湍流普遍具有多重分形特征，其空间两点速度差的高阶矩具有幂函数特征，幂指数是关于阶次的非线性函数，该函数是普适的，可用对数泊松模型很好地拟合 。研究表明，大气湍流风速增量的高阶矩也具有类似的多重分形特征 ，且常用对数正态模型来拟合 。图 2 是大气湍流风速增量的高阶矩的一个示例，可见其在小尺度具有幂函数特征。大气湍流的多重分形特征与大尺度涡旋结构有关，并不像实验室湍流那样是普适规律，而是随着时间、平均风速和稳定度变化 。 图 2 大气湍流风速增量的高 阶矩 2.3 长程相关 所谓长程相关，在数学上指的是时间序列的关联函数具有幂函数的形式，且幂指数在(0,1)区间内。对于无关联或短程相关的时间序列，关联函数具有有限的全局积分，而对于长程相关的时间序列，关联函数的全局积分发散。研究表明，看起来平坦的白噪声随机时间序列，加入长程关联特征后，会出现大尺度波动特征，这种波动可以导致极值事件集中出现 。因此，湍流风速脉动长程相关特征的研究，不仅用于统计建模，在设计抗风结构等工程应用方面也具有重要意义。 研究表明，大气湍流风速脉动具有长程相关特征，且刻画长程相关程度的关联指数随时间变化，这表明湍流风速脉动的长程相关特征也与大尺度涡旋结构有关 。此外，长程相关会影响极值重现时间的分布，作者通过数据分析发现，大气湍流风速脉动的极值重现时间呈扩展指数分布，偏离无关联时的指数分布 。基于上述发现，我们提出了一种基于长程相关的极值统计方法，修正了基于独立样本假设的传统方法对T年一遇极值风速的高估 。 3 大气边界层湍流风速脉动的统计模拟 随着人们对湍流统计特征的深入研究，大气边界层湍流风速脉动的统计模拟从早期单一的仅针对功率谱的模拟，逐步发展到现今融合非高斯、分形、长程相关等特征的全方位模拟。早期的线性滤波法和谐波合成法虽然能真实反映实际风速功率谱，但未考虑到湍流风速脉动的分形特征 。随后，单分形确定型 Weierstrass-Mandelbrot 函数（简称 W-M 函数）被用来模拟湍流风速脉动时间序列 。确定型 W-M 函数模拟随机湍流风速脉动显然不合适，因此作者将 W-M 函数的模拟推广到随机型 。虽然 W-M 函数可以较好模拟出单分形特征，但该函数不能模拟风速脉动的长尾分布，也不能很好模拟功率谱的低频结构 。为此，作者将谐波合成法和 W-M 函数进行融合，提出了谐波 - 分形模拟法，较好地解决了 W-M 函数 不能模拟湍流风速低频结构的问题 。图 3 显示了谐波 - 分形模拟法模拟风速分形特征方面的能力。除了单分形模拟，目前也开展了湍流风速脉动的多重分形模拟 。此外，基于 Fokker-Plank 方程的多尺度统计模拟方法，在模拟不同尺度湍流速度增量概率密度函数等方面具有良好的性能，也是值得关注的一类方法 。 图 3覆盖脉动风速曲线的盒子数和盒子尺度的对应关系：（a）顺风向，（b）侧风向，（c）垂直方向（ ∆ ：实测值， ○：模拟值，实线斜率为5/3）. 基于前期研究工作，作者开发了一套“湍流统计模拟系统 V1.0 （ TurbSS V1.0 ）” 。该系统采用交互式设计，操作简便，具有快速实现多种方法的湍流统计模拟的功能，可广泛用于风能、风工程、航空设计等领域，也可用于湍流模拟的科研和教学展示（图 4 ）。 图 4 湍流统计模拟系统V1.0界面 4 展望 湍流的科学研究虽然经过了上百年的发展，仍未取得实质性突破。湍流研究的著名学者 Lumley 和 Yaglom 甚至断言，即使再经过一百年的发展，湍流研究依然处在滥觞期 。相比于实验室湍流，具有高雷诺数、远离平衡态、非平稳、非均匀和非各向同性以及拥有复杂边界条件的大气湍流的研究工作更是任重道远。对于大气湍流风速脉动的多尺度统计特征，作者认为目前可以开展以下几个方面的研究工作: （ 1 ）大气湍流的多尺度统计特征，如小尺度间歇性特征、分形特征、长程相关特征是相互独立的，还是之间有某种联系？虽然 Muzy 和 Bacry 提出的多重分形随机过程模型揭示了某些特征之间的数学联系 ，但我们仍需要验证这种联系是否适用于大气湍流以及在多大程度上适用。 （ 2 ）在前文的回顾中提到过，大气湍流风速脉动小尺度统计特征在定性上与实验室湍流类似，只不过后者的统计特征具有普适性，前者与大尺度涡旋或边界层结构相关，不具有普适性。大气湍流的多尺度统计特征与哪些物理量相关？如何建立其与相关物理量的定量关系？ （3）目前开展的湍流风速脉动的模拟多是针对单点时间序列。在实际应用中，有时需要用到空间多点的风速脉动模拟，例如风力发电机叶片上多点载荷的分析。因此，大气湍流风速脉动在空间多点的关联统计特征分析以及时-空协同的统计模拟，也是值得研究的问题。 （4）近年来，超统计( superstatistics )理论被用来拟合湍流风速脉动的概率的函数 。超统计给出了可能不同于对数无穷可分分布的另一类统计分布。超统计根源于非平衡统计物理学的随机动力理论，具有较强的物理意义。然而，与数据拟合较好的对数正态分布既属于对数无穷可分分布，又属于超统计分布，目前尚未从实验中区分出湍流风速脉动究竟属于哪一类分布。大气湍流作为典型的非平衡复杂系统，是否与超统计相关？其背后的随机动力学是什么？对这些问题的研究，可能会加深我们对多尺度统计特征物理本质的认识。 参考文献 Peinke J, Barth S, Boettcher F, et al. 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Neil Kelley 风能咨询气象专家。 年龄应该有70多岁，2011年获得 NREL Chairman's Outstanding Achievement Award。 他的研究主要包括大气湍流对风机结 构 的影 响和风机低频噪声的产生等方面。作为一名将大气科学有关的知识应用于风力发电研究的气象专家， 从1980年代开始（属于 最早 一批气象 领域做风能应用研究的人），持续几十年一直研究与风能应用有关的问题， 是我的楷模。 Neil Kelley's Education Penn State University Ph.D Candidate , Meteorology 1968–1971 Penn State University M.S. , Meteorology 1965–1968 St. Louis University B.S. in Professional Meteorology , Meteorology 1959–1963 Neil Kelley's Publications Turbulence-Turbine Interaction: The Basis for the Development of the TurbSim Stochastic Simulator National Renewable Energy Laboratory, NREL/TP-5000-52353 November 2011 Authors: Neil Kelley A combination of taller wind turbines with more flexible rotors and towers operating in turbulent conditions that are not well understood is contributing to much higher than anticipated maintenance and repairs costs and is associated with lower energy production. This report documents evidence of this and offers the turbine designers an expanded tool that resolves many of these shortcomings. It... more Overview of the TurbSim Stochastic Inflow Turbulence Simulator: Version 1.21 (Revised Feb 1, 2007) National Renewable Energy Laboratory, NREL/TP-500-41137 April 2007 Authors: Neil Kelley , Bonnie J. Jonkman The TurbSim stochastic inflow turbulence simulator was developed to provide a numerical simulation of a full-field inflow to a wind turbine that contains bursts of coherent turublence seen in atmospheric instabilties associated with nocturnal boundary layer flows. This document provides the user with a generalized overview of how the code was developed and some of the theory behind it. Comparing Pulsed Doppler LIDAR with SODAR and Direct Measurements for Wind Assessment National Renewable Energy Laboratory, NREL/TP-500-41192 July 2007 Authors: Neil Kelley , Bonnie J. Jonkman, George N. Scott, Yelena L. Pichugina There is a pressing need for good wind-speed measurements at greater and greater heights to assess the availability of the resource in terms of power production and to identify any frequently occurring atmospheric structural characteristics that may create turbulence that impacts the operational reliability and lifetime of their components. This paper summarizes the results of a short study that... more The Great Plains Turbulence Enviroment: Its Origins, Impact, and Simulation National Renewable Energy Laboratory, NREL/TP-500-40176 December 2006 Authors: Neil Kelley , Bonnie J. Jonkman, George N. Scott This paper summarizes the known impacts of nocturnal turbulence on wind turbine performance and operations and discusses NREL's progress in numerically simulating coherent inflow turbulent conditions generated by atmospheric instabilities that are frequently associated with a Great Plains nocturnal low-level jet stream. The Impact of Coherent Turbulence on Wind Turbine Aeroelastic Response and Its Simulation National Renewable Energy Laboratory, NREL/TP-500-41192 August 2005 Authors: Neil Kelley , Bonnie J. Jonkman, George N. Scott, Jan T. Bialasiewicz, and Lisa S. Redmond In this paper, we present a brief overview of our recent research results regarding the impact of organized or coherent inflow turbulence on the dynamic response of operating wind turbines. Previous field measurements has demonstrated that the greatest structural fatigue tends to occur during the nighttime hours from coherent turbulence that develops in the stable, nocturnal atmospheric boundary... more Using Wavelet Analysis to Assess Turbulence/Rotor Interactions Wind Energy, Vol. 3., No. 3 2000 Authors: Neil Kelley , Richard M. Osgood, Jan T. Bialasiewicz Large loading events on wind turbine rotor blades are often associated with transient bursts of coherent turbulent energy in the turbine inflow. These coherent turbulent structures are identified as peaks in the three-dimensional, instantaneous, turbulent shearing stress field. Such organized inflow structures and the accompanying rotor aeroelastic responses typically have timescales of only a few... more Using Time-Frequency and Wavelet Analysis to Assess Turbulence/Rotor Interactions National Renewable Energy Laboratory, NREL/CP-500-32242 2000 Authors: Neil Kelley , Richard M. Osgood, Jan T. Bialasiewicz, Andre Jakubowski Large loading events on wind turbine rotor blades are often associated with transient bursts of coherent turbulent energy in the turbine inflow. These coherent turbulent structures are identified as peaks in the three-dimensional, instantaneous, turbulent shearing stress field. Such organized inflow structures and the accompanying rotor aeroelastic responses typically have time scales of only a... more A Case for Including Atmospheric Thermodynamic Variables In Wind Turbine Fatigue Loading Parameter Identification National Renewable Energy Laboratory, NREL/CP-500-26829 July 1999 Authors: Neil Kelley This paper makes the case for establishing efficient predictor variables for atmospheric thermodynamics that can be used to statistically correlate the fatigue accumulation seen on wind turbines. Recently, two approaches to this issue have been reported. One uses multiple linear-regression analysis to establish the relative causality between a number of predictors related to the turbulent inflow... more A Progress Report on the Characterization and Modeling of a Very Flexible Wind Turbine Design National Renewable Energy Laboratory, NREL/CP-500-25513 October 1998 Authors: Neil Kelley , Alan Wright, Richard Osgood In this paper we discuss a few early results from our recently completed field measurement effort. We found that the turbine rotor response was dominated by a once per-revolution oscillation that was responsible for large cyclic variations in the output power. The available evidence points to a rotor imbalance related to structural differences in one of the blades and a misalignment of the pitch... more Long-Term Simulation of Turbulence-Induced Loads Using the SNLWIND-3D, FAST, YawDyn, and ADAMS(TM) Numerical Codes American Institute of Aeronautics Astronautics January 9, 1997 Authors: Neil Kelley , Alan Wright, Marshall Buhl, James Tangler Collection of the 1997 ASME Wind Energy Symposium Technical Papers Presented at the 35th AIAA Aerospace Sciences Meeting and Exhibit, 6-9 January 1997, Reno, Nevada. Washington, DC: American Institute of Aeronautics and Astronautics pp. 74-85; NREL Report No. 23277. Damage Estimates from Long-Term Structural Analysis of a Wind Turbine in a U.S. Wind Farm Environment American Institute of Aeronautics Astronautics January 9, 1997 Authors: Neil Kelley , Herbert Sutherland Collection of the 1997 ASME Wind Energy Symposium Technical Papers Presented at the 35th AIAA Aerospace Sciences Meeting and Exhibit, 6-9 January 1997, Reno, Nevada. Washington, DC: American Institute of Aeronautics and Astronautics pp. 74-85; NREL Report No. 23277. Observed Acoustic and Aeroelastic Spectral Responses of a MOD-2 Turbine Blade to Turbulence Excitation DOE/NASA 1995 Authors: Neil Kelley , Ed McKenna, Eric Jacobs Spera, D. A., ed. Collected Papers on Wind Turbine Technology. DOE/NASA/5776-2. pp. 221-227; NREL Report No. 20614 Lamar Low-Level Jet Project: Interim Report National Renewable Energy Laboratory, NREL/TP-500-34593 January 2004 Authors: Neil Kelley , Mari Shirazi, David Jager, Scott Wilde, James Adams, Marshall Buhl, Peter Sullivan, Ned Patton This interim report presents the results to date from the Lamar Low-Level Jet Program (LLLJP) that has been established as a joint effort between the U.S. Department of Energy (DOE), the National Wind Technology Center (NWTC) of the National Renewable Energy Laboratory (NREL), and General Electric Wind Energy (GE Wind). The purpose of this project was to develop an understanding of the influence... more Discussion of the Results of the Rainflow Counting of a Wide Range of Dynamics Associated with the Simultaneous Operation of Adjacent Wind Turbines Windpower '92: Proceedings of the American Wind Energy Association Conference, 19-23 October 1992, Seattle, Washington October 1993 Authors: Neil Kelley , Gary Desrochers, James Tangler, Brian Smith The comparison of the rainflow fatigue counting results from structural measurements on two adjacent 65-kW wind turbines at Row 37 in a 41-row wind farm in Southern California Full Vector (3-D) Inflow Simulation in Natural and Wind Farm Environments Using An Expanded Version of the SNLWIND (Veers) Turbulence Code National Renewable Energy Laboratory, NREL/TP-442-5225 November 1992 Authors: Neil Kelley Recent measurements have indicated that the temporal and spatial coherence of the inflow turbulence may be associated with many of the observed extreme structural oad events. Several such extreme structural and peak power episodes have been traced to periods when the turbine rotor encountered patches of coherent turbulence. These coherent structures are identified by short-lived excursions in the... more Comparison of Predicted and Observed Turbulent Wind Fields Present in Natural and Internal Wind Park Environments National Renewable Energy Laboratory, NREL/TP-257-4508 September 1991 Authors: Neil Kelley , Alan Wright American Wind Energy Association, Windpower '91 Conference and Exposition, Palm Springs, California, 24-27 September, 1991 Discussion of the Results of an In-Situ Comparison of Three Full-Vector Anemometers National Renewable Energy Laboratory, NREL/TP-257-4019 1990 Authors: Neil Kelley , George Scott, Jack Allread for the 7th Symposium on Meterological Observations and Instrumentation, American Meteorological Society 71st Annual Meeting, 13-18 January 1991, New Orleans, Louisiana An Initial Look at the Dynamics of the Microscale Flow Field within a Large Wind Farm in Response to Variations in the Natural Inf National Renewable Energy Laboratory, NREL/TP-257-3591 1989 Authors: Neil Kelley Prepared for the American Wind Energy Association Wind Power '89 Conference and Exposition, San Francisco, California, 24-27 September 1989 The MOD-2 Wind Turbine: Aeroacoustical Noise Sources, Emissions, and Potential Impact Solar Energy Research Insitutute (now NREL) SERI/TR-217-3036 January 1988 Authors: Neil Kelley , Edward McKenna, Eric Jacobs, Robert Hemphill, Nancy Birkenheuer This report summarizes research into characteristics of acoustic noise emissions of the 2.5 MW DOE/NASA MOD-2 wind turbine. The results of this study showed that the MOD-2 noise levels are well below annoyance thresholds within residential structures a kilometer or more from the turbine rotor. It was also found that the inflow turbulent structure has a major influence on the level and... more A Proposed Metric for Assessing the Potential of Community Annoyance from Wind Turbine Low-Frequency Noise Emissions Solar Energy Research Insitutute (now NREL) SERI/TR-217-3261 November 1987 Authors: Neil Kelley Given our initial experience with the low-frequency, impulsive noise emissions from the MOD-1 wind turbine and their impact on the surrounding community, the ability to assess the potential of interior low-frequency annoyance in homes located near wind turbine installations may be important. Since there are currently no universally accepted metrics or descriptors for. Iow-frequency community... more Acoustic Noise Associated with the MOD-1 Wind Turbine: Its Source, Impact, and Control Solar Energy Research Insitutute (now NREL) SERI/TR-635-1166 February 1985 Authors: Neil Kelley , Edward McKenna, Robert Hemphill, Carol Etter, Richard Garrelts, N. Linn This document summarizes the results of an extensive investigation into the factors surrounding noise complaints related to the operation of the 2-MW DOE/NASA wind turbine installed atop Howard's Knob near Boone, North Carolina Observed Acoustic and Aeroeleastic Spectral Responses of a MOD-2 Turbine Blade to Turbulence Excitation National Renewable Energy Laboratory, NREL/TP-214-2374 1984 Authors: Neil Kelley , Edward McKenna, Eric Jacobs This document summarizes the results of an extensive investigation into the factors relating to the acoustic emissions associated with the operation of a MOD-2 wind turbine. Three of the turbines used for the work reported here were located at the Goodnoe Hills Wind Turbine Site near Goldendale, WA. Acoustic Ranging Technique for Assessing Low-Frequency Acoustic Noise from Wind Turbines Wind Engineering, Vol. 8 (1), pp. 19-22 1984 Authors: Neil Kelley , Robert Hemphill 以上内容，主要参考来自http://www.linkedin.com/pub/neil-kelley/13/888/b58
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