Generalized variational principles with several arbitrary parameters and the variable substitution and multiplier method

The functional transformations of variational principles in elasticity are classified as three patterns: Ⅰ relaxation pattern, Ⅱ augmented pattern and III equivalent pattern.On the basis of pattern Ⅲ, the generalized variational principles with several arbitrary parameters are formulated and their functionals are defined. They are: the generalized principle of single variable u with several parameters, the generalized principle of two variables u, σ with several parameters, the generalized principle of two variables u, ε with several parameters, and the generalized principle of three veriables u, ε, σ with several parameters. From these principles, a series of new forms of equivalent functionals can be obtained. When the values of these parameters are properly chosen, a series of finite element models can be formulated.In this paper, the question of losing effectiveness for Lagrange multiplier method is also discussed. In order to "recover" effectiveness for multiplier method, a modified method, namely, the variable substitution and multiplier method, is proposed.     

A new representation of energy spectra in fully developed turbulence

It is well known that the Kolmogorov 1941 theory is based on global invariance, in the limit of Reynolds number tending to infinity. Experimentally, it is well verified only for very high Reynolds numbers, namelyR 2000 (Monin and Yaglom 1975).We propose a new experimental representation for energy spectra. Using the Kolmogorov scales, a compilation of dimensionless spectra (E= (k)/(v ⁵)^1/4 andK=k(v ³/)^1/4) shows that log(0.154E)/log(R /R*) is a universal function of log(5.42K)/log(R /R*) withR*=75. This new representation is not compatible with neither local nor global scaling invariance. The constant 5.42 takes into account the small scale intermittency. Similar results have been obtained for velocity structure functions of order 2, 3 and 6. In particular the wavenumber constant 5.42 is independent on the order of the moments.     

Structure Functions in Complex Flows

The turbulence in the ocean and atmosphere is most of the time non-homogeneous in nature. These spatial changes could affect the structure of the turbulence. In this work a classification is proposed to determine the intermittency and mixing ability. The variation of the structure functions and the scaling exponent in decaying non-homogeneous turbulence produced by a grid and by a jet is measured with a sonic velocimeter SONTEK3-D. We use Extended Self Similarity (ESS) to obtain better estimates of the scaling exponents of the structure functions of order up to the 6th. We study the variation of the absolute scaling exponents _p and relative scaling exponents ¯_p as a function of distance from the source of turbulence. In most cases, the absolute scaling exponent ₃ is shown to vary as function of the separation distance l. On the other hand the relative scaling exponents ¯_p depend on the location of the flow and in most cases the deviations from the Kolmogorov 1941 scaling are related to the intermittency.     

EXPERIMENTAL STUDY OF MEASUREMENT FOR DISSIPATION RATE SCALING EXPONENT IN HEATED WALL TURBULENCE

Experimental investigations have been devoted to the study of scaling law of coarse-grained dissipation rate structure function for velocity and temperature fluctuation of non-isotropic and inhomogeneous turbulent flows at moderate Reynolds number. Much attention has been paid to the case of turbulent boundary layer, which is typically the non-istropic and inhomogeneous trubulence because of the dynamically important existence of organized coherent structure burst process in the near wall region . Longitudinal velocity and temperature have been measured at different vertical positions in turbulent boundary layer over a heated and unheated flat plate in a wind tunnel using hot wire anemometer. The influence of non-isotropy and inhomogeneity and heating the wall on the scaling law of the dissipation rate structure function is studied because of the existence of organized coherent structure burst process in the near wall region . The scaling law of coarse-grained dissipation rate structure function is foun     

湍流中的层次结构和标度律

湍流是由各种不同尺度、不同幅度和不同相干度的层次结构组成的．在从积分尺度到耗散尺度连续分布的每个尺度上,都存在具有最大振幅和最高相干度的结构──最强间歇结构．幅度较小的结构按照一定的层次对称关系与最强间歇结构相联系．这就是连接多尺度和多幅度脉动结构的层次结构模型（She和Leveque,Phys．Rev．Lett,1994;72,336）．本文对湍流层次结构理论的内容、基本观念及其新发展进行了一些综述和讨论,希望对国内的湍流基础研究能起一定的推动作用．     

Second-order relative exponent of isotropic turbulence

Theoretical results on the scaling properties of turbulent velocity fields are reported in this letter. Based on the Kolmogorov equation and typical models of the second-order statistical moments (energy spectrum and the second-order structure function), we have studied the relative scaling using the ESS method. It is found that the relative EES scaling exponent S₂ is greater than the real or theoretical inertial range scaling exponent ξ₂, which is attributed to an evident bump in the ESS range.     

可解尺度各向同性湍流的标度律

针对大涡模拟, 首先利用 EDQNM 能谱和传输谱理论, 在3种不同的过滤器下分别计算可解尺度各向同性湍流的二阶、三阶结构函数标度律, 并通过速度差扭率验证了可解尺度湍流的 ESS 理论. 研究了该可解尺度湍流标度律及速度差扭率与多个因素的关系, 这些因素包括: 两点距离与过滤尺度的比、大涡模拟雷诺数和过滤器类型. 结果显示, 当两点距离位于过滤尺度量级时或大涡模拟雷诺数较小时, 可解尺度标度律与未过滤流场的标度律相差很大进而必须加以修正, 而且可解尺度流场也不再总是满足 ESS 理论进而对应的速度差扭率也需要修正. 然后通过3个例子介绍了这些结果在大涡模拟亚格子模型中的应用.      

湍流最高激发态的局部结构及其绝对标度律

通过对湍流层次结构模型中提出的最高激发态的进一步研究发现,最高激发态 存在绝对标度律,且该绝对标度律是由信号中最强耗散涨落的局部结构产生的,并由此推测 出局部强间歇结构一般具有绝对标度的结论.     

金属丝壁面加热湍流标度律的实验研究

通过在固壁表面的平板湍流边界层沿流向平行放置若干通电加热的金属细丝,在平板表面形成沿展向周期性分布的温度场,利用该温度场引起的空气热对流,在湍流边界层近壁区域产生一组沿湍流边界层展向周期分布的流向涡结构。对壁湍流小尺度结构标度律统计特性的研究表明,金属丝加热后形成的规则流向涡结构将壁湍流各种尺度湍涡结构不规则的脉动有序地组织起来,增强了湍流小尺度结构的层次结构相似性,减小了壁湍流中小尺度结构的间歇性和奇异性,抑制了壁湍流中奇异的湍涡结构。     

）IRECT NUMERICAL SIMULATION OF DECAYING COMPRESSIBLE ISOTROPIC TURBULENCE

采用五阶有限差分WENO格式直接模拟了高初始湍流Mach数的可压缩均匀各向同性湍流,主要分析了湍流的统计特性和压缩性的影响,包括能谱特征、激波串、耗散率、标度律等.研究表明,湍动能主要来自于速度场螺旋分量的贡献;各向同性湍流的小尺度脉动对压缩性更为敏感,并且压缩性的增强加快了湍流大尺度脉动向小尺度脉动的湍动能输运;随着湍流Mach数的升高,胀量（压缩）耗散率所占比率也显著增长.标度律分析表明,强可压缩湍流的横向速度结构函数仍然具有扩展自相似性;当阶数较高（p≥5）时,纵向速度结构函数的扩展自相似性则不再成立.对于压缩性较弱的湍流,与不可压缩湍流一致,横向湍流脉动的间歇性要强于纵向湍流脉动;而对于强可压缩湍流,纵向湍流脉动的间歇性要强于横向湍流脉动.     

可压缩各向同性衰减湍流直接数值模拟研究

采用五阶有限差分WENO格式直接模拟了高初始湍流Mach数的可压缩均匀各向同性湍流,主要分析了湍流的统计特性 和压缩性的影响,包括能谱特征、激波串、耗散率、标度律等. 研究表明,湍动能主要来自于速度场螺旋分量的贡献;各向同性湍流的小尺度脉动对压缩性更为敏感,并且压缩性的增强加快了湍流大 尺度脉动向小尺度脉动的湍动能输运;随着湍流Mach数的升高,胀量(压缩)耗散率所占比率也显著增长. 标度律分析表明,强可压缩湍流的横向速度结构函数仍然具有扩展自相似性;当阶数较高(p ≥ 5)时,纵向速度结构函数的扩展自相似性则不再成立. 对于压缩性较弱的湍流,与不可压缩湍流一致,横向湍流脉动的间歇性要强于纵向湍流脉动;而对于强可压缩湍流,纵向湍流脉动的 间歇性要强于横向湍流脉动.     

关于湍流标度律的争鸣

研究湍流结构函数的标度律。实验或数值模拟得到的湍流结构函数的标度指数是奇异的。很多学者认为:这一实验事实否定Kolmogorov1941年(K41)提出的正常标度律,各向同性湍流惯性区的标度律是奇异的。近年来作者发表一系列文章,提出不同的观点:由于有限雷诺数效应,有限雷诺数湍流的标度指数不等于真正的惯性区标度指数,湍流结构函数的标度指数的实验数据并不否定K41正常标度律,各向同性湍流惯性区的标度律可能是正常的。惯性区奇异标度律和正常标度律对应的湍流物理本质是完全不同的,因而研究解决这个争论具有重要的意义。      

壁湍流扩展的自相似标度律的实验研究

对风洞中零压力梯度平板湍流边界层进行了实验研究,用热线风速仪测量了不同法向位置的脉动速度,研究了湍流边界层不同法向位置速度结构函数的扩展的自相似标度律。     

在我国开展工程湍流研究的设想

本文包括三部分：１）提出开展工程湍流研究的背景;２）工程湍流研究的特征和内容;３）开展工程湍流研究的设想,其中包括：ａ）湍流理论的概念鉴别和在工程中的应用,ｂ）湍流模式理论的应用和完善,ｃ）湍流测量和ｄ）湍流控制．     

关于植被中湍流的研究

本文从实验和模式理论两个方面介绍了近年来在植被湍流研究方面的进展.实验研究表明,植被内湍流是高度间歇性的,大尺度涡在湍流输运中起主导作用.植物枝、干、叶打碎了大尺度涡,产生的迹湍流中的小尺度涡更容易耗散成热。因此,植被内能量不按一般的能量级串理论预示的方式进行,而要发生所谓“短路”现象,使得功率谱曲线的斜率在惯性区比-2/3律更负.现有的高阶封闭模式虽然取得了很大成功,但在模拟湍流强度上高估了其大小,还需根据实验加以改进.