【作者】 张道祥；

【导师】 刘宇陆；

【作者基本信息】 上海大学 ， 流体力学， 2009， 博士

【摘要】 分层湍流足自然界常见的一种流动现象，广泛存在于海洋、大气边界层以及工程实际应用中。对分层湍流的深入研究，具骨重要的理论和直用价值。本文采用实验和理论相结合的方法对稳定分层湍流特性，特别是湍流逆梯度输运特性进行研究，主要工作和结果如下：第一部分：建立了分层湍流流动实验装置，运用粒子动态分析仪(PDA)对稳定的间断温度分层槽道湍流进行了实验研究。实验结果表明：(1)随着流动向下游发展，混合层厚度沿流向逐渐增加，在分层和剪切的共同作用下，混合层的发展是非线陛的。剪切使得混合层向速度较小的一侧偏移，剪切越强偏移程度越大。而分层使得混合层偏移程度减小，并使得混合层厚度变薄，混合层两侧的厚度差变小。(2)流向湍流强度大于垂向的湍流强度，流向和垂向湍流强度在水槽中心线4<x／M<20内按幂函数律衰减。流向湍流强度衰减幂指数在-O．68至-1．29之间，垂向衰减幂指数在-1．20至-1．55之间。不论剪切和分层强弱，垂向的湍流强度比流向强度衰减得快。(3)在混合层的中心处，湍流咏动速度的概率密度分布比较接近于高斯分布。在混合层内的上下两侧，流速较大一侧脉动速度与高斯分布偏离程度小于流速较小的一侧。在混合层上下边界处，湍流脉动强烈偏离高斯分布，说明在混合层边界处概率密度函数具有较大的非对称性。(4)强剪切工况中发现了动量逆梯度输运，而弱剪切工况中未发现，即上下两层流体只有在速度非对称性有较大差异时才出现动量逆梯度输运现象。在强剪切工况中逆梯度输运区域偏向速度较大的一侧，在－2．8<y／M<－1．4范围内。而两层流体的交界面处未发现动量逆梯度输运现象。第二部分：运用新近发展起来的Hilbert—Huang变换(HHT)和任意阶Hilbert谱分析方法分析了湍流脉动速度信号。首次得到动量在HHT频谱空间中的输运特性。主要结果包括：(1)在中心位置处湍流能谱具有较宽的惯性子区。在无分层强剪切实验中，能谱标度律接近-7／3，而在有分层强剪切实验中，标度律偏离-7／3。f2)不论分层与否，在水槽中心线上，流向脉动速度的间歇性均大于垂向咏动速度的间歇性。(3)动量输运主要受到大尺度结构控制，垂向动量输运随着分层增强而降低。动量的局部逆梯度输运现象在不同的尺度上或不同的频率上普遍存在，但是整体输运效果为各个尺度上或各频率上的局部逆悌度输运和顺梯度输运的综合。第三部分：通过双尺度直接相互作用原理(TSDIA)对含有浮力效应项的分层湍流的能谱和温度脉动能谱进行了理论预测。(1)显式地得到了分层湍流的能谱和温度脉动能谱的表达式。(2)所得结果预测了能谱和温度咏动能谱具有的不同标度律行为，包括-11／3律，-9／3律，-7／3律以及-5／3律；(3)所得结果克服了Lumley的结果在预测稳定分层湍流能谱和温度咏动能谱时在小波数区域为负的缺陷。更多还原

【Abstract】 Stably stratified turbulence widely occurs in the ocean,atmospheric boundary layerand in many engineering applications. Stably stratified -ows have been investigatedextensively because they play a very important role in both theory and application.The main work of this paper is focused on the turbulent characteristics, especially onthe turbulent momentum counter-gradient transport features via the experimental andtheoretical investigations. The main results are given as follows:First, the system of experimental facilities on turbulent stratified -ow was con-structed in our laboratory, and experiments were conducted in stably stratified turbu-lence with a sharp interface, using Particle Dynamic Analysis (PDA ). The results showthat: (1) The width of turbulent mixing layer increases along the streamwise directionwhen the -ow develops in the -ow direction. The mixing layer appears to exhibit non-linear growth duo to the e-ects of shear and stratification.The o-set of the mixing layerto the side with the smaller inlet velocity is calculated quantitatively. The stronger themean shear rate,the larger the o-set of the mixing layer to the side with the smaller inletvelocity, while the stronger the stratification,the weaker the o-set of the mixing layer.The depth of the mixing layer is thinner and the di-erence of the thickness betweenupper mixing layer and lower mixing layer is smaller in the strong stratification .(2)The streamwise turbulent intensity is larger than the vertical one. The turbulent kineticenergies in both streamwise and vertical directions show a decaying scaling power lawin the range of 4 < x/M < 20. The decaying exponent for streamwise direction is from-0.68 to -1.29,for vertical one is from -1.22 to -1.55. The vertical component decaysfaster than the streamwise one regardless of the intensity of shear and stratification.(3)The probability density function (PDF) of -uctuating velocity is close to Gaussiandistribution at the center of the mixing layer. In the two sides of the mixing layer, thedegree of the deviation of the -atness and skewness of turbulent -uctuating velocityin the upper region with the smaller inlet velocity from the values of the Gaussiandistribution is less than that of the lower region with the larger inlet velocity. At theedges of the mixing layer, the -uctuating velocity shows asymmetric pdf. (4)Turbulentmomentum counter-gradient transport occurs only in the strong shear cases and is notfound at the center of mixing layer. The turbulent counter-gradient momentum trans-port is found to occur in the side of larger inlet velocity. The range of counter-gradientmomentum transport is in -2.8 < y/M < -1.4. Second, Hilbert-Huang transform (HHT) and arbitrary order Hilbert spectral areapplied to analyze the times series of velocities of stratified turbulence . The mo-mentum counter-gradient transport characteristic is firstly obtained in the space of fre-quency. It is found that: (1)There is a wide inertial subrange in the spectrum of the?uctuating velocity via applying HHT. The power law of the turbulent energy spec-trum is close to -7/3 in the non-stratified case with strong shear,but deviates form -7/3in the stratified case. (2)At the central region,the streamwise intermittency factor islarger than the vertical one. (3)Coherent structures play a principal role in turbulentmomentum transport.Vertical momentum transport is suppressed at the presence ofstratification. Local counter-gradient transport phenomena occur at certain modes(orat certain frequencies) , but the global counter-gradient momentum transport resultsfrom the total contributions of all modes (or all frequencies).Third, using two-scale direct interaction approximation (TSDIA), the energy spec-tra and the thermal intensity spectra in buoyancy-driven stratified ?ows are theoreti-cally investigated . (1)The theoretical representations for the turbulent energy spectraand thermal intensity spectra are explicitly deduced . (2)Di?erent scaling power laws,such as -5/3 law,-7/3 law, -9/3 law and -11/3 law corresponding to di?erent ?ow condi-tions, which are often observed in previous experiments are derived theoretically . (3)The results presented here overcome the defect of Lumley’s result ,i.e., the turbulentspectra should be positive for small wave number.更多还原