稳定分层湍流的实验与理论研究
|
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 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。
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.
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
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。
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.
引文
[1] Davies, J. T., Turbulence phenomena: an introduction to the eddy tran sfer of momentum, mass, and heat, particularly at interfaces. Academic, New York, 1972.
[2] Twonsend,A. A., The structure of turbulent shear flow. Cambridge Press, Cambridge,1956.
[3] Corrsin, S., Investigation of flow in an axially symmetric heated jet of air. NACA, Adv.Conf. Rep. 1943. 3L23.
[4] Veeravalli, S. and Warhaft, Z., The shearless sturbulence mixing layer. J. Fluid Mech.,1989. 207: p. 191-229.
[5] Jayesh, Yoon, K. and Warhaft, Z., Turbulent mixning and transport in a thermallystratified interfacial layer in decaying grid turbulence. Phys. Fluids A, 1991. 3: p. 1143-1155.
[6] Jayesh and Warhaft, Z., Turbulent penetration of a thermally stratified interfacial layerin a wind tunnel. J. Fluid Mech., 1994. 277: p. 23-54.
[7] Spedding, G.R., Browand, F.K. and Fincham, A.M., Turbulence, similarity scaling andvortex geometry in the wake of a towed sphere in a stably stratified fluid. J. Fluid Mech.,2002. 450: p. 1-32.
[8] Spedding, G.R., Vertical structure in stratified wakes with high initial Froude number.J. Fluid Mech. , 1996. 314: p. 53-103.
[9]邱翔，黄永祥，卢志明，刘宇陆，稳定分层湍流的PIV实验研究．实验流体力学，2008.22(2)：p.1-9.
[10] Thoroddsen, S. T., Atta, C. W V. and Collins, J. J., The influence of stable stratificationon small-scale anisotropy and disspation in turbulence. J. Geophys. Res., 1992. 97: p.3647-3658.
[11] Piccirillo, P. and Atta,C.WV., The evolution of uniformly sheared thermally stratifiedturbulent flow. J. Fluid Mech. , 1997. 334: p. 61-86.
[12]金海生，温度分层剪切流的实验和数学模型研究．河海大学学报，1991. 19(4)：p. 59-67.
[13] Thoroddsen, S. T. and Atta, C. W. V., Experimental study of the effects of grid configuration on stably stratified frid-turbulence. Dyn. Atmos. Oceans, 1993. 19: p. 259-288.
[14]Prastowo，T.，Griffiths，R.W.，Hughes，G. and Hogg，A.M.，Mixing efficiencyin con- trolled exchange flows. J. Fluid Mech．,2008.600：p.235-244.
[15]Jackson，P.R. and Rehmann，C.R.，Kinematic effects of differential transport on mixing efficiency in a diffusively stable turbulent flow. J. Phys. Oceanogr．,2003.33：p.299-304.
[16]褚克坚，华祖林，王惠民，邢领航，张鸿星，明渠剪切分层流垂向扩散特性试验研究．水科学进展，2005.16(1)：p.13-17.
[17]华祖林，褚克坚，邢领航，强弯条件下分层流运动特性试验研究．水科学进展，2005.16(2)：p.203-209.
[18]华祖林，邢领航，褚克坚，弯段温差剪切分层流断面环流结构与掺混强度研究．水科学进展，2007.18(4)：p.531-537.
[19]White，B.L. and Helfrich，K.R.，Gravity currents and internal waves in a stratifed fluid．J.Fluid Mech.2008.616：p.327-356.
[20]Lin，J.T. and Veenhuizen，S.D.，Measurements of the decay of grid generated turbu- lence.Flow Research Note，1975.10：p.1-20.
[21]Dickey,T.D. and Mellor,G.L.，Decaying Turbulence in neutral and stratified fluids.J. Fluid Mech.，1980.99：p.13-31.
[22]Britter,R.E.，Hunt，J.C.R.，Marsh，G.L. and Snyder,W.H.，The effect of stable statification on turbulence diffusion and the decay of grid turbulence．J.Fluid Mech.，1983.127：p.27-44.
[23]Yoon，K.and Warhaft，Z.，The evolution of grid-generated turbulence under condition of stable thermal stratification. J. Fluid Mech.，1990.215：p.601-638.
[24]Hsien，T.L.，Energetics of grid turbulence in a stably stratified fluid J. Fluid Mech.，1995.296：p.127-157.
[25]Hurst，D. and Vassilicos J. C.，Scaling and decay of decay of fractal-generated turbu- lence. Phys. Fluids，2007.19：35103.
[26]Itsweire，E.C and Helland K.N.，Spectra and energy transfer in stably stratified turbulence Journal of Fluid．Mechanics，1989.207：p.419-452.
[27]Lienhard，J. H. and Atta，C.W.V.，The decay of turbulence in thermally stratified flow. J.Fluid Mech．, 1990.210：p.57-112.
[28]Vinnichenko，N.K.，Pinus，N.Z. and Shur，G.N.，Fine-scale structure of atmosphere. Proc. Int. Coll. Acad. Sci．,USSR．Moscow,1965.
[29]Komori，S.，Ueda，H.，Ogino，F. and Mizushina，T.，Turbulence structure in stablystratified open-channel flow．J.Fluid Mech．,1983.130：p.13-26.
[30] Komori, S. and Nagata, K., Effects of molecular diffusivities on counter-gradient scalarand momentum transfer in strongly stable stratification. J. Fluid Mech., 1996. 326: p.205-237.
[31] Stillinger, D. C, Helland, K. N. and Atta, C. W. V, Experiments on the transition ofhomogenous turbulence to internal waves in a stratified fluid. J. Fluid Mech., 1983. 131:p. 91-122.
[32] Rohr, J. J., Itsweire, E. C, Helland, K. N. and Atta,C. W. V, CGrowth and decay ofturbulencein a stably stratified shear flow. J.Fluid Mech., 1988. 195: p. 77-111.
[33] Veeravalli, S. and Warhaft, Z., Thermal dispersion from a linesource in the shearlessturbulence mixing layer. J. Fluid Mech., 1990. 216: p. 35-70.
[34]张晓航，许春晓，张兆顺，Serge，S. and Ayrault，M.，无剪切湍流混合层中被动标量扩散的实验实验研究．流体力学实验与测量，2003.17(4)：p.22-27.
[35] Deissler, R. G., Analysis of multipoint-multitime correlations and diffusion in decayinghomogeneous turbulence, in NASA Tech. Rep. 1961. p. R-96.
[36] Deissler, R. G., Turbulence in the presence ofaveritical body and temperature gradient.J. Geophys. Res., 1962. 67: p. 3049-3062.
[37] Deissler, R. G., Effect of Initial Condition on Weak Homogeneous Turbulence withUniform Shear. Phys. Fluids, 1970. 13(7): p. 1868-1869.
[38]邱翔，分层流动中湍流结构和湍流逆梯度输运特性研究．2006.上海大学博士学位论文：上海．
[39] Hunt, J. C. R., Stretch, D. D. and Britter, R. E., Length scales in stably stratified turbulent flows and their use in turbulence models. In: Puttock, J. S., (ed.) Stably Stratified Flow and Dense Gas Dispersion. Clarendon Press, Oxford, Great Britain, 1988.
[40] Miyazaki, T., Parametric excitation of buoyancy ocillation and formation of internal boundary layers in a stably stratified fluid. Phys. Fluids A, 1992. 4(10): p. 2145-2150.
[41] Hanazaki, H. and Hunt,J. C. R., Linear processes in unsteady stably stratified turbulence. J. Fluid Mech., 1996. 318: p. 303-337.
[42] Galmiche, M., Hunt, J. C. R., Thual, O. and Bonneton, P., Turbulence-mean field interactions and layer formation in a stratified fluid. Eur. J. Mech. -B/Fluids, 2001. 20: p. 577-585.
[43] Galmiche, M. and Hunt, J. C. R., The formation of shear and density layers in stablystratied turbulent flows: linear processes. J. Fluid Mech. , 2002. 455: p. 243-262.
[44] Hanazaki, H. and Hunt, J. C. R., Structure of unsteady stably stratified turbulence withmean shear. J. Fluid Mech. , 2004. 507: p. 1-42.
[45] Jackson, P.R. and Rehmann, C. R., Theory for differential transport of scalars insheared stratified turbulence. J. Fluid Mech., 2009. 621: p.1-21.
[46] Kraichnan R. H., Irreversible statistical mechanics of incompressible hydromagneticturbulence. Phys. Rev., 1958. 109: p. 1407-1422.
[47] Shimomura, Y, A theoretical study of the turbulent diffusion in incompressible shearflows and in passive scalars. Phys. Fluids, 1998. 10(10): p. 2636-2646.
[48] Okamoto, M., Theoretical investigation of energy and thermal intensity spectra inbuoyancy-driven turbulence flows. J. Phys. Soc. Jan., 1996. 65(10): p. 3193-3201.
[49] Okamoto, M., Theoretical modeling of buoyancy-driven turbulent flows. J. Phys. Soc.Jan., 1996. 65(7): p. 2044-2059.
[50]蒋剑波，刘宁陆，卢志明，湍流动量、标量及能量的逆梯度输运模型．应用数学和力学，2001.22(3)：p.267-274.
[51]蒋剑波，刘宇陆，卢志明，湍流逆梯度输运的理论与实验研究．力学进展，2000.30(3)：p.425-432.
[52] Riley, J. J., Metcalfe, R. W. and Weissman, M. A., Direct numerical simulations ofhomogeneous turbulence in density stratified fluids, in Proc. AIP Conf. Nonlinear properties of internal waves, 1981.
[53] Metais, O. and Herring, J. R., Numerical simulation of freely evolving turbulence instably stratified fluids. J. Fluid Mech., 1989. 202: p. 117-148.
[54] Gerz, T., Schumann, U. and Elghorashi, S. E., Direct numerical simulation of stratifiedhomogenous turbulent shear flows. J.Fluid Mech., 1989. 200: p. 563-594.
[55] Gerz, T. and Schumann, U., Direct simulation of homogenous turbulence and gravitywave in sheared an unsheared stratified flows. Turbulence Shear Flow 7, ed. Durst, F. etal., Springer, 1991: p. 27-45.
[56] Holt, S. E., Koseff, J. R. and Ferziger, H., A numerical study of the evenolution andstructure of homogeneous stably stratified sheared turbulence. J.Fluid Mech., 1992.237: p. 499-539.
[57] Gerz, T. and Yamazaki, H., Direct simulation of buoyancy-driven turbulence in stablystratified fluid. J. fluid Mech., 1993. 249: p. 415-440.
[58] Kaltenbach, H. J., Gerz, T. and Schumann, U., HLarge-eddy simulation of homogeneous and diffusion in stably stratified shear flow. J. Fluid Mech., 1994. 280: p. 1-40.
[59] Jin, H. S. and Zhang, S. N., Numerical Simulation of stratified flow with both vertical temperature gradient and vertical salinity gradient. Journal of Hydrodynamics, Ser.B, 1992. 2: p. 24-30.
[60] Kyle, A. B. and Sarkar, S., Evolution of an initially turbulent stratified shear layer. Phys. Fluids, 2007. 19: 105105.
[61] Brethouwer, G., Billant, P., Lindborg, E. and Chomaz, J. M., Scaling analyzing and simulation of strongly stratified turbulent flows. J. Fluid Mech., 2007. 585: p. 343-368.
[62] Lvescu, D. and Ristorcelli, J. R., Variable-density mixing in buoyancy-driven turbulence. J. Fluid Mech., 2008. 605: p. 145-180.
[63] Briggs, D. A., Ferziger, J. H., Koseff, J. R. and Monismith, S. G., Entrainment in a shear-free Turbulent mixing layer. J. Fluid Mech., 1996. 310: p. 215-241.
[64]金海生，张书农，同时存在温度和盐度梯度的分层流的数值模拟．水动力学研究与进展A，1991.6(4)：p.72-78.
[65]沈永明，胡振红，刘才广，魏文礼，温度和盐度分层流的二维应力2通量代数湍流模型．环境科学学报，2004.24(3)：p.389-393.
[66]邱晨霞，汗德，许协庆，应用模型模拟三维分层流．水利学报，1997.7：p.7-12.
[67]俞剑冬，刘桦，朱志伟，二层密度分层流体重力流的数值模拟．力学季刊，2007.28(4)：p.539-548.
[68] Yoshizawa, A., A statistical theory of thermally driven turbulent shear flow , with thederivation of subgrid model. J. Phys. Soc. Japan, 1983. 52 : p.1194-1205.
[69] Yu-hong, D., Feng-quan, Z., Xi-yun, L. and Li-xian, Z.,An investigation of turbulentheat transfer in channel flows by large eddy simulation. Journal of Hydrodynamics,Ser.B, 2002. 14(2): p. 32-38.
[70] Yu-Hong, D., Xi-Yun, L. and Li-Xian, Z., Large eddy simulation of turbulent channelflow with mass transfer at high-Schmidt numbers. International Journal of Heat and MassTransfer 2003. 46(9): p. 1529-1539.
[71]仲峰泉，庄礼贤，刘难生，陆夕云，An improved dynamic subgrid-scale modeland its application to large eddy simulation of stratified channel flows. Science in China,Ser. A, 2002. 45(7): p. 74-85.
[72]董宇红，陆夕云，庄礼贤，LES OF Thermally-stratified Turbulent Channel flow with temperature oscillation on the bottom wall. Journal of Hydrodynamics，Ser.B，2004(1)：p.34-38.
[73]张华，许桂生，二维分层流的格子Boltzmann数值模拟．水利学报，2006 37(11)：p.1367-1371.
[74]Junmei，J.，Xiang，Q. and Yulu，L.，Numerical Study of Turbulent Counter-Gradient Momentum Transport in Stable Stratified Flows.水动力学研究与进展A，2005. 20(4)：p. 426-435.
[75]Minjie，T. and Zhiming，L.，Numerical study of turbulent characteristics in convective boundary layer.力学季刊，2005.26(3)：p.354-360.
[76]邱翔，黄永祥，卢志明，刘宇陆，稳定分层流动中湍流统计特性和输运特性的数值研究．应用数学和力学，2009.30(2)：p.149-159.
[77]邱翔，张道祥，卢志明，刘宇陆，Turbulent mixing and evolution in a stably stratifiedflow with a temperature step. Journal of Hydrodynamics, 2009. 21(1): p. 84-92.
[78] Pope, S. B., turbulent flows. Cambridge University Press, 2000.
[79] Townsend,A.A., Strcture of turbulent shear flow. Cambridge Univ. Press, Cambridge,2nd, 1976.
[80] Bell, J. H. and Mehta, R. D., Development of a two-stream mixing layer from trippedand untripped boundary layers. AIAA Journal, 1990. 28(12): p. 2034-2042.
[81] Phillips, O. M., Atmosheric turbulence and radio-wave propagation, eds. Yaglom, A.M. and Tatarskii, U. I., Nauka, Moscow,1967.
[82] Posmentier, E. S., The generation of salinity finestructure by verical diffusion. J. Phy.Oceanogr., 1977. 7: p. 298-300.
[83] Galaktionov, O., Maderich, V. and Nikishov, V, Evolution of layered structures in thefinal stage of turbulent decay in a stably stratified fluid. Dynamics of Atmosphere andoceans, 2001.34: p. 125-144.
[84] Godeferd R S. and Cambon, C, Detailed investigation of the energy transfer in homogenous stratified turbulence. Phys. Fluids, 1994. 6(6): p. 2084-2100.
[85] Huq, P. and Blitter, R. E., Turbulence evolution and mixing in a two-layer stably stratified fluid. J. Fluid Mech., 1995. 285: p. 41-67.
[86]褚克坚，温差剪切分层流运动特性试验及数值模拟研究．2006.河海大学博士学位论文：南京．
[87] Taylor, G. I., Statistical Theory of Turbulence Proc. R. Soc. Lond. A September 2,1935. 151: p. 421-444.
[88] Tan, H. S. and Ling, S. C, Final stage decay of grid-produced turbulence. Phys. Fluids,1963. 6: p. 1693-1699.
[89] Paulsson , Comte-Bellot, G. and Corrsin ,S., The use of contraction to improve theisotropy of grid-generated turbulence. J. Fluid Mech., 1966. 25: p. 657-682.
[90] Warhaft, Z. and Lumley, J. L., An experimental study of the decay of temperaturefluctuations in grid-generated turbulence. J. Fluid Mech., 1978. 88: p. 659-684.
[91] Tavoularis, S. and Corrsin, S., Experiment in nearly homogeneous turbulent shear flowswith a uniform mean temperature gradient. Part I. J. Fluid Mech., 1981. 104: p. 311-347.
[92] Tavoularis, S., Asymptotic laws for transversely homogeneous turbulent shear flows.Phys. fluid, 1985. 28: p.999-1001.
[93]陈景仁，湍流模型及有限分析法．上海交通大学出版社，1989.
[94]李玲，徐忠，颗粒存在对网栅后气相流动湍流特性的影响．应用力学学报，2000.17(1)：p.36-41.
[95] Kang, H. S., Chester, S. and Meneveau, C, Decaying turbulence in an active-grid-generated flow and comparisons with large-eddy simulation. J. Fluid Mech., 2003. 480: p. 129-160.
[96] Eskinazi, S. and Yeh, H.,An investigatioin of fully developed turbulent flows in a curved channel. J. Aeronaut. Sci., 1956. 23: p. 23-31.
[97] Beguier, C, Giraltl, F., Fulachier, L. and Keffer, J. F., Negative production in turbulent shear flows . Lecture notes in physics, 1978. 76: p. 22-35.
[98]蒋剑波，湍流逆梯度输运的理论与实验研究．2002，上海大学博士学位论文：上海．
[99] Bunker, A.F., Measurements of counter-gradient heat flux in the atmospheres. Austr. J.Phys., 1956. 9: p. 133-143
[100] Starr, V, Physics of negative viscosity phenomena. Mc-Graw-Hill Book Co., NewYork, 1968.
[101] Deardorff, J. W., The Counter-gradient heat flux in the lower atmoaphere and in thelaboratory. 1. Atmosph. Sci., 1966. 23: p. 503-506.
[102] Yoshizawa, A., Statistical analysis of the deviation of the Reynlods stress from its eddy-viscosity represention. Phys. Fluids 1984. 27(6): p. 1377-1387.
[103] Okamoto, M., Theoretical investigation of energy and thermal intensity spectra inbuoyancy-driven turbulence ?ows. J.Phys. Soc. Jan., 1996, 65(10): p. 3193-3201.
[104] Deardor?, J. W. and Willis, G. E., Further results from a laboratory model of theconvective planetary boundary layer. Boundary-Layer Meteorol, 1985. 32: p. 205-236.
[105] Nagata, K. and Komori, S., The di?erence in turbulent di?usion between active andpassive scalars in stable thermal stratification. J. Fluid Mech., 2001. 430: p. 361-380.
[106] Gerz, T. and Schumann, U., Direct simulation of homogenous turbulence and gravitywave in sheared an unsheared stratified ?ows. In turbulence Shear Flow 7 (ed. Durst, F.,Launder, B. E., Reynolds, W. C., Schmidit, F. W. and Whitelaw, J. H. ), Springer,1991.p. 27-45.
[107] Schumann, U., Elghobashi, S. E. and Gerz, T., Direct simulation of stably stratifiedturbulent homogeneous shear ?ow, Direct and Large Eddy Simulation of Turbulence,ed.Schumann, U. F., Braunschweig: Vieweg-V., 1986. 15: p. 245-264.
[108] Kolmogorov, A. N., A local structure of turbulence in incompressible viscous ?uid forvery large Reynolds numbers. Dokl. Akad. Nauk SSSR, 1941. 30: p. 299-303.
[109] Batchelor, G. K., Howells, I. D. and Townsend, A. A., Small-scale variation of con-vected quantities like temperature in turbulent ?uid Part 2. The case of large conductiv-ity. J. Fluid Mech., 1959. 5: p. 134-139.
[110] Von Karman, T., Progress in Statistical Theory of Turbulence. Proc. Natl. Acad. Sci.(USA), 1948. 34: p. 530-539.
[111] Corrsin, S., On the spectrum of isotropic temperature ?uctuations in an isotropic tur-bulence. J. Appl. Phys., 1951. 22(4): p. 469-473.
[112] Heisenberg, W., On the Theory of Statistical and Isotropic Turbulence. Proc. R. Soc.Lond. A , 1948. 195: p. 402-406.
[113] Chandrasekhar, S., The theory of statistical and isotropic turbulence. Phys. Rev. , 1949.75(5): p. 896-897.
[114] Kovaszanay,L.S.G., Spectrum of locally isotropic turbulence. J. Aeronaut. Sci.,1948.15:p.745-753.
[115] Kraichnan, R. H. Small-scale structure of a scalar field convected by turbulence. Phys.Fluids, 1968. 11(5): p. 945-953.
[116] Obukhov, A. M., Structure of the temperature field in turbulent ?ows. Izv. Akad. NaukSSSR Geogr. Geofiz. 1949. 13: p. 58-69.
[117] Lumley, J. L., Similarity and the Turbulent Energy Spectrum. Phys. Fluids, 1967. 10:855. DOI:10.1063/1.1762200
[118] Saddoughi, S. G. and Veeravalli, S. V., Local isotropy in turbulent boundary layers athigh Reynolds number . J. Fluid Mech., 1994. 268: p. 333-372.
[119] Lohse, D., Temperature spectra in shear ?ow and thermal convection. Phys. Lett. A ,1994. 196: p. 70-75.
[120] Sreenivasan, K., On local isotropy of passive scalars in turbulent shear ?ows. Proc. R.Soc. London, Ser. A, 1991. 434: p. 165-182.
[121] Oboukhov, A. M., Structure of the temperature field in turbulent ?ow. Izv. Akad. Nauk.SSSR, Ser. Geogr. I Geofiz., 1949. 13: p. 58-69.
[122] Hill, R. J., Models of the scalar spectrum for turbulent advection. J. Fluid Mech., 1978.88: p. 541-562.
[123] Hill, R. J. and Cli?ord, S. F., Modified spectrum of atmospheric temperature ?uctu-ations and its application to optical propagation. J. Opt. Soc. Am., 1978. 68(7): p.892-899.
[124] Tatarskii, V. I., The E?ects of the Turbulent Atmosphere on Wave Propagation. Keter,Jerusalem, 1971.
[125] Bolgiano, R., Turbulent spectra in a stably stratified atmosphere.J. Geophys. Res.,1959. 64: p. 2226-2229.
[126] Bolgiano, R., Structure of turbulence in stratified media. J. Geophys. Res., 1962. 67: p.3015-3023.
[127] Shur,G,N., Experimental investigation of the energy spectrum of atmospheric turbu-lence. Trudy of Aerological Observation,1962. 43:p. 79-90.
[128] Nastrom, G. D., Gage, K. S. and Jasperson, W. H., Kinetic energy spectrum of largeand mesoscale atmospheric processes. Nature, 1984. 310: p. 36-38.
[129] Dalaudier, F., and Sidi, C., Evidence and interpretation of a spectral gap in the turbulentatmospheric temperature spectra. J. Atmos. Sci., 1987. 44: p. 3121-3126.
[130] Lumley, J. L., The spectrum nearly inertial turbulence in a stably stratified ?uid. J. ofAtmospheric Sciences, 1964. 21: p. 99-102.
[131] Grant, H. L., Stewart, R. W. and Moilliet, A., Turbulence spectra from a tidal channel.J. Fluid Mech., 1962. 12: p. 241-263.
[132] Gargett, A. E., Evolution of scalar spectra with the decay of turbulence in a stratified fluid J. Fluid Mech., 1985. 159: p. 379-407.
[133] Kotsovinos, N. E., Stewart, R.W. and Moilliet, A., Turbulence spectra in free convection flow. Physics. Fluids A, 1991. 3(1): p. 163-167.
[134] Papailiou, D. D. and Lykoudis, P. S., Turbulent free convection flow. Int. J. Heat Mass Transfer, 1974. 17: p. 161-172.
[135] Bill, R. G. and Gebhart, B., The development of turbulent transport in a vertical natural convection. Int. J. Heat Mass Transfer, 1979. 22: p. 267-277.
[136] Xia, H., Punzmann, H., Falkovich, G. and Shats, M. G.,Turbulence-Condensate Interaction in Two Dimensions. P.R.L., 2008.101:194504.
[137]是勋刚，湍流．天津大学出版社，1984
[138] Hannoun, I. A., Fernando, H. J. S. and List, E. J., Turbulence structure near a sharp density interface. J. FluidMech., 1988. 189: p. 189-209.
[139] Shy, S. S. and Breidenthal, R. E., Laboratory experiments on the cloud-top entrainment instability. J. FluidMech., 1990. 214: p. 1-15.
[140] Venkataramani, K. S. and Shevray, R., Statistical features of heat transfer in grid-generated turbulence: constant-gradient case. J. Fluid Mech., 1978. 86: p. 513-543.
[141] Sirivat, A. and Warhaft, Z., The effect of a passive cross-stream temperature gradient on the evolution of variance and heat flux in grid turbulence. J. Fluid Mech., 1983. 128: p. 323-346.
[142] Webster, C, An experimental study of turbulence in a density stratified shear flow. J. Fluid Mech., 1964. 19: p. 221-245.
[143]冯素晓，稳定分层湍流中湍流混合层和动量梯度输运特性的实验研究．2008.上海大学硕士学位论文：上海．
[144]张贤达，保铮，非平稳信号分析与处理．国防工业出版社，1998
[145] Frisch, U., Turbulence: The legacy of A. N. Kolmogorov. Cambridge University Press,1995.
[146] Sreenivasan, K. R. and Antonia, R. A., The phenomenology of small-scale turbulence.Annual Rev. of Fluid Mechanics, 1997. 29: p. 435-472.
[147] Anselmet, F., Djeridi, H. and Fulachier, L., Joint statistics between a passive scalar andits dissipation in turbulent flows. Journal of Fluid Mechanics, 1994. 280: p. 173-197.
[148] Acharya, S. and Panigrahi, P. K., Analysis of large scale structures in separated shearlayers. Experimental thermal and fluid science, 2003. 27: p. 817-828.
[149] Orlandi, P., Energy spectra power laws and structures. J. Fluid Mech., 2009. 623: p.353-374.
[150] Voropayev, S. I., Fernando, H. J. S., and Morrison, R., Dipolar eddies in a decayingstratified turbulent flow. Phys. Fluids, 2008. 20: 026602.
[151] Costa-Patry, E. and Mydlarski, Mixing of two thermal fields emitted from line sourcesin turbulent channel flow. J. Fluid Mech., 2008. 609: p. 349-375.
[152]孟庆国，蔡庆东，李存标，能谱在解释湍流能量级串中值得注意的一个问题．物理学报，2004，53(9)：p.3090-3093.
[153] Cohen, L., Time-frequency Analysis . eds. Cliffs, E.,New Jersey: Prentice-Hall, 1995.
[154] Monin, A. S. and Yaglom, A. M., Statistical Fluid Mechanics: Mechanics of Turbulence. Vol. 1. MIT Press, Cambridge, Massachusetts, 1971.
[155]蔡树棠，刘宇陆，湍流理论．上海交通大学出版社，上海，1993.
[156] Antonia, R. A., Conditional sampling in turbulence measurement. Ann. Rev. FluidMech., 1981. 13: p. 131-156.
[157] Robinson, S. K., Coherent motions in the turbulent boundary layer. Ann. Rev. FluidMech., 1991. 23: p. 601-639.
[158] Falco, R. E., Coherent motions in the outer region of turbulent boundary layers Phys.Phys.Fluids, 1977. 20: p. 124-132.
[159] Fiedler, H. E., Coherent structures in turbulent flows. Prog. Aerospace Sci., 1988. 25:p. 231-269.
[160] Berkooz, G., Holmes, P. and Lumely, J. L, The proper orthogonal decomposition inanalysis of turbulent flows. Annu. Rev. Fluid Mech., 1993. 25: p. 539-575.
[161] Farge, M., A Wavelet Transforms and their Applications to Turbulence. Annu. Rev.Fluid Mech., 1992. 24: p. 395-457.
[162] Argoul,F, Ameodo,A., Grasseau, Hop finger, E. J. and Frisch, U., Wavelet analysis ofturbulence reveals the multifractal nature of the Richardson cascade. Nature, 1989. 338:p. 51-53.
[163] Farge, M., Schneider, K., Analysis anad computing turbulent flows using wavelets:Newtrends in turbulence:aspects nouveaux. eds. Lesieur,M., Yaglom, A., and David, F.Spring, 2001. p. 450-503.
[164] Daubechies, I., Ten lectures on wavelets: SIAM, 1992.
[165] Huang, N. E., Shen, Z. and Long, S. R., et.al, The Empirical Mode Decomposition andthe Hilbert Spectrum for Nonlinear and Non-stationary Time Series Analysis. Proc. R.Soc. London. A, 1998. 454: p. 903-995.
[166] Huang, N.E., Z. Shen, and S.R. Long, A New View of Nonlinear Water Waves: theHilbert Spectrum. Annu. Rev. Fluid Mech., 1999. 31: p. 417-437.
[167] Huang, N. E., Computer implicated empirical mode decomposition method. Apparatus,and Article of Manufacture., U.S. Pending, 1999.
[168] Huang, N. E., Long, S. R. and Shen, Z., The Mechanism for Frequency Downshift InNonlinear Wave Evolution. Adcances in Applied Mechanics, 1996. 32: p. 59-111.
[169] Huang, N. E., Long, S. R. and Qu ,W. D., Application of Hilbert-Huang Transform toNon-stationary financial tome series analysis. Appl. Stochastic Models Bus. Ind., 2003.19: p. 245-268.
[170] Tsinober, A., An informal introducton to turbulence. Kluwer, 2001.
[171] Wu, Z. and Huang, N. E., A study of the characteristics of white noise using the em-pirical mode decomposition method Flandrin, P. Gonc?alve′s, P. Empirical Mode De-compositions as Data-Driven Wavelet-Like Expansions. Int. J. Wavelets, Multires. Info.Proc., 2004. 2: p. 477-496.
[172] Huang, Y., Schmitt, F. G., Lu, Z., and Liu, Y., An amplitude-frequency study of turbulentscaling intermittency using Hilbert spectral analysis. Europhys. Lett., 2008. 84: 40010.
[173] Rilling, G., Flandrin, P. and Goncalves, P., On Empirical Mode Decomposition and itsAlgorithms. in IEEE-EURASIP Workshop on Nonlinear Signal and Image ProcessingNSIP-03.Grado, Italy, 2003.
[174] Long, S. R., Huang, N. E. and Tung, C. C., The Hilbert Techniques: an AlternateApproach for Non-steady Time Series Analysis. IEEE Geosci. Remote Sensing Soc.Lett., 1993. 3: p. 6-11.
[175] Jones,G. and Boashash,B. Instantaneous frequency,instantaneous bandwidth and theanalysis of multicomponent signals. Proc. IEEE ICASSP-90,1990.5:p.2467-2470.
[176] Loughlin, P. and Tacer, B., Comments on the interpretation of instantaneous frequency.IEEE Signal Process. Lett., 1997. 4(5): p. 123-125.
[177] Picinbono, B., Some remarks on instantaneous amplitude and frequency ofsignals,time-frequency and time scale analysis. Proceedings of the IEEE-SP Interna-tional symposium on, 1998. p. 293-300.
[178] Penner, P. C, On the Hilbert, Fourier, and Wavelet transforms. Comm. Pure Appl.Math., 2002. 55: p. 772-814.
[179] Long, D. G., Comments On Hilbert Tansform-based signal analysis. MERS Report,2004.04-001.
[180] Huang, N. E. and Shen, S. S. (ed.), Hilbert-Huang Transform and Its Applications 1.Introduction to the hilbert huang trasnform and its related mathmetical problems WorldScientific. 2005. p. 1-26.
[181] Huang, N. E. and Wu, Z., A review on Hilbert-Huang transform: methodand its applications to geophysical studies. Rev. Geophys., 2008. 46, RG2006,doi:10.1029/2007RG000228
[182]黄永祥，圆柱绕流和大气湍流的Hilbert-Huang变换分析．2006，上海大学硕士学位论文：上海．
[183] Huang Y. X., Schmitt, F. G., Lu, Z. M. and Liu, Y. L., An amplitude-frequency study of turbulent scaling intermittency using Hilbert spectral analysis. Europhys.Lett., 2008. 84: 40010.
[184]黄永祥，任意阶Hilbert谱分析：定义及其在充分发展湍流和环境数据中的应用．2009，上海大学博上学位论文：上海．
[185] Su, Z. Y, Wang, C. C, Wu, T., Wang, Y T. and Feng, C. T., Instantaneous frequency-time analysis of physiology signals: The application of pregnant women's radial artery pulse signals . Physica A, 2008. 387: p. 485-494.
[186] Janosi, I. and Muller, R., Empirical mode decomposition and correlation properties of long daily ozone records. Phys. Rev. E, 2005. 71: 56126.
[187] Sole, J., Turiel, A. and Llebot, J., Using empirical mode decomposition to correlate paleoclimatic time-series. Nat. Hazards Earth Syst. Sci., 2007. 7: p. 299-307.
[188] Chen, J., Xu, Y L. and Zhang, R. C, Modal parameter identification of Tsing Ma suspension bridge under Typhoon Victor: EMD-HT method. J. Wind Eng. Ind. Aerodyn., 2004. 92(10): p. 805-827.
[189] Loutridis, S. J., Resonance identification in loudspeaker driver units: A comparison of techniques . Appl. Acoust., 2005. 66(12): p. 1399-1426.
[190] Gerz, T., Schumann, U., A possible explanation of counter-gradient fluxes in homogeneous turbulence . Theor. Comput. Fluid Dyn., 1996. 8: p. 169-181.
[191] Deissler, R. G., Effects of inhomogeneity and of shear flow in weak turbulent fields.Phys.Fluids,1961.4：p.1187-1198.
[192]刘宇陆，蒋剑波，卢志明，湍流直接相互作用原理与湍流逆输运．湍流研究最新进展，王晋军等编，2001：p.50-57.
[193]Kraichnan，R.H.，Lagrangian-history closure approximation for turbulences.Phys. Fluids．1965.8：p.575-598.
[194]Kraichnan，R.H.，Isotropic turbulence and inertial-range structure in the abridged LHDI approximation.Phys.Fluids,1965.9：p.1728-1752.
[195]Leslie，D.C.，Developments in the theory of turbulence．Clarendo，oxford，1972.
[196]Yoshizawa，A.，Statistical modelling of a passive-scale diffusion in turbulent shear flows.J.Fluid Mech.,1988.195：p.541-555.
[197]Hamba，F.，Towards modellding inhomogeneous compressible turbulence using a two- scale statistical theory. Phys.Fluids，1997.(9)：p.2749-2768.
[198]Kraichnan，R.H.，Developments in the theory ofturbulence.Clarendon Press，Oxford，1973.
[199]Holloway,G.，TConsiderations on the theory of temperature spectra in stably stratified turbulence.Journal of Physical Oceanography,1986.16(12)：p. 2179-2183.
[200]Yoshizawa，A.and Nisizima，S.，A nonequilibrium representation of the turbulent vis- cosity based on a two-scale turbulence theory.Phys.Fluids A,1993.4：p.3302-3305.
[201] Speziale, C. G., Analytical Methods for the Development of Reynolds-Stress Closuresin Turbulence. Ann. Rev. Fluid Mech., 1991. 23: p. 107-157.
[202] Okamoto, M., Theoretical investigation of an eddy-viscosity-type representation of theReynolds stress. J. Phys. Soc. Jpn., 1994. 63: p. 2102-2122.
[2] Twonsend,A. A., The structure of turbulent shear flow. Cambridge Press, Cambridge,1956.
[3] Corrsin, S., Investigation of flow in an axially symmetric heated jet of air. NACA, Adv.Conf. Rep. 1943. 3L23.
[4] Veeravalli, S. and Warhaft, Z., The shearless sturbulence mixing layer. J. Fluid Mech.,1989. 207: p. 191-229.
[5] Jayesh, Yoon, K. and Warhaft, Z., Turbulent mixning and transport in a thermallystratified interfacial layer in decaying grid turbulence. Phys. Fluids A, 1991. 3: p. 1143-1155.
[6] Jayesh and Warhaft, Z., Turbulent penetration of a thermally stratified interfacial layerin a wind tunnel. J. Fluid Mech., 1994. 277: p. 23-54.
[7] Spedding, G.R., Browand, F.K. and Fincham, A.M., Turbulence, similarity scaling andvortex geometry in the wake of a towed sphere in a stably stratified fluid. J. Fluid Mech.,2002. 450: p. 1-32.
[8] Spedding, G.R., Vertical structure in stratified wakes with high initial Froude number.J. Fluid Mech. , 1996. 314: p. 53-103.
[9]邱翔，黄永祥，卢志明，刘宇陆，稳定分层湍流的PIV实验研究．实验流体力学，2008.22(2)：p.1-9.
[10] Thoroddsen, S. T., Atta, C. W V. and Collins, J. J., The influence of stable stratificationon small-scale anisotropy and disspation in turbulence. J. Geophys. Res., 1992. 97: p.3647-3658.
[11] Piccirillo, P. and Atta,C.WV., The evolution of uniformly sheared thermally stratifiedturbulent flow. J. Fluid Mech. , 1997. 334: p. 61-86.
[12]金海生，温度分层剪切流的实验和数学模型研究．河海大学学报，1991. 19(4)：p. 59-67.
[13] Thoroddsen, S. T. and Atta, C. W. V., Experimental study of the effects of grid configuration on stably stratified frid-turbulence. Dyn. Atmos. Oceans, 1993. 19: p. 259-288.
[14]Prastowo，T.，Griffiths，R.W.，Hughes，G. and Hogg，A.M.，Mixing efficiencyin con- trolled exchange flows. J. Fluid Mech．,2008.600：p.235-244.
[15]Jackson，P.R. and Rehmann，C.R.，Kinematic effects of differential transport on mixing efficiency in a diffusively stable turbulent flow. J. Phys. Oceanogr．,2003.33：p.299-304.
[16]褚克坚，华祖林，王惠民，邢领航，张鸿星，明渠剪切分层流垂向扩散特性试验研究．水科学进展，2005.16(1)：p.13-17.
[17]华祖林，褚克坚，邢领航，强弯条件下分层流运动特性试验研究．水科学进展，2005.16(2)：p.203-209.
[18]华祖林，邢领航，褚克坚，弯段温差剪切分层流断面环流结构与掺混强度研究．水科学进展，2007.18(4)：p.531-537.
[19]White，B.L. and Helfrich，K.R.，Gravity currents and internal waves in a stratifed fluid．J.Fluid Mech.2008.616：p.327-356.
[20]Lin，J.T. and Veenhuizen，S.D.，Measurements of the decay of grid generated turbu- lence.Flow Research Note，1975.10：p.1-20.
[21]Dickey,T.D. and Mellor,G.L.，Decaying Turbulence in neutral and stratified fluids.J. Fluid Mech.，1980.99：p.13-31.
[22]Britter,R.E.，Hunt，J.C.R.，Marsh，G.L. and Snyder,W.H.，The effect of stable statification on turbulence diffusion and the decay of grid turbulence．J.Fluid Mech.，1983.127：p.27-44.
[23]Yoon，K.and Warhaft，Z.，The evolution of grid-generated turbulence under condition of stable thermal stratification. J. Fluid Mech.，1990.215：p.601-638.
[24]Hsien，T.L.，Energetics of grid turbulence in a stably stratified fluid J. Fluid Mech.，1995.296：p.127-157.
[25]Hurst，D. and Vassilicos J. C.，Scaling and decay of decay of fractal-generated turbu- lence. Phys. Fluids，2007.19：35103.
[26]Itsweire，E.C and Helland K.N.，Spectra and energy transfer in stably stratified turbulence Journal of Fluid．Mechanics，1989.207：p.419-452.
[27]Lienhard，J. H. and Atta，C.W.V.，The decay of turbulence in thermally stratified flow. J.Fluid Mech．, 1990.210：p.57-112.
[28]Vinnichenko，N.K.，Pinus，N.Z. and Shur，G.N.，Fine-scale structure of atmosphere. Proc. Int. Coll. Acad. Sci．,USSR．Moscow,1965.
[29]Komori，S.，Ueda，H.，Ogino，F. and Mizushina，T.，Turbulence structure in stablystratified open-channel flow．J.Fluid Mech．,1983.130：p.13-26.
[30] Komori, S. and Nagata, K., Effects of molecular diffusivities on counter-gradient scalarand momentum transfer in strongly stable stratification. J. Fluid Mech., 1996. 326: p.205-237.
[31] Stillinger, D. C, Helland, K. N. and Atta, C. W. V, Experiments on the transition ofhomogenous turbulence to internal waves in a stratified fluid. J. Fluid Mech., 1983. 131:p. 91-122.
[32] Rohr, J. J., Itsweire, E. C, Helland, K. N. and Atta,C. W. V, CGrowth and decay ofturbulencein a stably stratified shear flow. J.Fluid Mech., 1988. 195: p. 77-111.
[33] Veeravalli, S. and Warhaft, Z., Thermal dispersion from a linesource in the shearlessturbulence mixing layer. J. Fluid Mech., 1990. 216: p. 35-70.
[34]张晓航，许春晓，张兆顺，Serge，S. and Ayrault，M.，无剪切湍流混合层中被动标量扩散的实验实验研究．流体力学实验与测量，2003.17(4)：p.22-27.
[35] Deissler, R. G., Analysis of multipoint-multitime correlations and diffusion in decayinghomogeneous turbulence, in NASA Tech. Rep. 1961. p. R-96.
[36] Deissler, R. G., Turbulence in the presence ofaveritical body and temperature gradient.J. Geophys. Res., 1962. 67: p. 3049-3062.
[37] Deissler, R. G., Effect of Initial Condition on Weak Homogeneous Turbulence withUniform Shear. Phys. Fluids, 1970. 13(7): p. 1868-1869.
[38]邱翔，分层流动中湍流结构和湍流逆梯度输运特性研究．2006.上海大学博士学位论文：上海．
[39] Hunt, J. C. R., Stretch, D. D. and Britter, R. E., Length scales in stably stratified turbulent flows and their use in turbulence models. In: Puttock, J. S., (ed.) Stably Stratified Flow and Dense Gas Dispersion. Clarendon Press, Oxford, Great Britain, 1988.
[40] Miyazaki, T., Parametric excitation of buoyancy ocillation and formation of internal boundary layers in a stably stratified fluid. Phys. Fluids A, 1992. 4(10): p. 2145-2150.
[41] Hanazaki, H. and Hunt,J. C. R., Linear processes in unsteady stably stratified turbulence. J. Fluid Mech., 1996. 318: p. 303-337.
[42] Galmiche, M., Hunt, J. C. R., Thual, O. and Bonneton, P., Turbulence-mean field interactions and layer formation in a stratified fluid. Eur. J. Mech. -B/Fluids, 2001. 20: p. 577-585.
[43] Galmiche, M. and Hunt, J. C. R., The formation of shear and density layers in stablystratied turbulent flows: linear processes. J. Fluid Mech. , 2002. 455: p. 243-262.
[44] Hanazaki, H. and Hunt, J. C. R., Structure of unsteady stably stratified turbulence withmean shear. J. Fluid Mech. , 2004. 507: p. 1-42.
[45] Jackson, P.R. and Rehmann, C. R., Theory for differential transport of scalars insheared stratified turbulence. J. Fluid Mech., 2009. 621: p.1-21.
[46] Kraichnan R. H., Irreversible statistical mechanics of incompressible hydromagneticturbulence. Phys. Rev., 1958. 109: p. 1407-1422.
[47] Shimomura, Y, A theoretical study of the turbulent diffusion in incompressible shearflows and in passive scalars. Phys. Fluids, 1998. 10(10): p. 2636-2646.
[48] Okamoto, M., Theoretical investigation of energy and thermal intensity spectra inbuoyancy-driven turbulence flows. J. Phys. Soc. Jan., 1996. 65(10): p. 3193-3201.
[49] Okamoto, M., Theoretical modeling of buoyancy-driven turbulent flows. J. Phys. Soc.Jan., 1996. 65(7): p. 2044-2059.
[50]蒋剑波，刘宁陆，卢志明，湍流动量、标量及能量的逆梯度输运模型．应用数学和力学，2001.22(3)：p.267-274.
[51]蒋剑波，刘宇陆，卢志明，湍流逆梯度输运的理论与实验研究．力学进展，2000.30(3)：p.425-432.
[52] Riley, J. J., Metcalfe, R. W. and Weissman, M. A., Direct numerical simulations ofhomogeneous turbulence in density stratified fluids, in Proc. AIP Conf. Nonlinear properties of internal waves, 1981.
[53] Metais, O. and Herring, J. R., Numerical simulation of freely evolving turbulence instably stratified fluids. J. Fluid Mech., 1989. 202: p. 117-148.
[54] Gerz, T., Schumann, U. and Elghorashi, S. E., Direct numerical simulation of stratifiedhomogenous turbulent shear flows. J.Fluid Mech., 1989. 200: p. 563-594.
[55] Gerz, T. and Schumann, U., Direct simulation of homogenous turbulence and gravitywave in sheared an unsheared stratified flows. Turbulence Shear Flow 7, ed. Durst, F. etal., Springer, 1991: p. 27-45.
[56] Holt, S. E., Koseff, J. R. and Ferziger, H., A numerical study of the evenolution andstructure of homogeneous stably stratified sheared turbulence. J.Fluid Mech., 1992.237: p. 499-539.
[57] Gerz, T. and Yamazaki, H., Direct simulation of buoyancy-driven turbulence in stablystratified fluid. J. fluid Mech., 1993. 249: p. 415-440.
[58] Kaltenbach, H. J., Gerz, T. and Schumann, U., HLarge-eddy simulation of homogeneous and diffusion in stably stratified shear flow. J. Fluid Mech., 1994. 280: p. 1-40.
[59] Jin, H. S. and Zhang, S. N., Numerical Simulation of stratified flow with both vertical temperature gradient and vertical salinity gradient. Journal of Hydrodynamics, Ser.B, 1992. 2: p. 24-30.
[60] Kyle, A. B. and Sarkar, S., Evolution of an initially turbulent stratified shear layer. Phys. Fluids, 2007. 19: 105105.
[61] Brethouwer, G., Billant, P., Lindborg, E. and Chomaz, J. M., Scaling analyzing and simulation of strongly stratified turbulent flows. J. Fluid Mech., 2007. 585: p. 343-368.
[62] Lvescu, D. and Ristorcelli, J. R., Variable-density mixing in buoyancy-driven turbulence. J. Fluid Mech., 2008. 605: p. 145-180.
[63] Briggs, D. A., Ferziger, J. H., Koseff, J. R. and Monismith, S. G., Entrainment in a shear-free Turbulent mixing layer. J. Fluid Mech., 1996. 310: p. 215-241.
[64]金海生，张书农，同时存在温度和盐度梯度的分层流的数值模拟．水动力学研究与进展A，1991.6(4)：p.72-78.
[65]沈永明，胡振红，刘才广，魏文礼，温度和盐度分层流的二维应力2通量代数湍流模型．环境科学学报，2004.24(3)：p.389-393.
[66]邱晨霞，汗德，许协庆，应用模型模拟三维分层流．水利学报，1997.7：p.7-12.
[67]俞剑冬，刘桦，朱志伟，二层密度分层流体重力流的数值模拟．力学季刊，2007.28(4)：p.539-548.
[68] Yoshizawa, A., A statistical theory of thermally driven turbulent shear flow , with thederivation of subgrid model. J. Phys. Soc. Japan, 1983. 52 : p.1194-1205.
[69] Yu-hong, D., Feng-quan, Z., Xi-yun, L. and Li-xian, Z.,An investigation of turbulentheat transfer in channel flows by large eddy simulation. Journal of Hydrodynamics,Ser.B, 2002. 14(2): p. 32-38.
[70] Yu-Hong, D., Xi-Yun, L. and Li-Xian, Z., Large eddy simulation of turbulent channelflow with mass transfer at high-Schmidt numbers. International Journal of Heat and MassTransfer 2003. 46(9): p. 1529-1539.
[71]仲峰泉，庄礼贤，刘难生，陆夕云，An improved dynamic subgrid-scale modeland its application to large eddy simulation of stratified channel flows. Science in China,Ser. A, 2002. 45(7): p. 74-85.
[72]董宇红，陆夕云，庄礼贤，LES OF Thermally-stratified Turbulent Channel flow with temperature oscillation on the bottom wall. Journal of Hydrodynamics，Ser.B，2004(1)：p.34-38.
[73]张华，许桂生，二维分层流的格子Boltzmann数值模拟．水利学报，2006 37(11)：p.1367-1371.
[74]Junmei，J.，Xiang，Q. and Yulu，L.，Numerical Study of Turbulent Counter-Gradient Momentum Transport in Stable Stratified Flows.水动力学研究与进展A，2005. 20(4)：p. 426-435.
[75]Minjie，T. and Zhiming，L.，Numerical study of turbulent characteristics in convective boundary layer.力学季刊，2005.26(3)：p.354-360.
[76]邱翔，黄永祥，卢志明，刘宇陆，稳定分层流动中湍流统计特性和输运特性的数值研究．应用数学和力学，2009.30(2)：p.149-159.
[77]邱翔，张道祥，卢志明，刘宇陆，Turbulent mixing and evolution in a stably stratifiedflow with a temperature step. Journal of Hydrodynamics, 2009. 21(1): p. 84-92.
[78] Pope, S. B., turbulent flows. Cambridge University Press, 2000.
[79] Townsend,A.A., Strcture of turbulent shear flow. Cambridge Univ. Press, Cambridge,2nd, 1976.
[80] Bell, J. H. and Mehta, R. D., Development of a two-stream mixing layer from trippedand untripped boundary layers. AIAA Journal, 1990. 28(12): p. 2034-2042.
[81] Phillips, O. M., Atmosheric turbulence and radio-wave propagation, eds. Yaglom, A.M. and Tatarskii, U. I., Nauka, Moscow,1967.
[82] Posmentier, E. S., The generation of salinity finestructure by verical diffusion. J. Phy.Oceanogr., 1977. 7: p. 298-300.
[83] Galaktionov, O., Maderich, V. and Nikishov, V, Evolution of layered structures in thefinal stage of turbulent decay in a stably stratified fluid. Dynamics of Atmosphere andoceans, 2001.34: p. 125-144.
[84] Godeferd R S. and Cambon, C, Detailed investigation of the energy transfer in homogenous stratified turbulence. Phys. Fluids, 1994. 6(6): p. 2084-2100.
[85] Huq, P. and Blitter, R. E., Turbulence evolution and mixing in a two-layer stably stratified fluid. J. Fluid Mech., 1995. 285: p. 41-67.
[86]褚克坚，温差剪切分层流运动特性试验及数值模拟研究．2006.河海大学博士学位论文：南京．
[87] Taylor, G. I., Statistical Theory of Turbulence Proc. R. Soc. Lond. A September 2,1935. 151: p. 421-444.
[88] Tan, H. S. and Ling, S. C, Final stage decay of grid-produced turbulence. Phys. Fluids,1963. 6: p. 1693-1699.
[89] Paulsson , Comte-Bellot, G. and Corrsin ,S., The use of contraction to improve theisotropy of grid-generated turbulence. J. Fluid Mech., 1966. 25: p. 657-682.
[90] Warhaft, Z. and Lumley, J. L., An experimental study of the decay of temperaturefluctuations in grid-generated turbulence. J. Fluid Mech., 1978. 88: p. 659-684.
[91] Tavoularis, S. and Corrsin, S., Experiment in nearly homogeneous turbulent shear flowswith a uniform mean temperature gradient. Part I. J. Fluid Mech., 1981. 104: p. 311-347.
[92] Tavoularis, S., Asymptotic laws for transversely homogeneous turbulent shear flows.Phys. fluid, 1985. 28: p.999-1001.
[93]陈景仁，湍流模型及有限分析法．上海交通大学出版社，1989.
[94]李玲，徐忠，颗粒存在对网栅后气相流动湍流特性的影响．应用力学学报，2000.17(1)：p.36-41.
[95] Kang, H. S., Chester, S. and Meneveau, C, Decaying turbulence in an active-grid-generated flow and comparisons with large-eddy simulation. J. Fluid Mech., 2003. 480: p. 129-160.
[96] Eskinazi, S. and Yeh, H.,An investigatioin of fully developed turbulent flows in a curved channel. J. Aeronaut. Sci., 1956. 23: p. 23-31.
[97] Beguier, C, Giraltl, F., Fulachier, L. and Keffer, J. F., Negative production in turbulent shear flows . Lecture notes in physics, 1978. 76: p. 22-35.
[98]蒋剑波，湍流逆梯度输运的理论与实验研究．2002，上海大学博士学位论文：上海．
[99] Bunker, A.F., Measurements of counter-gradient heat flux in the atmospheres. Austr. J.Phys., 1956. 9: p. 133-143
[100] Starr, V, Physics of negative viscosity phenomena. Mc-Graw-Hill Book Co., NewYork, 1968.
[101] Deardorff, J. W., The Counter-gradient heat flux in the lower atmoaphere and in thelaboratory. 1. Atmosph. Sci., 1966. 23: p. 503-506.
[102] Yoshizawa, A., Statistical analysis of the deviation of the Reynlods stress from its eddy-viscosity represention. Phys. Fluids 1984. 27(6): p. 1377-1387.
[103] Okamoto, M., Theoretical investigation of energy and thermal intensity spectra inbuoyancy-driven turbulence ?ows. J.Phys. Soc. Jan., 1996, 65(10): p. 3193-3201.
[104] Deardor?, J. W. and Willis, G. E., Further results from a laboratory model of theconvective planetary boundary layer. Boundary-Layer Meteorol, 1985. 32: p. 205-236.
[105] Nagata, K. and Komori, S., The di?erence in turbulent di?usion between active andpassive scalars in stable thermal stratification. J. Fluid Mech., 2001. 430: p. 361-380.
[106] Gerz, T. and Schumann, U., Direct simulation of homogenous turbulence and gravitywave in sheared an unsheared stratified ?ows. In turbulence Shear Flow 7 (ed. Durst, F.,Launder, B. E., Reynolds, W. C., Schmidit, F. W. and Whitelaw, J. H. ), Springer,1991.p. 27-45.
[107] Schumann, U., Elghobashi, S. E. and Gerz, T., Direct simulation of stably stratifiedturbulent homogeneous shear ?ow, Direct and Large Eddy Simulation of Turbulence,ed.Schumann, U. F., Braunschweig: Vieweg-V., 1986. 15: p. 245-264.
[108] Kolmogorov, A. N., A local structure of turbulence in incompressible viscous ?uid forvery large Reynolds numbers. Dokl. Akad. Nauk SSSR, 1941. 30: p. 299-303.
[109] Batchelor, G. K., Howells, I. D. and Townsend, A. A., Small-scale variation of con-vected quantities like temperature in turbulent ?uid Part 2. The case of large conductiv-ity. J. Fluid Mech., 1959. 5: p. 134-139.
[110] Von Karman, T., Progress in Statistical Theory of Turbulence. Proc. Natl. Acad. Sci.(USA), 1948. 34: p. 530-539.
[111] Corrsin, S., On the spectrum of isotropic temperature ?uctuations in an isotropic tur-bulence. J. Appl. Phys., 1951. 22(4): p. 469-473.
[112] Heisenberg, W., On the Theory of Statistical and Isotropic Turbulence. Proc. R. Soc.Lond. A , 1948. 195: p. 402-406.
[113] Chandrasekhar, S., The theory of statistical and isotropic turbulence. Phys. Rev. , 1949.75(5): p. 896-897.
[114] Kovaszanay,L.S.G., Spectrum of locally isotropic turbulence. J. Aeronaut. Sci.,1948.15:p.745-753.
[115] Kraichnan, R. H. Small-scale structure of a scalar field convected by turbulence. Phys.Fluids, 1968. 11(5): p. 945-953.
[116] Obukhov, A. M., Structure of the temperature field in turbulent ?ows. Izv. Akad. NaukSSSR Geogr. Geofiz. 1949. 13: p. 58-69.
[117] Lumley, J. L., Similarity and the Turbulent Energy Spectrum. Phys. Fluids, 1967. 10:855. DOI:10.1063/1.1762200
[118] Saddoughi, S. G. and Veeravalli, S. V., Local isotropy in turbulent boundary layers athigh Reynolds number . J. Fluid Mech., 1994. 268: p. 333-372.
[119] Lohse, D., Temperature spectra in shear ?ow and thermal convection. Phys. Lett. A ,1994. 196: p. 70-75.
[120] Sreenivasan, K., On local isotropy of passive scalars in turbulent shear ?ows. Proc. R.Soc. London, Ser. A, 1991. 434: p. 165-182.
[121] Oboukhov, A. M., Structure of the temperature field in turbulent ?ow. Izv. Akad. Nauk.SSSR, Ser. Geogr. I Geofiz., 1949. 13: p. 58-69.
[122] Hill, R. J., Models of the scalar spectrum for turbulent advection. J. Fluid Mech., 1978.88: p. 541-562.
[123] Hill, R. J. and Cli?ord, S. F., Modified spectrum of atmospheric temperature ?uctu-ations and its application to optical propagation. J. Opt. Soc. Am., 1978. 68(7): p.892-899.
[124] Tatarskii, V. I., The E?ects of the Turbulent Atmosphere on Wave Propagation. Keter,Jerusalem, 1971.
[125] Bolgiano, R., Turbulent spectra in a stably stratified atmosphere.J. Geophys. Res.,1959. 64: p. 2226-2229.
[126] Bolgiano, R., Structure of turbulence in stratified media. J. Geophys. Res., 1962. 67: p.3015-3023.
[127] Shur,G,N., Experimental investigation of the energy spectrum of atmospheric turbu-lence. Trudy of Aerological Observation,1962. 43:p. 79-90.
[128] Nastrom, G. D., Gage, K. S. and Jasperson, W. H., Kinetic energy spectrum of largeand mesoscale atmospheric processes. Nature, 1984. 310: p. 36-38.
[129] Dalaudier, F., and Sidi, C., Evidence and interpretation of a spectral gap in the turbulentatmospheric temperature spectra. J. Atmos. Sci., 1987. 44: p. 3121-3126.
[130] Lumley, J. L., The spectrum nearly inertial turbulence in a stably stratified ?uid. J. ofAtmospheric Sciences, 1964. 21: p. 99-102.
[131] Grant, H. L., Stewart, R. W. and Moilliet, A., Turbulence spectra from a tidal channel.J. Fluid Mech., 1962. 12: p. 241-263.
[132] Gargett, A. E., Evolution of scalar spectra with the decay of turbulence in a stratified fluid J. Fluid Mech., 1985. 159: p. 379-407.
[133] Kotsovinos, N. E., Stewart, R.W. and Moilliet, A., Turbulence spectra in free convection flow. Physics. Fluids A, 1991. 3(1): p. 163-167.
[134] Papailiou, D. D. and Lykoudis, P. S., Turbulent free convection flow. Int. J. Heat Mass Transfer, 1974. 17: p. 161-172.
[135] Bill, R. G. and Gebhart, B., The development of turbulent transport in a vertical natural convection. Int. J. Heat Mass Transfer, 1979. 22: p. 267-277.
[136] Xia, H., Punzmann, H., Falkovich, G. and Shats, M. G.,Turbulence-Condensate Interaction in Two Dimensions. P.R.L., 2008.101:194504.
[137]是勋刚，湍流．天津大学出版社，1984
[138] Hannoun, I. A., Fernando, H. J. S. and List, E. J., Turbulence structure near a sharp density interface. J. FluidMech., 1988. 189: p. 189-209.
[139] Shy, S. S. and Breidenthal, R. E., Laboratory experiments on the cloud-top entrainment instability. J. FluidMech., 1990. 214: p. 1-15.
[140] Venkataramani, K. S. and Shevray, R., Statistical features of heat transfer in grid-generated turbulence: constant-gradient case. J. Fluid Mech., 1978. 86: p. 513-543.
[141] Sirivat, A. and Warhaft, Z., The effect of a passive cross-stream temperature gradient on the evolution of variance and heat flux in grid turbulence. J. Fluid Mech., 1983. 128: p. 323-346.
[142] Webster, C, An experimental study of turbulence in a density stratified shear flow. J. Fluid Mech., 1964. 19: p. 221-245.
[143]冯素晓，稳定分层湍流中湍流混合层和动量梯度输运特性的实验研究．2008.上海大学硕士学位论文：上海．
[144]张贤达，保铮，非平稳信号分析与处理．国防工业出版社，1998
[145] Frisch, U., Turbulence: The legacy of A. N. Kolmogorov. Cambridge University Press,1995.
[146] Sreenivasan, K. R. and Antonia, R. A., The phenomenology of small-scale turbulence.Annual Rev. of Fluid Mechanics, 1997. 29: p. 435-472.
[147] Anselmet, F., Djeridi, H. and Fulachier, L., Joint statistics between a passive scalar andits dissipation in turbulent flows. Journal of Fluid Mechanics, 1994. 280: p. 173-197.
[148] Acharya, S. and Panigrahi, P. K., Analysis of large scale structures in separated shearlayers. Experimental thermal and fluid science, 2003. 27: p. 817-828.
[149] Orlandi, P., Energy spectra power laws and structures. J. Fluid Mech., 2009. 623: p.353-374.
[150] Voropayev, S. I., Fernando, H. J. S., and Morrison, R., Dipolar eddies in a decayingstratified turbulent flow. Phys. Fluids, 2008. 20: 026602.
[151] Costa-Patry, E. and Mydlarski, Mixing of two thermal fields emitted from line sourcesin turbulent channel flow. J. Fluid Mech., 2008. 609: p. 349-375.
[152]孟庆国，蔡庆东，李存标，能谱在解释湍流能量级串中值得注意的一个问题．物理学报，2004，53(9)：p.3090-3093.
[153] Cohen, L., Time-frequency Analysis . eds. Cliffs, E.,New Jersey: Prentice-Hall, 1995.
[154] Monin, A. S. and Yaglom, A. M., Statistical Fluid Mechanics: Mechanics of Turbulence. Vol. 1. MIT Press, Cambridge, Massachusetts, 1971.
[155]蔡树棠，刘宇陆，湍流理论．上海交通大学出版社，上海，1993.
[156] Antonia, R. A., Conditional sampling in turbulence measurement. Ann. Rev. FluidMech., 1981. 13: p. 131-156.
[157] Robinson, S. K., Coherent motions in the turbulent boundary layer. Ann. Rev. FluidMech., 1991. 23: p. 601-639.
[158] Falco, R. E., Coherent motions in the outer region of turbulent boundary layers Phys.Phys.Fluids, 1977. 20: p. 124-132.
[159] Fiedler, H. E., Coherent structures in turbulent flows. Prog. Aerospace Sci., 1988. 25:p. 231-269.
[160] Berkooz, G., Holmes, P. and Lumely, J. L, The proper orthogonal decomposition inanalysis of turbulent flows. Annu. Rev. Fluid Mech., 1993. 25: p. 539-575.
[161] Farge, M., A Wavelet Transforms and their Applications to Turbulence. Annu. Rev.Fluid Mech., 1992. 24: p. 395-457.
[162] Argoul,F, Ameodo,A., Grasseau, Hop finger, E. J. and Frisch, U., Wavelet analysis ofturbulence reveals the multifractal nature of the Richardson cascade. Nature, 1989. 338:p. 51-53.
[163] Farge, M., Schneider, K., Analysis anad computing turbulent flows using wavelets:Newtrends in turbulence:aspects nouveaux. eds. Lesieur,M., Yaglom, A., and David, F.Spring, 2001. p. 450-503.
[164] Daubechies, I., Ten lectures on wavelets: SIAM, 1992.
[165] Huang, N. E., Shen, Z. and Long, S. R., et.al, The Empirical Mode Decomposition andthe Hilbert Spectrum for Nonlinear and Non-stationary Time Series Analysis. Proc. R.Soc. London. A, 1998. 454: p. 903-995.
[166] Huang, N.E., Z. Shen, and S.R. Long, A New View of Nonlinear Water Waves: theHilbert Spectrum. Annu. Rev. Fluid Mech., 1999. 31: p. 417-437.
[167] Huang, N. E., Computer implicated empirical mode decomposition method. Apparatus,and Article of Manufacture., U.S. Pending, 1999.
[168] Huang, N. E., Long, S. R. and Shen, Z., The Mechanism for Frequency Downshift InNonlinear Wave Evolution. Adcances in Applied Mechanics, 1996. 32: p. 59-111.
[169] Huang, N. E., Long, S. R. and Qu ,W. D., Application of Hilbert-Huang Transform toNon-stationary financial tome series analysis. Appl. Stochastic Models Bus. Ind., 2003.19: p. 245-268.
[170] Tsinober, A., An informal introducton to turbulence. Kluwer, 2001.
[171] Wu, Z. and Huang, N. E., A study of the characteristics of white noise using the em-pirical mode decomposition method Flandrin, P. Gonc?alve′s, P. Empirical Mode De-compositions as Data-Driven Wavelet-Like Expansions. Int. J. Wavelets, Multires. Info.Proc., 2004. 2: p. 477-496.
[172] Huang, Y., Schmitt, F. G., Lu, Z., and Liu, Y., An amplitude-frequency study of turbulentscaling intermittency using Hilbert spectral analysis. Europhys. Lett., 2008. 84: 40010.
[173] Rilling, G., Flandrin, P. and Goncalves, P., On Empirical Mode Decomposition and itsAlgorithms. in IEEE-EURASIP Workshop on Nonlinear Signal and Image ProcessingNSIP-03.Grado, Italy, 2003.
[174] Long, S. R., Huang, N. E. and Tung, C. C., The Hilbert Techniques: an AlternateApproach for Non-steady Time Series Analysis. IEEE Geosci. Remote Sensing Soc.Lett., 1993. 3: p. 6-11.
[175] Jones,G. and Boashash,B. Instantaneous frequency,instantaneous bandwidth and theanalysis of multicomponent signals. Proc. IEEE ICASSP-90,1990.5:p.2467-2470.
[176] Loughlin, P. and Tacer, B., Comments on the interpretation of instantaneous frequency.IEEE Signal Process. Lett., 1997. 4(5): p. 123-125.
[177] Picinbono, B., Some remarks on instantaneous amplitude and frequency ofsignals,time-frequency and time scale analysis. Proceedings of the IEEE-SP Interna-tional symposium on, 1998. p. 293-300.
[178] Penner, P. C, On the Hilbert, Fourier, and Wavelet transforms. Comm. Pure Appl.Math., 2002. 55: p. 772-814.
[179] Long, D. G., Comments On Hilbert Tansform-based signal analysis. MERS Report,2004.04-001.
[180] Huang, N. E. and Shen, S. S. (ed.), Hilbert-Huang Transform and Its Applications 1.Introduction to the hilbert huang trasnform and its related mathmetical problems WorldScientific. 2005. p. 1-26.
[181] Huang, N. E. and Wu, Z., A review on Hilbert-Huang transform: methodand its applications to geophysical studies. Rev. Geophys., 2008. 46, RG2006,doi:10.1029/2007RG000228
[182]黄永祥，圆柱绕流和大气湍流的Hilbert-Huang变换分析．2006，上海大学硕士学位论文：上海．
[183] Huang Y. X., Schmitt, F. G., Lu, Z. M. and Liu, Y. L., An amplitude-frequency study of turbulent scaling intermittency using Hilbert spectral analysis. Europhys.Lett., 2008. 84: 40010.
[184]黄永祥，任意阶Hilbert谱分析：定义及其在充分发展湍流和环境数据中的应用．2009，上海大学博上学位论文：上海．
[185] Su, Z. Y, Wang, C. C, Wu, T., Wang, Y T. and Feng, C. T., Instantaneous frequency-time analysis of physiology signals: The application of pregnant women's radial artery pulse signals . Physica A, 2008. 387: p. 485-494.
[186] Janosi, I. and Muller, R., Empirical mode decomposition and correlation properties of long daily ozone records. Phys. Rev. E, 2005. 71: 56126.
[187] Sole, J., Turiel, A. and Llebot, J., Using empirical mode decomposition to correlate paleoclimatic time-series. Nat. Hazards Earth Syst. Sci., 2007. 7: p. 299-307.
[188] Chen, J., Xu, Y L. and Zhang, R. C, Modal parameter identification of Tsing Ma suspension bridge under Typhoon Victor: EMD-HT method. J. Wind Eng. Ind. Aerodyn., 2004. 92(10): p. 805-827.
[189] Loutridis, S. J., Resonance identification in loudspeaker driver units: A comparison of techniques . Appl. Acoust., 2005. 66(12): p. 1399-1426.
[190] Gerz, T., Schumann, U., A possible explanation of counter-gradient fluxes in homogeneous turbulence . Theor. Comput. Fluid Dyn., 1996. 8: p. 169-181.
[191] Deissler, R. G., Effects of inhomogeneity and of shear flow in weak turbulent fields.Phys.Fluids,1961.4：p.1187-1198.
[192]刘宇陆，蒋剑波，卢志明，湍流直接相互作用原理与湍流逆输运．湍流研究最新进展，王晋军等编，2001：p.50-57.
[193]Kraichnan，R.H.，Lagrangian-history closure approximation for turbulences.Phys. Fluids．1965.8：p.575-598.
[194]Kraichnan，R.H.，Isotropic turbulence and inertial-range structure in the abridged LHDI approximation.Phys.Fluids,1965.9：p.1728-1752.
[195]Leslie，D.C.，Developments in the theory of turbulence．Clarendo，oxford，1972.
[196]Yoshizawa，A.，Statistical modelling of a passive-scale diffusion in turbulent shear flows.J.Fluid Mech.,1988.195：p.541-555.
[197]Hamba，F.，Towards modellding inhomogeneous compressible turbulence using a two- scale statistical theory. Phys.Fluids，1997.(9)：p.2749-2768.
[198]Kraichnan，R.H.，Developments in the theory ofturbulence.Clarendon Press，Oxford，1973.
[199]Holloway,G.，TConsiderations on the theory of temperature spectra in stably stratified turbulence.Journal of Physical Oceanography,1986.16(12)：p. 2179-2183.
[200]Yoshizawa，A.and Nisizima，S.，A nonequilibrium representation of the turbulent vis- cosity based on a two-scale turbulence theory.Phys.Fluids A,1993.4：p.3302-3305.
[201] Speziale, C. G., Analytical Methods for the Development of Reynolds-Stress Closuresin Turbulence. Ann. Rev. Fluid Mech., 1991. 23: p. 107-157.
[202] Okamoto, M., Theoretical investigation of an eddy-viscosity-type representation of theReynolds stress. J. Phys. Soc. Jpn., 1994. 63: p. 2102-2122.