边界层转捩过程的涡系结构和转捩机理研究
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摘要
在流体力学的研究领域中,从层流向湍流过渡的转捩问题是一个十分重要而又极为复杂的难题,至今仍有许多问题有待进一步的深入研究。本文采用了最为精确的直接数值模拟方法,对可压缩流平板边界层转捩过程中的涡系结构和转捩机理进行了研究和探索,展示了基于空间模式的边界层转捩后阶段的全过程,验证了以前的数值模拟和实验结果,基于我们的精确模拟结果,进行探索和讨论,提出自己的新观念,分析和揭示边界层转捩的新机理。
文中采用直接数值模拟方法,通过三阶TVD Runge-Kutta法求解非定常Navier-Stokes方程,空间离散采用高精度的六阶中心紧致格式,并采用了隐式六阶紧致滤波方法。为了更好地抑制边界处的非物理的数值反射波,在远场和出口边界处采用了考虑横流项和粘性项效应的特征无反射边界条件。入流条件设置为层流速度型叠加二维和三维T-S扰动波。采用MPI信息传输协议和区域分解方法来实现并行化处理。直接数值模拟的结果表明统计平均的流动特性,如摩擦阻力系数,均流速度型,近壁剪切层的线性率,湍流区的对数率,以及扰动模态的空间发展与理论和实验结果很好地吻合。
文中对边界层转捩过程进行了深入细致的研究,主要是转捩过程的非线性的后阶段的涡系结构,包括典型涡系的形成,转捩过程的重要现象及其联系,以及转捩晚期阶段的涡结构和流动无序化过程,探索边界层转捩机理,其研究工作主要有:
1.研究了转捩过程中的典型涡系问题,着重于涡系结构,特别是流向涡和环状涡生成演化的一些新机理。数值结果表明,尽管两种转捩模式(K型和H型)在弱非线性阶段具有不同的特征性质和相应的空间分布模式,但是在边界层转捩的后阶段扰动发展的机理具有一致的典型涡系结构。直接数值模拟了转捩过程的细节,发现一种新的环状涡形成机理,是主流向涡和次生流向涡共同作用的结果。环状涡在流动转捩过程有着重要作用,环状涡的旋转运动将导致从无粘的高能量区到边界层内部的低能量区的巨大的动量和能量传输,没有环状涡就没有湍流的形成。
2.基于细网格的DNS数值模拟结果,详细分析研究了转捩过程的一些重要现象及其对转捩流场的影响。复杂的上喷下扫现象,是和转捩流场的涡结构紧密相关。仔细地研究了Λ-涡和环状涡周围的具体流动结构,得到的典型涡结构与上喷下扫运动相互联系的结论是和实验结果一致的。研究揭示了二次下扫运动、正负尖峰结构和高剪切层、雷诺应力分布的形成机理,以及它们与环状涡的联系。特别是,数值结果表明环状涡结构在近壁区诱发形成了正尖峰结构,其传播速度比包围它的附近流体的速度大好几倍,等于环状涡的传播速度。
3.在转捩的晚期阶段,对复杂的U形涡和桶形涡结构、湍流斑生成和小尺度涡等进行了研究。结果发现,环状涡链结构是稳定的,随着新环状涡形成,最前方的环状涡的涡量变弱、逐步耗散;另一方面,小尺度涡生成是次生涡和壁面间的干扰以及大涡结构的演化和诱导的结果。
概言之,文中发展了可压缩流边界层转捩的高精度、高效率的数值模拟方法,通过对可压缩流边界层转捩过程中的涡系结构的精确数值模拟和和转捩机理的深入研究和探讨,清晰地描述了边界层转捩后阶段的整个过程,分析和揭示了一些新的机理,如环状涡的形成和演化、二次下扫现象、正尖峰结构特性以及小尺度涡结构的生成原理等,其研究工作有着重要的理论意义和应用前景。
Transition from laminar flow to turbulent flow is one of the most important and complex problems in the field of fluid mechanics research. Vortical structures and transition mechanisms in the transition process of compressible boundary layer flow over a flat plate are investigated and explored using the most accurate method, direct numerical simulation of Navier-Stokes equations. The details of late stages of boundary layer transition based on the spatial model are revealed. Previous numerical simulation and experimental results are verified. Based on our accurate simulation results, some new ideas are put forward and some new mechanisms are studied and revealed.
In this paper, direct numerical simulation has been carried out. The time-dependent Navier-Stokes equations are solved directly by a third-order TVD Runge-Kutta method. A sixth order central compact scheme that facilitates high resolution of the flow field is used for spatial discretization together with a sixth order implicit compact filter. To avoid possible non-physical wave reflection from the boundaries, the non-reflecting boundary conditions including transverse and viscous effects are specified at the far field and the outflow boundaries. The inflow is specified by laminar flow profile with imposed eigenmodes of two-dimensional and three-dimensional Tollmien-Schlichting (T-S) waves. The parallel computation is accomplished through the Message Passing Interface (MPI) together with a domain decomposition approach. The DNS results show the mean flow properties, such as the skin friction coefficients and the mean velocity profile, wall shear linear law, log law in the turbulent region, as well as the spatial evolution of disturbance modes, which agree very well with the theoretic and experimental results.
This paper is devoted to thorough and considerate researches of transition process in a boundary layer, especially the vortical structures at the late stages of nonlinear transition process, including the formation of typical vortical structures, important flow transition events and their relationship, voritcal structures at very late stages of transition and the flow randomization process. The mechanisms of boundary layer transition are investigated, and the major research works include:
1. Typical vortical structures in transition process are discussed, focused on vortical structures and some new mechanism of the formation and evolution of streamwise vortex and ring-like vortex. Our numerical results shown that the mechanisms of disturbance development predominant at late stages of boundary-layer transition have universal typical vortex structure, despite the two regimes of transition (K- and H-regimes) have different peculiar properties and relative spatial positions at weakly nonlinear stages. In this paper, a new study for the mechanism of the ring-like vortex formation is discovered. According to our recent DNS results, the ring-like vortices generation is caused by the interaction between the prime streamwise vortices and secondary streamwise vortices. The ring-like vortex formation is a key issue of flow transition. The rotation movements of ring-like vortices induce huge momentum and energy transfer form high energy inviscid outer part of boundary layer to low energy inner part of boundary layer. There is no turbulence without ring-like vortices.
2. Some important events in transition process and the corresponding effects on transitional flow field are studied by fine gird direct numerical simulation results. Complex ejection and sweep movements have close relationship with vorical structures. The details of flow structure aroundΛvortex and ring-like vortex are studied. The relationship between ejection/sweep movements and vorical structures has been verified, which is consistent with experimental work. It is revealed that the mechanism of the second sweep generation, the positive spike formation, high shear layer and Reynolds stress distribution, and their relationship with ring-like vortices. In particular, numerical results show that positive spikes in the near-wall region induced by the ring-like vortices, propagate downstream with the same speed as the ring-like vortices, and the speed is several time faster than surrounding flow.
3. At the very late stages of transition, complex U-shaped vortex, barrel vortex, turbulent spot and small scale vortex are investigated. In particular, It is found that while new ring-like vortex are generated, vorticity of the leading ring-like vortex became weaker and dissipated gradually; on the other hand, small scale vortex is generated under the interaction between secondary vortex and solid wall, and induced by the evolution of large vortex structure.
In brief, a high-precision and high efficiency of numerical simulation method for compressible boundary layer transition is developed. Through the accurate numerical simulation of the vortical structures and analysis of the mechanism in transition process of compressible boundary layer flow, the whole procedure at the late stage of boundary layer transition has been clearly presented. Several new mechanisms are analyzed and revealed, such as the formation and evolution of ring-like vortices, the production of second sweep and positive spikes, and the formation theory of small-scale vortex structure. The research has important theoretical significance and application prospects.
文中采用直接数值模拟方法,通过三阶TVD Runge-Kutta法求解非定常Navier-Stokes方程,空间离散采用高精度的六阶中心紧致格式,并采用了隐式六阶紧致滤波方法。为了更好地抑制边界处的非物理的数值反射波,在远场和出口边界处采用了考虑横流项和粘性项效应的特征无反射边界条件。入流条件设置为层流速度型叠加二维和三维T-S扰动波。采用MPI信息传输协议和区域分解方法来实现并行化处理。直接数值模拟的结果表明统计平均的流动特性,如摩擦阻力系数,均流速度型,近壁剪切层的线性率,湍流区的对数率,以及扰动模态的空间发展与理论和实验结果很好地吻合。
文中对边界层转捩过程进行了深入细致的研究,主要是转捩过程的非线性的后阶段的涡系结构,包括典型涡系的形成,转捩过程的重要现象及其联系,以及转捩晚期阶段的涡结构和流动无序化过程,探索边界层转捩机理,其研究工作主要有:
1.研究了转捩过程中的典型涡系问题,着重于涡系结构,特别是流向涡和环状涡生成演化的一些新机理。数值结果表明,尽管两种转捩模式(K型和H型)在弱非线性阶段具有不同的特征性质和相应的空间分布模式,但是在边界层转捩的后阶段扰动发展的机理具有一致的典型涡系结构。直接数值模拟了转捩过程的细节,发现一种新的环状涡形成机理,是主流向涡和次生流向涡共同作用的结果。环状涡在流动转捩过程有着重要作用,环状涡的旋转运动将导致从无粘的高能量区到边界层内部的低能量区的巨大的动量和能量传输,没有环状涡就没有湍流的形成。
2.基于细网格的DNS数值模拟结果,详细分析研究了转捩过程的一些重要现象及其对转捩流场的影响。复杂的上喷下扫现象,是和转捩流场的涡结构紧密相关。仔细地研究了Λ-涡和环状涡周围的具体流动结构,得到的典型涡结构与上喷下扫运动相互联系的结论是和实验结果一致的。研究揭示了二次下扫运动、正负尖峰结构和高剪切层、雷诺应力分布的形成机理,以及它们与环状涡的联系。特别是,数值结果表明环状涡结构在近壁区诱发形成了正尖峰结构,其传播速度比包围它的附近流体的速度大好几倍,等于环状涡的传播速度。
3.在转捩的晚期阶段,对复杂的U形涡和桶形涡结构、湍流斑生成和小尺度涡等进行了研究。结果发现,环状涡链结构是稳定的,随着新环状涡形成,最前方的环状涡的涡量变弱、逐步耗散;另一方面,小尺度涡生成是次生涡和壁面间的干扰以及大涡结构的演化和诱导的结果。
概言之,文中发展了可压缩流边界层转捩的高精度、高效率的数值模拟方法,通过对可压缩流边界层转捩过程中的涡系结构的精确数值模拟和和转捩机理的深入研究和探讨,清晰地描述了边界层转捩后阶段的整个过程,分析和揭示了一些新的机理,如环状涡的形成和演化、二次下扫现象、正尖峰结构特性以及小尺度涡结构的生成原理等,其研究工作有着重要的理论意义和应用前景。
Transition from laminar flow to turbulent flow is one of the most important and complex problems in the field of fluid mechanics research. Vortical structures and transition mechanisms in the transition process of compressible boundary layer flow over a flat plate are investigated and explored using the most accurate method, direct numerical simulation of Navier-Stokes equations. The details of late stages of boundary layer transition based on the spatial model are revealed. Previous numerical simulation and experimental results are verified. Based on our accurate simulation results, some new ideas are put forward and some new mechanisms are studied and revealed.
In this paper, direct numerical simulation has been carried out. The time-dependent Navier-Stokes equations are solved directly by a third-order TVD Runge-Kutta method. A sixth order central compact scheme that facilitates high resolution of the flow field is used for spatial discretization together with a sixth order implicit compact filter. To avoid possible non-physical wave reflection from the boundaries, the non-reflecting boundary conditions including transverse and viscous effects are specified at the far field and the outflow boundaries. The inflow is specified by laminar flow profile with imposed eigenmodes of two-dimensional and three-dimensional Tollmien-Schlichting (T-S) waves. The parallel computation is accomplished through the Message Passing Interface (MPI) together with a domain decomposition approach. The DNS results show the mean flow properties, such as the skin friction coefficients and the mean velocity profile, wall shear linear law, log law in the turbulent region, as well as the spatial evolution of disturbance modes, which agree very well with the theoretic and experimental results.
This paper is devoted to thorough and considerate researches of transition process in a boundary layer, especially the vortical structures at the late stages of nonlinear transition process, including the formation of typical vortical structures, important flow transition events and their relationship, voritcal structures at very late stages of transition and the flow randomization process. The mechanisms of boundary layer transition are investigated, and the major research works include:
1. Typical vortical structures in transition process are discussed, focused on vortical structures and some new mechanism of the formation and evolution of streamwise vortex and ring-like vortex. Our numerical results shown that the mechanisms of disturbance development predominant at late stages of boundary-layer transition have universal typical vortex structure, despite the two regimes of transition (K- and H-regimes) have different peculiar properties and relative spatial positions at weakly nonlinear stages. In this paper, a new study for the mechanism of the ring-like vortex formation is discovered. According to our recent DNS results, the ring-like vortices generation is caused by the interaction between the prime streamwise vortices and secondary streamwise vortices. The ring-like vortex formation is a key issue of flow transition. The rotation movements of ring-like vortices induce huge momentum and energy transfer form high energy inviscid outer part of boundary layer to low energy inner part of boundary layer. There is no turbulence without ring-like vortices.
2. Some important events in transition process and the corresponding effects on transitional flow field are studied by fine gird direct numerical simulation results. Complex ejection and sweep movements have close relationship with vorical structures. The details of flow structure aroundΛvortex and ring-like vortex are studied. The relationship between ejection/sweep movements and vorical structures has been verified, which is consistent with experimental work. It is revealed that the mechanism of the second sweep generation, the positive spike formation, high shear layer and Reynolds stress distribution, and their relationship with ring-like vortices. In particular, numerical results show that positive spikes in the near-wall region induced by the ring-like vortices, propagate downstream with the same speed as the ring-like vortices, and the speed is several time faster than surrounding flow.
3. At the very late stages of transition, complex U-shaped vortex, barrel vortex, turbulent spot and small scale vortex are investigated. In particular, It is found that while new ring-like vortex are generated, vorticity of the leading ring-like vortex became weaker and dissipated gradually; on the other hand, small scale vortex is generated under the interaction between secondary vortex and solid wall, and induced by the evolution of large vortex structure.
In brief, a high-precision and high efficiency of numerical simulation method for compressible boundary layer transition is developed. Through the accurate numerical simulation of the vortical structures and analysis of the mechanism in transition process of compressible boundary layer flow, the whole procedure at the late stage of boundary layer transition has been clearly presented. Several new mechanisms are analyzed and revealed, such as the formation and evolution of ring-like vortices, the production of second sweep and positive spikes, and the formation theory of small-scale vortex structure. The research has important theoretical significance and application prospects.
引文
[1] Reshotko E. Boundary-layer stability and transition. Annu.Rev.Fluid.Mech, 1976, 8:311-349.
[2] Moin P, Mahesh K. Direct numerical simulation:a tool in turbulence research. Annu.Rev.Fluid Mech., 1998, 30:539-578.
[3]张涵信,周恒,流体力学的基础研究,世界科技研究与发展(院士论坛), 2001,23(1):15-19.
[4] Gad-el-Hak. Flow Control.Cambridge: The University of Cambridge, 2000:104-105
[5] Morkovin M V. Bypass transition to turbulence and research desiderata. Transition in Turbines, 1984, 161-204. NASA Conf. Pub. 2386.
[6] Herbert T. Secondary instability of boundary layers. Annu. Rev. Fluid Mech., 1988, 20:487–526.
[7] Kachanov Y S. Physical mechanisms of laminar-boundary-layer transition. Annu. Rev. Fluid Mech., 1994, 26:411-482.
[8] Schmid P J, Henningson D S. Channel flow transition induced by a pair of oblique waves. Hussaini M Y, Kumar A, Street C L. Instability, Transition and Turbulence, Spinger, 1992:356-366.
[9] Klebanoff P S, Tidstrom K D, Sargent L M. The three-dimensional nature of boundary layer instability. J.Fluid Mech., 1962, 12:1-34.
[10] Henningson D S, Gustavsson L H, Breuer K S. Localized disturbances in parallel shear flows. Applied Scientific Research, 1994, 53:51-97.
[11] Luchini P. Reynolds-number-independent instability of the boundary layer over a flat surface: optimal perturbations. J. Fluid Mech., 2000, 404:289-309.
[12] Wang J J, Pan C, Zhang P F. On the instability and reproduction mechanism of a laminar streak, J. Turbulence, 2009, 10(26): 1-27.
[13] Saric W S, Reed H L, Kerschen E J. Boundary layer receptivity to free stream disturbances. Annu.Rev.Fluid Mech., 2002, 34:291-319.
[14]周恒,赵耕夫,流动稳定性.北京:国防工业出版社,2004:1~255
[15] Borodulin V I, Kachanov Y S, Koptsev D B. Experimental study of resonant interactions of instability waves in self-similar boundary layer with an adverse pressure gradient, Part 1, Tuned resonances. J. Turbulence, 2002, 3(62): 1-38.
[16] Borodulin V I, Kachanov Y S, Koptsev D B, et al. Experimental study of resonant interactions of instability waves in self-similar boundary layer with an adverse pressure gradient, Part 2, Detuned resonances. J. Turbulence, 2002, 3(63): 1-22.
[17] Borodulin V I, Kachanov Y S, Koptsev D B. Experimental study of resonant interactions of instability waves in self-similar boundary layer with an adverse pressure gradient, Part 3, Broadband disturbances. J. Turbulence, 2002, 3(64): 1-19.
[18] Borodulin V I, Kachanov Y S, Roschektayev A P. Super-late stages of boundary-layer transition and deterministic post-transitional turbulence. Abstracts of 6-th EUROMECH fluid mechanics conference– Stockholm: Royal Institute of Technology, 2006, 1: 39.
[19] Borodulin V I, Kachanov Y S, Roschektayev A P. The deterministic wall turbulence is possible. Advances in Turbulence XI. Proceedings of 11th EUROMECH European Turbulence Conference, June 25–28, 2007, Porto, Portugal / J.M.L.M. Palma and A. Silva Lopes, eds.– Heidelberg: Springer, 2007:76–178.
[20] Hama F R, Long J D, Hegarty J C. On transition from laminar to turbulent flow. J. Appl.Phys., 1957, 28:388-394.
[21] Hama F R, Nutant J. Detailed flow-field obvservations in the transition process in a thick boundary layer. Heat Transfer&Fluid Mech. Inst.Pal Alto, CA, Stanford University Press, 1963:388-394
[22] Kovasznay L S, Komoda H, Vasudeva B R. Detailed flowfield transition. Heat Transfer&Fluid Mech. Inst.Pal Alto, CA, Stanford University Press, 1962: 1-26
[23] Kachanov Y S, Kozlo V V, Levchenko V Y, et al. Experimental study of K-regime breakdown of laminar boundary layer. Laminar-Turbulent Transition, 1985 IUTAM Symposium, 1984 Novosibirsk, USSR(ed.V.Kozlov).Springer.
[24] Borodulin V I, Gaponenko V R, Kachanov Y S. Generation and development of coherent structures in boundary layer at pulse excitation. 10th Intl Conf. on Methods of Aerophysical Research. Proceedings. Part II. (Novosibirsk: Inst. Theor. & Appl. Mech.), 2000:37-42.
[25] Rist U, Fasel H. Direct numerical simulation of controlled transition in a flat-plate boundary layer.J Fluid Mech. 1995,298:211-248.
[26] Kachanov Y S, Kozlov V V, Levchenko V Y. Nonlinear development of a wave in a boundary layer. Izv. Akad. Nauk SSSR, Mekh. Zhidk. I Gaza, 1977, 3:49-53 (in Russian) (Translated in Fluid Dyn., 1978, 12:383-390.).
[27] Herbert T. Subharmonic three-dimensional disturbances in unstable plane shear flows. AIAA Paper, 1983, No.1983-1759.
[28] Saric W S, Kozlov V V, Levchenko VY. Forced and unforced subharmonic resonance in boundary-layer transition. AIAA Paper, 1984, No. 84-0007.
[29] Craik A D D. Nonlinear resonant instability in boundary layers. J. Fluid Mech., 1971, 50: 393-413.
[30] Liu Jixue, Tang Dengbin, Yang Yingzhaoa. On nonlinear evolution of C-type instability in nonparallel boundary layers. Chinese Journal of Aeronautics, 2007,20:313-320
[31] Zelman M B, Maslennikova I I. Tollmien-Schlichting-wave resonant mechanism for subharmonic-type transition. J. Fluid Mech., 1993, 252:499-578.
[32] Herbert T. Analysis of the subharmonic rout to transition in boundary layers. AIAA Paper, 1984, No. 84-0009.
[33] Wang Weizhi, Tang Dengbin. Studies on Nonlinear Stability of Three-Dimensional H-Type Disturbance. Acta Mechanica Sinica, 2003, 19(6):517-526
[34] Kachanov Y S, Levchenko V Y. The resonant interaction of disturbances at laminar-turbulent transition in a boundary layer. J. Fluid Mech., 1984,138: 209-247.
[35] Saric W S, Thomas A S W. Experiments on the subharmonic route to turbulence in boundary layers. Tatsumi T, Turbulence and Chaotic Phenomena in Fluids, Amsterdam: North-Holland, 1984:117-122.
[36] Kachanov YS. On the resonant nature of the breakdown of a laminar boundary layer. J. Fluid Mech., 1987, 184: 43-74.
[37] Corke T C, Mangano R A. Resonant growth of three-dimensional modes in transitioning Blasius boundary layers. J. Fluid Mech., 1989,209:93-150.
[38] Bake S, Kachanov Y S, Fernholz H H. Subharmonic K-regime of boundary-layer breakdown. R.A.W.M. Henkes, J.L. van Ingen, Transitional Boundary Layers in Aeronautics,Amsterdam: North-Holland,1996,pp. 81-88.
[39] Bake S, Kachanov Y S, Fernholz H H. Resemblance of K- and N-regimes of boundary-layer transition at late stages. Eur. J. Mech., B/Fluids, 2000,19(1):1-22.
[40] Nishioka M, Asai M. Some observations of the subcritical transition in plane Poiseuille flow. J.Fluid Mech.1985, 150:441-450.
[41] Asai M, Nishioka M. Boundary-layer transition triggered by hairpin eddies at subcritical Reynolds numbers. J.Fluid Mech.1995,297:101-122.
[42] Asai M, Nishioka M. Development of wall turbulence structure in transitional flows. T.Tatsumi, E.Watanabe, T.Kambe, Theoretical and applied mechanics,19th IUTAM Congress, 1996 Kyoto,Japan, Elsevier,1996, 121-138.
[43] Asai M, Sawada K, Nishioka M. Development of turbulent patch in a subcritical boundary-layer transition.Fluid Dyn.Res.1996, 18:151-164.
[44] Nishioka M, Asai M, Iida S. Wall phenomena in the final stage of transition to turbulence. R.E.Meyer, Transition and turbulence, Proc.Of Symposium at the University ofWisconsin-Madison, 1980, Academic.1981
[45] Acarlar M S, Smith C R. A Study of hairpin vortice in a laminar boundary layer. Part 1. Hairpin vortices generated by a hemisphere protuberance. J.Fluid Mech., 1987a, 175:1-41 [46 ] Acarlar M S, Smith C R. A Study of hairpin vortice in a laminar boundary layer.Part 2. Hairpin vortices generated by fluid injection.J.Fluid Mech.,1987a, 175:43-83.
[47] Haidari A H, Smith C R. The generation and regeration of single hairpin vortex. J.Fluid Mech.,1994,277:135-162
[48]李新亮,傅德薰,马延文,可压缩钝楔边界层转捩到湍流的直接数值模拟,中国科学G辑物理学力学天文学2004, 34(4): 466~480
[49]袁湘江,陆利蓬,沈清等,钝体头部边界层“逾越”型转捩机理研究,航空动力学报,2008,23(1)
[50] Joslin R D, Street C L, Chang C L. Oblique wave breakdown in incompressible boundary layer computed by spatial DNS and PSE theory. M Y A Kumar, C L Street. Instability, Transition and Turbulence, Spinger, 1992:304-310.
[51] Berlin S, Lundbladh A, Henningson D. Spatial simulation of oblique transition in a boundary layer. Phys.Fluids,1994,6:1949-1951.
[52] Reddy S C, Schmid P J, Bagget J S, et al. On stability of stream wise streaks and transition thresholds in plane channel flows.J.Fluid Mech.1998, 365:269-303.
[53] Elofsson P A, Alferedsson P H. An experimental study of oblique transition in plane Poiseuille flow. J.Fluid Mech., 1998, 358:177-202.
[54] Elofsson P A. An experimental study of oblique transition in a Blasius boundary layer flow. TRITA-MEK,Tech.Rep.4,Dept.of Mechanics,KTH,Stockholm,Sweden.1998.
[55] Berlin S, Wiegel M, Henningson D S. Numerical and experimental investigations of oblique boundary layer transition.J.Fluid Mech.1999,393:23-57.
[56] Nishioka M, Asai M, Iida S. An experimental investigation of the secondary instability. R. Eppler, H. Fasel, Laminar-Turbulent Transition,Berlin: Springer,1980:37-46.
[57] Moin P, Leonard A, Kim J. Evolution of curved vortex filament into a vortex ring. Phys. Fluids, 1986, 29(4):955-963.
[58] Knapp C F, Roache P J. A combined visual and hot-wire anemometer investigation of boundary-layer transition. AIAA J., 1968, 6:29-36.
[59] Kachanov YS, Kozlov V V, Levchenko V Y, et al. Experimental study of K-regime breakdown of laminar boundary layer. (Novosibirsk: Inst. Theor. & Appl. Mech., Siberian Div. USSR Acad. Sci.) 1984, Preprint No. 9-84 (in Russian) (See also: Kachanov et al. 1985, In: V.V. Kozlov (Ed.) Laminar Turbulent Transition (Berlin: Springer) pp. 61-73.)
[60] Dryganets S V, Kachanov Y S, Levchenko V Y, et al. Resonant flow randomization in K-regime of boundary layer transition. J. Appl. Mech. Tech. Phys., 1990, 31(2):239-249.
[61] Borodulin V I, Kachanov Y S. Role of the mechanism of local secondary instability in K-breakdown of boundary layer. Soviet J. Appl. Phys., 1989,3(2), 70-81.
[62] Borodulin V I, Kachanov Y S. Formation and development of coherent structures in transitional boundary layer. J. Appl. Mech. Tech. Phys., 1995,36(4):532-564.
[63] Kleiser L, Zang T A. Numerical simulation of transition in wall-bounded shear flows. Annu. Rev. Fluid Mech., 1991, 23: 495-537.
[64] Rist U, Kachanov Y S. Numerical and experimental investigation of the K-regime of boundary-layer transition. R. Kobayashi, Laminar-Turbulent Transition, Berlin: Springer, 1995:405-412.
[65] Borodulin V I, Gaponenko V R, Kachanov Y S, et al. Late-stage transitional boundary-layer structures. Direct numerical simulation and experiment. Theoret. Comp. Fluid Dyn., 2002:15, 317-337.
[66] Huang Zhangfeng, Cao Wei, Zhou Heng. The mechanism of breakdown in laminar-turbulent transition of a supersonic boundary layer on a flat plate--temporal mode.Science in China, Series G, 2005, 48(5):614-625.
[67] Borodulin V I, Kachanov Y S, Roschektayev A P. Experimental study of late stages of the laminar-turbulent transition in a boundary layer with an adverse pressure gradient. Thermophysics and Aeromechanics, 2003, 10(1): 1-26.
[68] Betchov R. On the mechanism of turbulent transition. Phys. Fluids., 1960, 3:1026-1027.
[69] Landahl M T. Wave mechanics of breakdown. J. Fluid Mech., 1972,56(4):755-802.
[70] Kachanov Y S. On a universal nonlinear mechanism of turbulence production in wall shear flows. In: 10th Int. Conference on Methods of Aerophysical Research. Proceedings. Part 2 (Novosibirsk: Inst. Theor. & Appl. Mech.) 2000:84-91.
[71] Kachanov Y S. On a universal mechanism of turbulence production in wall shear flows. In: Notes on Numerical Fluid Mechanics and Multidisciplinary Design. Vol. 86. Recent Results in Laminar-Turbulent Transition (Berlin: Springer) 2003:1-12.
[72] Kline S J, Reynolds W C, Schraub F A, et al. The structure of turbulent boundary layers. J. Fluid Mech., 1967, 30, 741-773.
[73] Repik E U,Sosedko U P. Studies of intermittent flow structure in near-wall region of turbulent boundary layer. In: Turbulent Flows (Moscow: Nauka Pub.) (in Russian) 1974.
[74] Blackwelder R F. Analogies between transitional and turbulent boundary layers. Phys. Fluids,1983,26(10), 2807-2815.
[75] Landahl M T. A wave-guide model for turbulent shear flow. J. Fluid Mech., 1967, 29:441-459.
[76] Landahl M T. Dynamics of boundary layer turbulence and the mechanisms of drag redaction. Phys. Fluids Suppl., 1977,20(10): 55-63.
[77] Bake S, Meyer D G W, Rist U. Turbulence mechanism in Klebanoff transition: a quantitative comparison of experiment and direct numerical simulation. J. Fluid Mech., 2002, 459:217-243.
[78] Shaikh F N, Gaster M. The nonlinear evolution of modulated waves in a boundary layer. J. Eng. Mathematics, 1994,28:55-71.
[79] Shaikh F N. Investigation of transition to turbulence using white-noise excitation and local analysis techniques. J. Fluid Mech., 1997, 348:29-83.
[80] Borodulin V I, Kachanov Y S, Roschektayev A P. Turbulence production in an APG-boundary-layer transition induced by randomized perturbations. J. Turbulence., 2006, 8(7) :1-30.
[81] Lee C B, Du X D, Lian Q X, et al. Combined study of mechanisms of evolution and breakdown of coherent structures in transitional boundary layer at controlled conditions. International Conference on Methods of Aerophysical Research. Proceedings. Part I. - Novosibirsk: Inst. Theor. & Appl. Mech., 1998:141-146.
[82] Guo H, Lian Q X, Li Y, et al. A visual study on complex flow structures and flow breakdown in a boundary layer transition. Experiments in Fluids, 2004,37(3):311-322.
[83] Müller K, Rist U, Wagner S. Enhanced visualization of late-stage transitional structures using vortex identification and automatic feature extraction. In Computational Fluid Dynamics’98 (Papailiou et al., eds.), Wiley, New York,1998:786–791.
[84] Rist U, Müller K, Wagner S. Visualization of late-stage transitional structures in numerical data using vortex identification and feature extraction. Proc. 8th International Symposium Flow Visualization, Sorrento, 1998,Paper No. 103.
[85] Kim H T, Kline S J, Reynolds W C. The production of turbulence near a smooth wall in a turbulent boundary layer, J. Fluid Mech., 1971, 50(1): 133-160.
[86] Lu L J, Smith C R. Use of flow visualization data to examine spatial-temporal velocity and burst-type characteristics in a turbulent boundary layer, J. Fluid Mech., 1991, 232: 303-340.
[87] Cantwell B. Organized Motion in Turbulent Flow. Annu. Rev. Fluid Mech., 1981, 13: 457–515.
[88] Robinson S K. Coherent Motions in the Turbulent Boundary Layer. Annu. Rev. Fluid Mech., 1991, 23: 601–639.
[89] Theodorsen T. The structure of turbulence. In: 50 Jahre Grenzschichtforsung, ed. H, Goertler, W.Tollmein, 1955:55–62. Braunschweig: F. Viewig.
[90] Fernholz H. Three-dimensional disturbances in a two-dimensional incompressible turbulent boundary layer. Aeronautical Research Council Reports and Memoranda, 1964, No.3368. London: Her Majesty’s Stationery Office.
[91] Falco R E. Coherent motions in the outer region of turbulent boundary layers. Phys. Fluids, 1977,20(10): 124-132.
[92] Head M R, Bandyopadhyay P. Flow visualization of turbulent boundary layer structure. In: AGARD-CPP-271: Turbulent Boundary Layers– Experiments, Theory and Modelling, 1979:25
[93] Head M R, Bandyopadhyay P. New aspects of turbulent boundary layer structure. J. Fluid Mech. 1981, 107: 297-338.
[94] Goldstein J E, Smits A J. Flow visualization of the three-dimensional, time-evolving structure of a turbulent boundary layer. Physics of Fluids, 1994,6(2): 577-587.
[95] Delo C, Poggie J, Smits A J. A system for imaging and displaying three-dimensional, time-evolving passive scalar concentration fields in fluid flow. Tech. Rep. No. 1992, Dept. Mech. & Aerosp. Eng., Princeton University, 1994.
[96] Delo C, Smits A J. Volumetric visualization of coherent structure in a low Reynolds number turbulent boundary layer. Intl. J. Fluid Dyn.,1997 ,1(3).
[97] Moin P, Mahesh K. Direct numerical simulation: a tool in turbulence research. Annu. Rev. Fluid Mech.,1988, 30: 539–578.
[98] Taimon A M, Kunen J M G., Oom G. Simultaneous flow visualization and Reynolds-stress measurement in a turbulent boundary layer. J. Fluid Mech., 1986, 163:459-478.
[99] Lian Q X. Coherent structures in the inner and outer region of a turbulent boundary layer. In: The Resent Developments in Turbulence Research (Z.S. Zhang, Y. Miyake eds.)– Beijing: Intl Academic Publishers,1994:109-131.
[100] Lian Q X. A kind of fast changing coherent structure in a turbulent boundary layer. ACTA Mechanica Sinica.1999, 15,(3): 193-200.
[101] Guo H, Wang J J, Lian Q X, et al. Spatial reconstruction of vortical structures in transitional boundary layer based on synchronous hydrogen-bubble visualization. In: 12th Intl Conf. on Methods of Aerophysical Research. Proceedings. Part I. (Novosibirsk: Inst. Theor. & Appl. Mech.) 2004:118-124.
[102] Jiang L, Shan H, Liu C. Direct numerical simulation of boundary-layer receptivity for subsonic flow around airfoil. In: Recent Advances in DNS and LES. Proceedings of the Second AFOSR International Conference on DNS/LES.– Rutgers - The State University of New Jersey, NewBrunswick, June 1999.
[103] Hermann Schlichting. Boundary Layer Theorys,springer,7th Revised,1979:336.
[104] Wasistho B. Spatial direct numerical simulation of compressible boundary layer flow, Thesis Universiteit Twente, Enschede, 1997.
[105] Malik M R. Numerical methods for hypersonic boundary layer stability. J. Comput. Phys., 1990, 86:376-413.
[106] Tuncer Cebeci. Stability and Transition: Theory and Application,Horizons Pubns (AZ), January 2004.
[107] Guo Xin, Tang Dengbin,Shen Qing, Nonparallel boundary layer stability in high speed flows, Transactions of Nanjing University of Aeronautics and Astronautics, 2008,25(2):81-88
[108]夏浩,唐登斌,陆昌根,三维扰动波的非平行稳定性研究,力学学报,2002,34(5):688-695
[109] Poinsot T J, Lele S K. Boundary conditions for direct simulations of compressible viscous flow . Journal of Computational Physics, 1992, 101:104-139.
[110] Engquist E, Majda A. Absorbing boundary conditions for the numerical simulation of waves. Mathematics of Computation, 1977, 31:629-651.
[111] Hedstrom G W. Non-reflecting boundary conditions for nonlinear hyperbolic systerms. Journal of Computational Physics, 1979, 30:222-237.
[112] Rudy D H, Strikwerda J C. A non-reflecting outflow boundary conditions for subsonic Navier-Stokes calculations. Journal of Computational Physics, 1980, 36:55-70.
[113] Rudy D H, Strikwerda J C. Boundary conditions for subsonic compressible Navier-Stokes calculations. Computers and Fluids,1981, 9:327-338
[114] Thompson K W. Time-dependent boundary conditions for hyperbolic systems. Journal of Computational Physics, 1987, 68: 1-24.
[115] Thompson K W. Time-dependent boundary conditions for hyperbolic systemsⅡ. Journal of Computational Physics, 1990, 89: 439-461.
[116] Strikwerda J C. Initial boundary-value problems for incompletely parabolic systems. Communication on pure and Applied Mathematics, 1977, 9:797-822.
[117] Gustafsson B, Sundstr?m A. Incompletely parabolic problems in fluid-dynamics. SIAM Journal on Applied Mathematics, 1987, 35: 343-357.
[118] Oliger J, Sundstr?m A. Theoretical and practical aspects of some initial boundary-value problems in fluid-dynamics. SIAM Journal on Applied Mathematics, 1978, 35:419-446.
[119] Halpern L. Artificial boundary conditions for incompletely parabolic perturbations of hyperbolic systems. SIAM Journal on Mathematical Analysis, 1991, 22: 1256-1283.
[120] Dutt P. Stable boundary conditions in and difference schemes for Navier-Stokes equations. SIAM Journal on Numerical Analysis, 1988, 25: 245-267.
[121] Baum M, Poinsot T J, Thévenin D. Accurate boundary conditions for multicomponent reactive flows. Journal of Computational Physics, 1994, 176: 247-261.
[122] Okong’O N, Bellan J. Consistent boundary conditions for multicomponent real gas mixtures based on characteristic waves. Journal of Computational Physics, 1994, 176:330-344.
[123] Poinsot T J, Veynante D. Theoretical and Numerical Combustion , Second Edition. R.T.Edwards Inc, Philadelphia. 2005
[124] Sutherland J C, Kennedy C A. Improved boundary conditions for viscous, reacting, compressible flows. Journal of Computational Physics, 2003, 191: 502-524.
[125] Yoo C S, Wang Y, TrouvéA, et al. Characteristic boundary conditions for direct numerical simulations of turbulent counterflow flames. Combustion Theory and Modelling, 2005,9: 617-646.
[126] Yoo C S, Im H G. Characteristic boundary conditions for simulations of compressible reacting flows with multi-dimensional, viscous, and reaction effects. Combustion Theory and Modelling 2007, 11(2):259-286
[127] Lele S K Compact Finite Difference Schemes with Spectral-like Resolution. Journal of Computational Physics, 1991, 103: 16-42.
[128] Chen Lin, Tang Dengbin. Navier-Stokes Characteristic Boundary Conditions for Simulations of Some Typical Flows. Applied Mathematical Sciences,2010,4(18) , 879– 893
[129] Chen Lin, Tang Dengbin, Guo Xin. Numerical Simulation of Free Vortex with Modified Navier-Stokes Characteristic Boundary Conditions, Modern Physics Letters B, 2010, 24(13):57?60
[130] Christopher K W T, Konstantin A K. A Wavenumber Based Extrapolation and Interpolation Method for use in Conjunction with High-Order Finite Difference Schemes. J. Comput. Phys., 2000,157(2):588-617
[131] Datta V G, Miguel R V. High-order schemes for Navier-Stokes equations: algorithm and implementation into FDL3DI. AFRL-VA-WP-TR-1998-3060
[132] Shu C W, Osher S. Efficient implementation of essentially non-oscillatory shock-capturing scheme. J. Comput. Phys. 1988, 77:439-471.
[133] Spekreuse S P. Elliptic grid generation based on Laplace equation and algebraic transformations,J Comp Phys,1995 (118).
[134] Jiang L, Shan H, Liu C. Non-reflecting boundary conditions for DNS in curvilinear coordinates. In: Recent Advances in DNS and LES. Proceedings of the Second AFOSR InternationalConference on DNS/LES. Rutgers - The State University of New Jersey, New Brunswick, U.S.A., June 7-9, 1999.
[135] Guo H, Lian XQ, Pan C, et al. Sweep and ejection events in transitional boundary layer. Synchronous visualization and spatial reconstruction. In: 13th Intl Conf. on Methods of Aerophysical Research. Proceedings. Part V.– Novosibirsk: Publ. House“Parallel”, 2007: 192–197.
[136]潘翀,王晋军,伍康,圆柱尾涡/边界层相互作用中二次涡特性研究实验流体力学. 2007, 21:41-45
[137] Pan C, Wang J J, Zhang P F, et al. Coherent structures in bypass transition induced by a cylinder wake. J.Fluid Mech.2008, 603:367-389
[138] Guo H, Borodulin V I, Kachanov YS, et al. Nature of sweep and ejection events in transitional and turbulent boundary layers. Journal of Turbulence, 2010, Vol.11, N34
[139] Ducros F, Comte P, Lesieur M. Large-eddy simulation of transition to turbulence in a boundary layer developing spatially over a flat plate. J. Fluid Mech. 1996, 326:1-36.
[140]Lesieur M, Metais O. New trends in large-eddey simulations of turbulence. Annu.Rev.Fluid. Mech.1996.28:45-82
[141]唐登斌,高等粘性流体力学,南京航空航天大学,2007
[142] Zhang Li, Tang Dengbin, Guo Linlin. Nonlinear Evolution of Turbulent Coherent Structures in Channel Flows. Modern Physics Letters B,2005,19(28-29) :1539-1542
[143]陈林,唐登斌等,边界层转捩过程中环状涡和尖峰结构的演化.中国科学G辑:物理学力学天文学,2009,39 (10): 1520-1526
[144] Jeong J, Hussain F. On the identification of a vortex. J. Fluid Mech. 1995, 285:69-94.
[145] Jie-Zhi Wu, Hui-Yang Ma, Ming-De Zhou. Vorticity and Vortex Dynamics. Springer,2006
[146]童秉纲,尹协远,朱克勤,涡运动理论,中国科技大学出版社,2009.
[147]郭辉,彭艺,李志勇等,逆压梯度转捩边界层流动结构显示,实验流体力学,2008,22(2)
[148] Lee C B. Possible universal transitional scenario in a plate boundary layer: measurement and visualization. Phys Rev E, 2000, 62: 3659-3671
[149] Lee C B, Fu S. On the formation of the chain of ring-like vortices in a transitional boundary layer. Exp Fluids, 2001, 303: 354-357
[150] Crow S C. Stability theory for a pair of trailing vortices. AIAA J, 1970, 8: 2172-21279
[151] Lee C B, Li R Q. A dominant structure in turbulent production of boundary layer transition. J Turbulence, 2007, 8(55)
[152]李存标,吴介之,壁流动中的转捩,力学进展,2009,39(4)
[153]连祺祥,郭辉,湍流边界层中下扫流与“反发卡涡”,物理学报,2004,53(7)
[154] Shaw R H, Tavangar J, Ward D P. Structure of Reynolds stress in a canopy layer. J. Clim. Appl. Meteorol. 1983,22: 1922-1931.
[155] Antonia R A. Conditional sampling in turbulence measurements. Annu. Rev. Fluid Mech. 1981,13: 131–156.
[156] Nishioka M, Asai M, Iida S. Proceedings of International Union of Theoretical and Applied Mechanics on Laminar-Turbulent Transition, Springer, New York, 1989
[157] Nishioka M, Asai M. Evolution of Tollmien-Schlichting Waves intoWall Turbulence, Turbulence and Chaotic Phe-nomena in Fluids T. Tatsumi, eds. North-Holland, Amsterdam: 87-92, 1984
[158] Singer B A, Joslin R D. Metamorphosis of a hairpin vortex into a young turbulent spot. Phys.Fluids, 1994, 6(11).
[159] Emmons H W. The lammar-turbulent transition in a boundary layer–part I. J.Aero.Sei., 1951, 18:490-498.
[160] Mitchner M. Propagation of turbulent from an instantaneous point disturbance. J.Aero.Sei., 1954,21:350-351.
[161] Elder J W. An experimental investigation of turbulent spots and breakdown to turbulence. J.Fluid Mech.,1960,9:235-246.
[162] Cantwell B, Coles D, Dimotakis. Structure and entrainment in the plane of symmetry of a turbulent spot. J.FluldMech.,1978,87:641-672.
[163]张立,唐登斌,近壁剪切流动中湍流斑的非线性演化,中国科学G辑物理学力学天文学,2006, 36(1): 103~112
[164] Chen Lin,Tang Dengbin. Study of turbulent spots in plane Couette flow. Transaction of Nanjing University of Aeronautics andAstronautics, 2007, 24(3), 211-217
[165] Hermann Schlichting, K. Gersten, Klaus Gersten. Boundary Layer Theorys, springer, 8th Revised, 2000:474
[2] Moin P, Mahesh K. Direct numerical simulation:a tool in turbulence research. Annu.Rev.Fluid Mech., 1998, 30:539-578.
[3]张涵信,周恒,流体力学的基础研究,世界科技研究与发展(院士论坛), 2001,23(1):15-19.
[4] Gad-el-Hak. Flow Control.Cambridge: The University of Cambridge, 2000:104-105
[5] Morkovin M V. Bypass transition to turbulence and research desiderata. Transition in Turbines, 1984, 161-204. NASA Conf. Pub. 2386.
[6] Herbert T. Secondary instability of boundary layers. Annu. Rev. Fluid Mech., 1988, 20:487–526.
[7] Kachanov Y S. Physical mechanisms of laminar-boundary-layer transition. Annu. Rev. Fluid Mech., 1994, 26:411-482.
[8] Schmid P J, Henningson D S. Channel flow transition induced by a pair of oblique waves. Hussaini M Y, Kumar A, Street C L. Instability, Transition and Turbulence, Spinger, 1992:356-366.
[9] Klebanoff P S, Tidstrom K D, Sargent L M. The three-dimensional nature of boundary layer instability. J.Fluid Mech., 1962, 12:1-34.
[10] Henningson D S, Gustavsson L H, Breuer K S. Localized disturbances in parallel shear flows. Applied Scientific Research, 1994, 53:51-97.
[11] Luchini P. Reynolds-number-independent instability of the boundary layer over a flat surface: optimal perturbations. J. Fluid Mech., 2000, 404:289-309.
[12] Wang J J, Pan C, Zhang P F. On the instability and reproduction mechanism of a laminar streak, J. Turbulence, 2009, 10(26): 1-27.
[13] Saric W S, Reed H L, Kerschen E J. Boundary layer receptivity to free stream disturbances. Annu.Rev.Fluid Mech., 2002, 34:291-319.
[14]周恒,赵耕夫,流动稳定性.北京:国防工业出版社,2004:1~255
[15] Borodulin V I, Kachanov Y S, Koptsev D B. Experimental study of resonant interactions of instability waves in self-similar boundary layer with an adverse pressure gradient, Part 1, Tuned resonances. J. Turbulence, 2002, 3(62): 1-38.
[16] Borodulin V I, Kachanov Y S, Koptsev D B, et al. Experimental study of resonant interactions of instability waves in self-similar boundary layer with an adverse pressure gradient, Part 2, Detuned resonances. J. Turbulence, 2002, 3(63): 1-22.
[17] Borodulin V I, Kachanov Y S, Koptsev D B. Experimental study of resonant interactions of instability waves in self-similar boundary layer with an adverse pressure gradient, Part 3, Broadband disturbances. J. Turbulence, 2002, 3(64): 1-19.
[18] Borodulin V I, Kachanov Y S, Roschektayev A P. Super-late stages of boundary-layer transition and deterministic post-transitional turbulence. Abstracts of 6-th EUROMECH fluid mechanics conference– Stockholm: Royal Institute of Technology, 2006, 1: 39.
[19] Borodulin V I, Kachanov Y S, Roschektayev A P. The deterministic wall turbulence is possible. Advances in Turbulence XI. Proceedings of 11th EUROMECH European Turbulence Conference, June 25–28, 2007, Porto, Portugal / J.M.L.M. Palma and A. Silva Lopes, eds.– Heidelberg: Springer, 2007:76–178.
[20] Hama F R, Long J D, Hegarty J C. On transition from laminar to turbulent flow. J. Appl.Phys., 1957, 28:388-394.
[21] Hama F R, Nutant J. Detailed flow-field obvservations in the transition process in a thick boundary layer. Heat Transfer&Fluid Mech. Inst.Pal Alto, CA, Stanford University Press, 1963:388-394
[22] Kovasznay L S, Komoda H, Vasudeva B R. Detailed flowfield transition. Heat Transfer&Fluid Mech. Inst.Pal Alto, CA, Stanford University Press, 1962: 1-26
[23] Kachanov Y S, Kozlo V V, Levchenko V Y, et al. Experimental study of K-regime breakdown of laminar boundary layer. Laminar-Turbulent Transition, 1985 IUTAM Symposium, 1984 Novosibirsk, USSR(ed.V.Kozlov).Springer.
[24] Borodulin V I, Gaponenko V R, Kachanov Y S. Generation and development of coherent structures in boundary layer at pulse excitation. 10th Intl Conf. on Methods of Aerophysical Research. Proceedings. Part II. (Novosibirsk: Inst. Theor. & Appl. Mech.), 2000:37-42.
[25] Rist U, Fasel H. Direct numerical simulation of controlled transition in a flat-plate boundary layer.J Fluid Mech. 1995,298:211-248.
[26] Kachanov Y S, Kozlov V V, Levchenko V Y. Nonlinear development of a wave in a boundary layer. Izv. Akad. Nauk SSSR, Mekh. Zhidk. I Gaza, 1977, 3:49-53 (in Russian) (Translated in Fluid Dyn., 1978, 12:383-390.).
[27] Herbert T. Subharmonic three-dimensional disturbances in unstable plane shear flows. AIAA Paper, 1983, No.1983-1759.
[28] Saric W S, Kozlov V V, Levchenko VY. Forced and unforced subharmonic resonance in boundary-layer transition. AIAA Paper, 1984, No. 84-0007.
[29] Craik A D D. Nonlinear resonant instability in boundary layers. J. Fluid Mech., 1971, 50: 393-413.
[30] Liu Jixue, Tang Dengbin, Yang Yingzhaoa. On nonlinear evolution of C-type instability in nonparallel boundary layers. Chinese Journal of Aeronautics, 2007,20:313-320
[31] Zelman M B, Maslennikova I I. Tollmien-Schlichting-wave resonant mechanism for subharmonic-type transition. J. Fluid Mech., 1993, 252:499-578.
[32] Herbert T. Analysis of the subharmonic rout to transition in boundary layers. AIAA Paper, 1984, No. 84-0009.
[33] Wang Weizhi, Tang Dengbin. Studies on Nonlinear Stability of Three-Dimensional H-Type Disturbance. Acta Mechanica Sinica, 2003, 19(6):517-526
[34] Kachanov Y S, Levchenko V Y. The resonant interaction of disturbances at laminar-turbulent transition in a boundary layer. J. Fluid Mech., 1984,138: 209-247.
[35] Saric W S, Thomas A S W. Experiments on the subharmonic route to turbulence in boundary layers. Tatsumi T, Turbulence and Chaotic Phenomena in Fluids, Amsterdam: North-Holland, 1984:117-122.
[36] Kachanov YS. On the resonant nature of the breakdown of a laminar boundary layer. J. Fluid Mech., 1987, 184: 43-74.
[37] Corke T C, Mangano R A. Resonant growth of three-dimensional modes in transitioning Blasius boundary layers. J. Fluid Mech., 1989,209:93-150.
[38] Bake S, Kachanov Y S, Fernholz H H. Subharmonic K-regime of boundary-layer breakdown. R.A.W.M. Henkes, J.L. van Ingen, Transitional Boundary Layers in Aeronautics,Amsterdam: North-Holland,1996,pp. 81-88.
[39] Bake S, Kachanov Y S, Fernholz H H. Resemblance of K- and N-regimes of boundary-layer transition at late stages. Eur. J. Mech., B/Fluids, 2000,19(1):1-22.
[40] Nishioka M, Asai M. Some observations of the subcritical transition in plane Poiseuille flow. J.Fluid Mech.1985, 150:441-450.
[41] Asai M, Nishioka M. Boundary-layer transition triggered by hairpin eddies at subcritical Reynolds numbers. J.Fluid Mech.1995,297:101-122.
[42] Asai M, Nishioka M. Development of wall turbulence structure in transitional flows. T.Tatsumi, E.Watanabe, T.Kambe, Theoretical and applied mechanics,19th IUTAM Congress, 1996 Kyoto,Japan, Elsevier,1996, 121-138.
[43] Asai M, Sawada K, Nishioka M. Development of turbulent patch in a subcritical boundary-layer transition.Fluid Dyn.Res.1996, 18:151-164.
[44] Nishioka M, Asai M, Iida S. Wall phenomena in the final stage of transition to turbulence. R.E.Meyer, Transition and turbulence, Proc.Of Symposium at the University ofWisconsin-Madison, 1980, Academic.1981
[45] Acarlar M S, Smith C R. A Study of hairpin vortice in a laminar boundary layer. Part 1. Hairpin vortices generated by a hemisphere protuberance. J.Fluid Mech., 1987a, 175:1-41 [46 ] Acarlar M S, Smith C R. A Study of hairpin vortice in a laminar boundary layer.Part 2. Hairpin vortices generated by fluid injection.J.Fluid Mech.,1987a, 175:43-83.
[47] Haidari A H, Smith C R. The generation and regeration of single hairpin vortex. J.Fluid Mech.,1994,277:135-162
[48]李新亮,傅德薰,马延文,可压缩钝楔边界层转捩到湍流的直接数值模拟,中国科学G辑物理学力学天文学2004, 34(4): 466~480
[49]袁湘江,陆利蓬,沈清等,钝体头部边界层“逾越”型转捩机理研究,航空动力学报,2008,23(1)
[50] Joslin R D, Street C L, Chang C L. Oblique wave breakdown in incompressible boundary layer computed by spatial DNS and PSE theory. M Y A Kumar, C L Street. Instability, Transition and Turbulence, Spinger, 1992:304-310.
[51] Berlin S, Lundbladh A, Henningson D. Spatial simulation of oblique transition in a boundary layer. Phys.Fluids,1994,6:1949-1951.
[52] Reddy S C, Schmid P J, Bagget J S, et al. On stability of stream wise streaks and transition thresholds in plane channel flows.J.Fluid Mech.1998, 365:269-303.
[53] Elofsson P A, Alferedsson P H. An experimental study of oblique transition in plane Poiseuille flow. J.Fluid Mech., 1998, 358:177-202.
[54] Elofsson P A. An experimental study of oblique transition in a Blasius boundary layer flow. TRITA-MEK,Tech.Rep.4,Dept.of Mechanics,KTH,Stockholm,Sweden.1998.
[55] Berlin S, Wiegel M, Henningson D S. Numerical and experimental investigations of oblique boundary layer transition.J.Fluid Mech.1999,393:23-57.
[56] Nishioka M, Asai M, Iida S. An experimental investigation of the secondary instability. R. Eppler, H. Fasel, Laminar-Turbulent Transition,Berlin: Springer,1980:37-46.
[57] Moin P, Leonard A, Kim J. Evolution of curved vortex filament into a vortex ring. Phys. Fluids, 1986, 29(4):955-963.
[58] Knapp C F, Roache P J. A combined visual and hot-wire anemometer investigation of boundary-layer transition. AIAA J., 1968, 6:29-36.
[59] Kachanov YS, Kozlov V V, Levchenko V Y, et al. Experimental study of K-regime breakdown of laminar boundary layer. (Novosibirsk: Inst. Theor. & Appl. Mech., Siberian Div. USSR Acad. Sci.) 1984, Preprint No. 9-84 (in Russian) (See also: Kachanov et al. 1985, In: V.V. Kozlov (Ed.) Laminar Turbulent Transition (Berlin: Springer) pp. 61-73.)
[60] Dryganets S V, Kachanov Y S, Levchenko V Y, et al. Resonant flow randomization in K-regime of boundary layer transition. J. Appl. Mech. Tech. Phys., 1990, 31(2):239-249.
[61] Borodulin V I, Kachanov Y S. Role of the mechanism of local secondary instability in K-breakdown of boundary layer. Soviet J. Appl. Phys., 1989,3(2), 70-81.
[62] Borodulin V I, Kachanov Y S. Formation and development of coherent structures in transitional boundary layer. J. Appl. Mech. Tech. Phys., 1995,36(4):532-564.
[63] Kleiser L, Zang T A. Numerical simulation of transition in wall-bounded shear flows. Annu. Rev. Fluid Mech., 1991, 23: 495-537.
[64] Rist U, Kachanov Y S. Numerical and experimental investigation of the K-regime of boundary-layer transition. R. Kobayashi, Laminar-Turbulent Transition, Berlin: Springer, 1995:405-412.
[65] Borodulin V I, Gaponenko V R, Kachanov Y S, et al. Late-stage transitional boundary-layer structures. Direct numerical simulation and experiment. Theoret. Comp. Fluid Dyn., 2002:15, 317-337.
[66] Huang Zhangfeng, Cao Wei, Zhou Heng. The mechanism of breakdown in laminar-turbulent transition of a supersonic boundary layer on a flat plate--temporal mode.Science in China, Series G, 2005, 48(5):614-625.
[67] Borodulin V I, Kachanov Y S, Roschektayev A P. Experimental study of late stages of the laminar-turbulent transition in a boundary layer with an adverse pressure gradient. Thermophysics and Aeromechanics, 2003, 10(1): 1-26.
[68] Betchov R. On the mechanism of turbulent transition. Phys. Fluids., 1960, 3:1026-1027.
[69] Landahl M T. Wave mechanics of breakdown. J. Fluid Mech., 1972,56(4):755-802.
[70] Kachanov Y S. On a universal nonlinear mechanism of turbulence production in wall shear flows. In: 10th Int. Conference on Methods of Aerophysical Research. Proceedings. Part 2 (Novosibirsk: Inst. Theor. & Appl. Mech.) 2000:84-91.
[71] Kachanov Y S. On a universal mechanism of turbulence production in wall shear flows. In: Notes on Numerical Fluid Mechanics and Multidisciplinary Design. Vol. 86. Recent Results in Laminar-Turbulent Transition (Berlin: Springer) 2003:1-12.
[72] Kline S J, Reynolds W C, Schraub F A, et al. The structure of turbulent boundary layers. J. Fluid Mech., 1967, 30, 741-773.
[73] Repik E U,Sosedko U P. Studies of intermittent flow structure in near-wall region of turbulent boundary layer. In: Turbulent Flows (Moscow: Nauka Pub.) (in Russian) 1974.
[74] Blackwelder R F. Analogies between transitional and turbulent boundary layers. Phys. Fluids,1983,26(10), 2807-2815.
[75] Landahl M T. A wave-guide model for turbulent shear flow. J. Fluid Mech., 1967, 29:441-459.
[76] Landahl M T. Dynamics of boundary layer turbulence and the mechanisms of drag redaction. Phys. Fluids Suppl., 1977,20(10): 55-63.
[77] Bake S, Meyer D G W, Rist U. Turbulence mechanism in Klebanoff transition: a quantitative comparison of experiment and direct numerical simulation. J. Fluid Mech., 2002, 459:217-243.
[78] Shaikh F N, Gaster M. The nonlinear evolution of modulated waves in a boundary layer. J. Eng. Mathematics, 1994,28:55-71.
[79] Shaikh F N. Investigation of transition to turbulence using white-noise excitation and local analysis techniques. J. Fluid Mech., 1997, 348:29-83.
[80] Borodulin V I, Kachanov Y S, Roschektayev A P. Turbulence production in an APG-boundary-layer transition induced by randomized perturbations. J. Turbulence., 2006, 8(7) :1-30.
[81] Lee C B, Du X D, Lian Q X, et al. Combined study of mechanisms of evolution and breakdown of coherent structures in transitional boundary layer at controlled conditions. International Conference on Methods of Aerophysical Research. Proceedings. Part I. - Novosibirsk: Inst. Theor. & Appl. Mech., 1998:141-146.
[82] Guo H, Lian Q X, Li Y, et al. A visual study on complex flow structures and flow breakdown in a boundary layer transition. Experiments in Fluids, 2004,37(3):311-322.
[83] Müller K, Rist U, Wagner S. Enhanced visualization of late-stage transitional structures using vortex identification and automatic feature extraction. In Computational Fluid Dynamics’98 (Papailiou et al., eds.), Wiley, New York,1998:786–791.
[84] Rist U, Müller K, Wagner S. Visualization of late-stage transitional structures in numerical data using vortex identification and feature extraction. Proc. 8th International Symposium Flow Visualization, Sorrento, 1998,Paper No. 103.
[85] Kim H T, Kline S J, Reynolds W C. The production of turbulence near a smooth wall in a turbulent boundary layer, J. Fluid Mech., 1971, 50(1): 133-160.
[86] Lu L J, Smith C R. Use of flow visualization data to examine spatial-temporal velocity and burst-type characteristics in a turbulent boundary layer, J. Fluid Mech., 1991, 232: 303-340.
[87] Cantwell B. Organized Motion in Turbulent Flow. Annu. Rev. Fluid Mech., 1981, 13: 457–515.
[88] Robinson S K. Coherent Motions in the Turbulent Boundary Layer. Annu. Rev. Fluid Mech., 1991, 23: 601–639.
[89] Theodorsen T. The structure of turbulence. In: 50 Jahre Grenzschichtforsung, ed. H, Goertler, W.Tollmein, 1955:55–62. Braunschweig: F. Viewig.
[90] Fernholz H. Three-dimensional disturbances in a two-dimensional incompressible turbulent boundary layer. Aeronautical Research Council Reports and Memoranda, 1964, No.3368. London: Her Majesty’s Stationery Office.
[91] Falco R E. Coherent motions in the outer region of turbulent boundary layers. Phys. Fluids, 1977,20(10): 124-132.
[92] Head M R, Bandyopadhyay P. Flow visualization of turbulent boundary layer structure. In: AGARD-CPP-271: Turbulent Boundary Layers– Experiments, Theory and Modelling, 1979:25
[93] Head M R, Bandyopadhyay P. New aspects of turbulent boundary layer structure. J. Fluid Mech. 1981, 107: 297-338.
[94] Goldstein J E, Smits A J. Flow visualization of the three-dimensional, time-evolving structure of a turbulent boundary layer. Physics of Fluids, 1994,6(2): 577-587.
[95] Delo C, Poggie J, Smits A J. A system for imaging and displaying three-dimensional, time-evolving passive scalar concentration fields in fluid flow. Tech. Rep. No. 1992, Dept. Mech. & Aerosp. Eng., Princeton University, 1994.
[96] Delo C, Smits A J. Volumetric visualization of coherent structure in a low Reynolds number turbulent boundary layer. Intl. J. Fluid Dyn.,1997 ,1(3).
[97] Moin P, Mahesh K. Direct numerical simulation: a tool in turbulence research. Annu. Rev. Fluid Mech.,1988, 30: 539–578.
[98] Taimon A M, Kunen J M G., Oom G. Simultaneous flow visualization and Reynolds-stress measurement in a turbulent boundary layer. J. Fluid Mech., 1986, 163:459-478.
[99] Lian Q X. Coherent structures in the inner and outer region of a turbulent boundary layer. In: The Resent Developments in Turbulence Research (Z.S. Zhang, Y. Miyake eds.)– Beijing: Intl Academic Publishers,1994:109-131.
[100] Lian Q X. A kind of fast changing coherent structure in a turbulent boundary layer. ACTA Mechanica Sinica.1999, 15,(3): 193-200.
[101] Guo H, Wang J J, Lian Q X, et al. Spatial reconstruction of vortical structures in transitional boundary layer based on synchronous hydrogen-bubble visualization. In: 12th Intl Conf. on Methods of Aerophysical Research. Proceedings. Part I. (Novosibirsk: Inst. Theor. & Appl. Mech.) 2004:118-124.
[102] Jiang L, Shan H, Liu C. Direct numerical simulation of boundary-layer receptivity for subsonic flow around airfoil. In: Recent Advances in DNS and LES. Proceedings of the Second AFOSR International Conference on DNS/LES.– Rutgers - The State University of New Jersey, NewBrunswick, June 1999.
[103] Hermann Schlichting. Boundary Layer Theorys,springer,7th Revised,1979:336.
[104] Wasistho B. Spatial direct numerical simulation of compressible boundary layer flow, Thesis Universiteit Twente, Enschede, 1997.
[105] Malik M R. Numerical methods for hypersonic boundary layer stability. J. Comput. Phys., 1990, 86:376-413.
[106] Tuncer Cebeci. Stability and Transition: Theory and Application,Horizons Pubns (AZ), January 2004.
[107] Guo Xin, Tang Dengbin,Shen Qing, Nonparallel boundary layer stability in high speed flows, Transactions of Nanjing University of Aeronautics and Astronautics, 2008,25(2):81-88
[108]夏浩,唐登斌,陆昌根,三维扰动波的非平行稳定性研究,力学学报,2002,34(5):688-695
[109] Poinsot T J, Lele S K. Boundary conditions for direct simulations of compressible viscous flow . Journal of Computational Physics, 1992, 101:104-139.
[110] Engquist E, Majda A. Absorbing boundary conditions for the numerical simulation of waves. Mathematics of Computation, 1977, 31:629-651.
[111] Hedstrom G W. Non-reflecting boundary conditions for nonlinear hyperbolic systerms. Journal of Computational Physics, 1979, 30:222-237.
[112] Rudy D H, Strikwerda J C. A non-reflecting outflow boundary conditions for subsonic Navier-Stokes calculations. Journal of Computational Physics, 1980, 36:55-70.
[113] Rudy D H, Strikwerda J C. Boundary conditions for subsonic compressible Navier-Stokes calculations. Computers and Fluids,1981, 9:327-338
[114] Thompson K W. Time-dependent boundary conditions for hyperbolic systems. Journal of Computational Physics, 1987, 68: 1-24.
[115] Thompson K W. Time-dependent boundary conditions for hyperbolic systemsⅡ. Journal of Computational Physics, 1990, 89: 439-461.
[116] Strikwerda J C. Initial boundary-value problems for incompletely parabolic systems. Communication on pure and Applied Mathematics, 1977, 9:797-822.
[117] Gustafsson B, Sundstr?m A. Incompletely parabolic problems in fluid-dynamics. SIAM Journal on Applied Mathematics, 1987, 35: 343-357.
[118] Oliger J, Sundstr?m A. Theoretical and practical aspects of some initial boundary-value problems in fluid-dynamics. SIAM Journal on Applied Mathematics, 1978, 35:419-446.
[119] Halpern L. Artificial boundary conditions for incompletely parabolic perturbations of hyperbolic systems. SIAM Journal on Mathematical Analysis, 1991, 22: 1256-1283.
[120] Dutt P. Stable boundary conditions in and difference schemes for Navier-Stokes equations. SIAM Journal on Numerical Analysis, 1988, 25: 245-267.
[121] Baum M, Poinsot T J, Thévenin D. Accurate boundary conditions for multicomponent reactive flows. Journal of Computational Physics, 1994, 176: 247-261.
[122] Okong’O N, Bellan J. Consistent boundary conditions for multicomponent real gas mixtures based on characteristic waves. Journal of Computational Physics, 1994, 176:330-344.
[123] Poinsot T J, Veynante D. Theoretical and Numerical Combustion , Second Edition. R.T.Edwards Inc, Philadelphia. 2005
[124] Sutherland J C, Kennedy C A. Improved boundary conditions for viscous, reacting, compressible flows. Journal of Computational Physics, 2003, 191: 502-524.
[125] Yoo C S, Wang Y, TrouvéA, et al. Characteristic boundary conditions for direct numerical simulations of turbulent counterflow flames. Combustion Theory and Modelling, 2005,9: 617-646.
[126] Yoo C S, Im H G. Characteristic boundary conditions for simulations of compressible reacting flows with multi-dimensional, viscous, and reaction effects. Combustion Theory and Modelling 2007, 11(2):259-286
[127] Lele S K Compact Finite Difference Schemes with Spectral-like Resolution. Journal of Computational Physics, 1991, 103: 16-42.
[128] Chen Lin, Tang Dengbin. Navier-Stokes Characteristic Boundary Conditions for Simulations of Some Typical Flows. Applied Mathematical Sciences,2010,4(18) , 879– 893
[129] Chen Lin, Tang Dengbin, Guo Xin. Numerical Simulation of Free Vortex with Modified Navier-Stokes Characteristic Boundary Conditions, Modern Physics Letters B, 2010, 24(13):57?60
[130] Christopher K W T, Konstantin A K. A Wavenumber Based Extrapolation and Interpolation Method for use in Conjunction with High-Order Finite Difference Schemes. J. Comput. Phys., 2000,157(2):588-617
[131] Datta V G, Miguel R V. High-order schemes for Navier-Stokes equations: algorithm and implementation into FDL3DI. AFRL-VA-WP-TR-1998-3060
[132] Shu C W, Osher S. Efficient implementation of essentially non-oscillatory shock-capturing scheme. J. Comput. Phys. 1988, 77:439-471.
[133] Spekreuse S P. Elliptic grid generation based on Laplace equation and algebraic transformations,J Comp Phys,1995 (118).
[134] Jiang L, Shan H, Liu C. Non-reflecting boundary conditions for DNS in curvilinear coordinates. In: Recent Advances in DNS and LES. Proceedings of the Second AFOSR InternationalConference on DNS/LES. Rutgers - The State University of New Jersey, New Brunswick, U.S.A., June 7-9, 1999.
[135] Guo H, Lian XQ, Pan C, et al. Sweep and ejection events in transitional boundary layer. Synchronous visualization and spatial reconstruction. In: 13th Intl Conf. on Methods of Aerophysical Research. Proceedings. Part V.– Novosibirsk: Publ. House“Parallel”, 2007: 192–197.
[136]潘翀,王晋军,伍康,圆柱尾涡/边界层相互作用中二次涡特性研究实验流体力学. 2007, 21:41-45
[137] Pan C, Wang J J, Zhang P F, et al. Coherent structures in bypass transition induced by a cylinder wake. J.Fluid Mech.2008, 603:367-389
[138] Guo H, Borodulin V I, Kachanov YS, et al. Nature of sweep and ejection events in transitional and turbulent boundary layers. Journal of Turbulence, 2010, Vol.11, N34
[139] Ducros F, Comte P, Lesieur M. Large-eddy simulation of transition to turbulence in a boundary layer developing spatially over a flat plate. J. Fluid Mech. 1996, 326:1-36.
[140]Lesieur M, Metais O. New trends in large-eddey simulations of turbulence. Annu.Rev.Fluid. Mech.1996.28:45-82
[141]唐登斌,高等粘性流体力学,南京航空航天大学,2007
[142] Zhang Li, Tang Dengbin, Guo Linlin. Nonlinear Evolution of Turbulent Coherent Structures in Channel Flows. Modern Physics Letters B,2005,19(28-29) :1539-1542
[143]陈林,唐登斌等,边界层转捩过程中环状涡和尖峰结构的演化.中国科学G辑:物理学力学天文学,2009,39 (10): 1520-1526
[144] Jeong J, Hussain F. On the identification of a vortex. J. Fluid Mech. 1995, 285:69-94.
[145] Jie-Zhi Wu, Hui-Yang Ma, Ming-De Zhou. Vorticity and Vortex Dynamics. Springer,2006
[146]童秉纲,尹协远,朱克勤,涡运动理论,中国科技大学出版社,2009.
[147]郭辉,彭艺,李志勇等,逆压梯度转捩边界层流动结构显示,实验流体力学,2008,22(2)
[148] Lee C B. Possible universal transitional scenario in a plate boundary layer: measurement and visualization. Phys Rev E, 2000, 62: 3659-3671
[149] Lee C B, Fu S. On the formation of the chain of ring-like vortices in a transitional boundary layer. Exp Fluids, 2001, 303: 354-357
[150] Crow S C. Stability theory for a pair of trailing vortices. AIAA J, 1970, 8: 2172-21279
[151] Lee C B, Li R Q. A dominant structure in turbulent production of boundary layer transition. J Turbulence, 2007, 8(55)
[152]李存标,吴介之,壁流动中的转捩,力学进展,2009,39(4)
[153]连祺祥,郭辉,湍流边界层中下扫流与“反发卡涡”,物理学报,2004,53(7)
[154] Shaw R H, Tavangar J, Ward D P. Structure of Reynolds stress in a canopy layer. J. Clim. Appl. Meteorol. 1983,22: 1922-1931.
[155] Antonia R A. Conditional sampling in turbulence measurements. Annu. Rev. Fluid Mech. 1981,13: 131–156.
[156] Nishioka M, Asai M, Iida S. Proceedings of International Union of Theoretical and Applied Mechanics on Laminar-Turbulent Transition, Springer, New York, 1989
[157] Nishioka M, Asai M. Evolution of Tollmien-Schlichting Waves intoWall Turbulence, Turbulence and Chaotic Phe-nomena in Fluids T. Tatsumi, eds. North-Holland, Amsterdam: 87-92, 1984
[158] Singer B A, Joslin R D. Metamorphosis of a hairpin vortex into a young turbulent spot. Phys.Fluids, 1994, 6(11).
[159] Emmons H W. The lammar-turbulent transition in a boundary layer–part I. J.Aero.Sei., 1951, 18:490-498.
[160] Mitchner M. Propagation of turbulent from an instantaneous point disturbance. J.Aero.Sei., 1954,21:350-351.
[161] Elder J W. An experimental investigation of turbulent spots and breakdown to turbulence. J.Fluid Mech.,1960,9:235-246.
[162] Cantwell B, Coles D, Dimotakis. Structure and entrainment in the plane of symmetry of a turbulent spot. J.FluldMech.,1978,87:641-672.
[163]张立,唐登斌,近壁剪切流动中湍流斑的非线性演化,中国科学G辑物理学力学天文学,2006, 36(1): 103~112
[164] Chen Lin,Tang Dengbin. Study of turbulent spots in plane Couette flow. Transaction of Nanjing University of Aeronautics andAstronautics, 2007, 24(3), 211-217
[165] Hermann Schlichting, K. Gersten, Klaus Gersten. Boundary Layer Theorys, springer, 8th Revised, 2000:474
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