人造发卡涡对湍流边界层相干结构的影响
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摘要
本文工作的主要目的是,通过向湍流边界层中引入单一人造发卡涡,对在湍流边界层中对数律区的大尺度低速条纹结构(>20δ)的产生机理进行探讨。
在层流边界中,流动显示和单丝热线探针测量的结果表明:4.8Hz、最大速度约1.1ms~(-1)(Rjet≈55%)的垂直于壁面的周期性射流,在自由来流约为2.0ms~(-1)、边界层厚度约为12mm的层流边界层中,形成单一发卡涡。在射流出口下游10mm处及其下游,相位平均的流向脉动速度和发卡涡标示函数在三维空间(运用Taylor冻结假设)中的分布表明,低速区形成于人造发卡涡的上游、内部区域,高速区形成于人造发卡涡的外侧。通过整合在流向六个横截面处的相位平均的流向脉动速度信号和发卡涡标示函数,得到在一个扰动周期时间内(209ms),人造发卡涡在层流边界层中随时间的发展、演化过程,且与流动显示结果相吻合。同时,在水平截面内,流向瞬时脉动速度呈现类似Hutchins等2007年在湍流边界层对数律区发现的大尺度条纹结构(>20δ)。
向来流约为2.0ms~(-1)、边界层厚度约为50mm的湍流边界层中,引入4.8Hz、最大速度约3.45ms~(-1)(Rjet≈172%)的垂直于壁面的周期性射流,同时,单丝热线探针在射流出口下游40mm处的(流向-展向)横截面内,对射流扰动的湍流边界层进行测量。相位平均的流向脉动速度与基于流向速度分量的发卡涡标示函数,呈现发卡形涡结构,而且在对数律区发现与Hutchins等2007年在湍流边界层对数律区发现的大尺度条纹结构相似的大尺度低速条纹结构。与较弱垂直于壁面的周期性射流(Rjet≈55%)在湍流边界层对数律区形成的低速条纹相比较,得知尾流区占主导地位的负展向涡是形成对数律区大尺度条纹结构的根本原因。
由流向平均速度的二阶导数与(层流和湍流)边界层中条纹结构的对应关系,得知足够强的边界层剪切,对在边界层中产生条纹结构,是必要的。通过对比两个不同雷诺数的湍流边界平均速度的二阶导数,解释了对数律区的大尺度低速条纹结构在高雷诺数的湍流边界层中较强,而易于发现的原因。
Mechanism of the large scale low-speed streaks (>20δ) found in logarithmic layer is experimentally investigated, by inducing a single synthetic hairpin vortex into turbulent boundary layers.
It is proved by both flow visualizations and single hot-wire measurements that a single synthetic hairpin is generated by 4.8Hz pulsing jet normal to the wall with a maximum velocity of 1.1ms~(-1) (Rjet≈55%) in laminar boundary layers with a thickness of around 12mm at a freestream velocity of about 2ms~(-1). The distribution of phase-averaged u fluctuations and marker function in three dimensional area (by using Taylor’s hypothesis) at each x-location 10mm downstream the hole, demonstreates that low-speed region is formed inside and upstream of the synthetic hairpin, which is surrounded by high-speed region. The combination of the phase-averaged signals shows the dynamics process of synthetic hairpin within a cycle (209ms), which is in consistent with the flow visualization in laminar boundary layers. Moreover, streaks similar to those found in logarithmic layer in turbulence flows by Hutchins et al. (2007) are observed in horizontal slices of the instantaneous u fluctuations.
By introducing a normal jet at 4.8Hz with a maximum velocity of 3.45ms~(-1) (Rjet≈172%), phase-averaged u fluctuations and marker function indicate a single synthetic hairpin vortex is formed 40mm downstream the exit of the jet, in a turbulent boundary layer with 50mm thickness at around 2ms~(-1). Moreover, low-speed streaks resemble those found in logarithmic layer of turbulence flows by Hutchins et al. (2007). In comparion with the u fluctuations associated with a single hairpin vortex generated by a relatively weak normal jet (Rjet≈55%), dominant passive spanwise vorticity in wake region is responsible for formation of the large scale streaks in logarithmic layer.
Due to relationship between a second derivative of mean streamwise velocity and existence of streaks, a strong enough boundary-layer shear is necessary for formation of steaks. By comparion of second derivatives of mean velocity at two Reynolds number, it is figured out the reason why large scale low-speed streaks in logarithmic layer are stronger and easier to be observed.
在层流边界中,流动显示和单丝热线探针测量的结果表明:4.8Hz、最大速度约1.1ms~(-1)(Rjet≈55%)的垂直于壁面的周期性射流,在自由来流约为2.0ms~(-1)、边界层厚度约为12mm的层流边界层中,形成单一发卡涡。在射流出口下游10mm处及其下游,相位平均的流向脉动速度和发卡涡标示函数在三维空间(运用Taylor冻结假设)中的分布表明,低速区形成于人造发卡涡的上游、内部区域,高速区形成于人造发卡涡的外侧。通过整合在流向六个横截面处的相位平均的流向脉动速度信号和发卡涡标示函数,得到在一个扰动周期时间内(209ms),人造发卡涡在层流边界层中随时间的发展、演化过程,且与流动显示结果相吻合。同时,在水平截面内,流向瞬时脉动速度呈现类似Hutchins等2007年在湍流边界层对数律区发现的大尺度条纹结构(>20δ)。
向来流约为2.0ms~(-1)、边界层厚度约为50mm的湍流边界层中,引入4.8Hz、最大速度约3.45ms~(-1)(Rjet≈172%)的垂直于壁面的周期性射流,同时,单丝热线探针在射流出口下游40mm处的(流向-展向)横截面内,对射流扰动的湍流边界层进行测量。相位平均的流向脉动速度与基于流向速度分量的发卡涡标示函数,呈现发卡形涡结构,而且在对数律区发现与Hutchins等2007年在湍流边界层对数律区发现的大尺度条纹结构相似的大尺度低速条纹结构。与较弱垂直于壁面的周期性射流(Rjet≈55%)在湍流边界层对数律区形成的低速条纹相比较,得知尾流区占主导地位的负展向涡是形成对数律区大尺度条纹结构的根本原因。
由流向平均速度的二阶导数与(层流和湍流)边界层中条纹结构的对应关系,得知足够强的边界层剪切,对在边界层中产生条纹结构,是必要的。通过对比两个不同雷诺数的湍流边界平均速度的二阶导数,解释了对数律区的大尺度低速条纹结构在高雷诺数的湍流边界层中较强,而易于发现的原因。
Mechanism of the large scale low-speed streaks (>20δ) found in logarithmic layer is experimentally investigated, by inducing a single synthetic hairpin vortex into turbulent boundary layers.
It is proved by both flow visualizations and single hot-wire measurements that a single synthetic hairpin is generated by 4.8Hz pulsing jet normal to the wall with a maximum velocity of 1.1ms~(-1) (Rjet≈55%) in laminar boundary layers with a thickness of around 12mm at a freestream velocity of about 2ms~(-1). The distribution of phase-averaged u fluctuations and marker function in three dimensional area (by using Taylor’s hypothesis) at each x-location 10mm downstream the hole, demonstreates that low-speed region is formed inside and upstream of the synthetic hairpin, which is surrounded by high-speed region. The combination of the phase-averaged signals shows the dynamics process of synthetic hairpin within a cycle (209ms), which is in consistent with the flow visualization in laminar boundary layers. Moreover, streaks similar to those found in logarithmic layer in turbulence flows by Hutchins et al. (2007) are observed in horizontal slices of the instantaneous u fluctuations.
By introducing a normal jet at 4.8Hz with a maximum velocity of 3.45ms~(-1) (Rjet≈172%), phase-averaged u fluctuations and marker function indicate a single synthetic hairpin vortex is formed 40mm downstream the exit of the jet, in a turbulent boundary layer with 50mm thickness at around 2ms~(-1). Moreover, low-speed streaks resemble those found in logarithmic layer of turbulence flows by Hutchins et al. (2007). In comparion with the u fluctuations associated with a single hairpin vortex generated by a relatively weak normal jet (Rjet≈55%), dominant passive spanwise vorticity in wake region is responsible for formation of the large scale streaks in logarithmic layer.
Due to relationship between a second derivative of mean streamwise velocity and existence of streaks, a strong enough boundary-layer shear is necessary for formation of steaks. By comparion of second derivatives of mean velocity at two Reynolds number, it is figured out the reason why large scale low-speed streaks in logarithmic layer are stronger and easier to be observed.
引文
[1]d'Alembert, J. L.R., Essai d'une nouvelle théorie de la résistance des fluides,1752
[2]Prandtl, L., Uber Flussigkeits bewegung bei sehr kleiner Reibung, Verhaldlg III Int. Math. Kong, (Heidelberg: Teubner) 1904,484～491; Also available in translation as: Motion of fluids with very little viscosity. NACA TM 1928,452: 484～491
[3]Roach, P. E. The generation of nearly isotropic turbulence by means of grids, Int J Heat Fluid Flow, 1987, 8(2): 82～92
[4]Spaid, F. W., Roos, F. W., Hicks, R. M. An experimental study of the turbulent boundary layer on atransport wing in subsonic and transonic flows, NASA TM, 1990, 102206
[5]Spalart, P. R., Direct numerical simulation of boundary layer upto Rθ= 1410, J. Fluid Mech., 1988, 187: 61～98
[6]Ramos, J. I., Sirignano, W. A., Study of turbulence in a motored four-stroke internal combustion engine, AIAA Journal, 1981, 19(5): 595～600
[7]Deng, G. B., Duvigneau,R., Queutey, P., Visonneau, M., Assessment of Turbulence Model for Ship Flow at Full Scale, Computational Mechanics WCCW VI in conjunction with APCOM'04, Beijing, China, Sept. 5～10, 2004
[8]Verhulst, F., Methods and Applications of Singular Perturbations: Boundary Layers and Multiple Timescale Dynamics, Springer, 2005, ISBN 0-387-22966-3
[9]Lumley, J. L.,A Century of Turbulence Flow, Turbulence and Combustion, 2001, 66: 241～286
[10]Tulaprkara, E. G., Hundred years of the boundary layer– Some aspects, Sˉadhanˉa, 2005, 30(4): 499～512
[11]Tani, I., History of Boundary Layer Theory,Ann. Rev. Fluid Mech., 1977, 9: 87～111
[12]White, F. M., Fluid Mechanics, 459～460
[13]von Karman, T., On laminar and turbulent friction, Z. Angew. Math. Mech., 1921, 1: 235～236
[14]White, F. M., Visous Fluid Flow, 416
[15]Millikan, C. B., A critical discussion of turbulent flows in channels and circular tubes, Proceedings of the Fifth International Congress of Applied Mechanics,Cambridge,1938,386～392
[16]Coles, D. E., The law of the wake in the turbulent boundary layer. J. Fluid Mech., 1956, 1: 97～160
[17]Schlichting, H., Gersten, K., Boundary layer theory, Berlin: Springer Verlag, 2000
[18]Corrsin, S., Kistler, A. L., Free-stream boundaries of turbulent flows, 1955, NACA TN3133
[19]Kolmogorov, A. N., A refinement of previous hypotheses concerning the local structure of turbulence in a viscous incompressible fluid at high Reynolds number, J. Fluid Mech., 1962, 13: 82～85
[20]Benzi, R., Ciliberto, S., Tripiccione, R., Baudet, C., Massaioli, F., Succi, S., Extended self-similarity in turbulent flows, Phys. Rev. E, 1993, 48(1): R29～R32
[21]She, Z-S, Leveque , E., Universal scaling laws in fully developed turbulence, Phys. Rev. Lett., 1994, 72(3): 336～339
[22]Kline, S. J., Reynolds, C., Schraubf, A., Runstadlepr, W., The structure of turbulent boundary layers, J. Fluid Mech., 1967, 30: 741～73
[23]Kim, H. T., Kline, S. J., Reynolds, W. C., The production of turbulence near a smooth wall, J. Fluid Mech., 1971, 50: 133～160
[24]Nychas, S. G., Hershey, H. C., Brodkey, R. S., A visual study of turbulent shear flow, J. Fluid Mech., 1973, 61: 513～540
[25]Xanthos, S., Gong, M., Andreopoulos, Y., Velocity and vorticity in weakly compressible isotropic turbulence under longitudinal expansive straining, J. Fluid Mech., 2007, 584: 301～335
[26]Cuypers, Y., Maurel, A., Petitjeans, P., Vortex Burst as a Source of Turbulence, Phys. Rev. Lett., 2003, 91(19): 194502
[27]Archer, P. J., Thomas, T. G., Coleman, G. N., Direct numerical simulation of vortex ring evolution from the laminar to the early turbulent regime, J. Fluid Mech., 2008, 598: 201～226
[28]Onsager, L., Statistical Hydrodynamics, Nuovo Cimento, 1949, 6(2): 279～287
[29]Wyngaard, J. C., Measurement of small-scale turbulence structure with hot wires, J. of Phys. E: Scientific Instruments, 1968, 2(1): 1105～1108
[30]Kaimal, J. C., Wyngaard, J. C., Haugen, D. A., Cote, O. R., Izumi, Y., Caughey, S. J., Readings, C. J., Turbulence Structure in the Convective Boundary Layer, Journal of the Atmospheric Sciences, 1976, 33(11): 2152～2169
[31]Blackwelder, R., On the role of phase information in conditional sampling, Phys. Fluids, 1977, 20(10): s232-242
[32]Antonia, R. A., Conditional Sampling in Turbulence Measurement, Ann. Rev. Fluid Mech., 1981, 13: 131～156
[33]Alfredsson, P. H., Johansson, A. V., On the detection of turbulence-generating events, J. Fluid Mech., 1984, 139: 325～345
[34]Patel, V. C., Rodi, W., Scheuerer, G., Turbulence models for near-wall and low Reynolds number flows - A review, AIAA Journal, 1985, 23(9): 1308～1319
[35]Flores, O., Jimenez, J., del Alamo, J. C., Vorticity organization in the outer layer of turbulent channels with disturbed walls, J. Fluid Mech., 2007,591: 145～154
[36]Bandyopadhyay, P. R., Watson, R. D., Structure of rough-wall turbulent boundary layers, Phys. Fluids, 1988, 31:1877～1883
[37]Park, S-H, Lee, I., Sung, H. J., Effect of local forcing on a turbulent boundary layer, Experiments in Fluids, 2001, 31: 384～393
[38]Choi, K-S, Near-wall structure of a turbulent boundary layer with riblets, J. Fluid Mech., 1989, 208: 417～458
[39]Rathnasingham, R., Breuer, K. S., System Identification and Active Control of a Turbulent Boundary Layer, 28th AIAA Fluid Dynamics Conference, June 29～July 2, 1997 Snowmass Village, CO AIAA 97–1793
[40]Jukes, T., Choi, K-S, Turbulent Boundary-Layer Control for Drag Reduction Using Surface Plasma, 2nd AIAA Flow Control Conference, Portland, Oregon, June 28-1, 2004, AIAA-2004-2216
[41]McComb, W. D., Allan, J., Greated, C. A., Effect of polymer additives on the small-scale structure of grid-generated turbulence, Phys. Fluids, 1977, 20(6): 873～879
[42]Wark, C. E., Nagib, H. M., Experimental investigation of coherent structures in turbulent boundary layers, J. Fluid Mech., 1991, 230: 183～208
[43]Tennekes, H., Lumley, J. L., A first course in turbulence, M.I.T. Press, Cambridge, Mass, 1972
[44]Kim, J., Moin, P., Moser, R., Turbulence statistics in fully developed channel flow at low Reynolds number, J. Fluid Mech., 1987, 177: 133～166
[45]Schoppa, W., Hussain, F., Coherent structure generation in near-wall turbulence, J. Fluid Mech., 2002, 453: 57～108
[46]Hinze, J. O., Turbulence, 2nd Edn, p. 579, New York: McGraw-Hill, 1975
[47]Hamilton, J. M., Kim, J., Waleffe, F., Regeneration mechanisms of near-wall turbulence structures, J. Fluid Mech., 1995, 287: 317～348
[48]Brandt, L., Henningson, D. S., Transition of streamwise streaks in zero-pressure-gradient boundary layers, J. Fluid Mech., 2002, 472: 229～261
[49]Hutchins, N., Marusic, I., Evidence of very long meandering features in the logarithmic region of turbulent boundary layers, J. Fluid Mech., 2007, 579: 1～28
[50]Cantwell, B. J., Organized motion in turbulent flow, Annu. Rev. Fluid Mech., 1981, 13: 457～515
[51]Smith, C. R., Schwartz, S. P., Observation of streamwise rotation in the near-wall region of a turbulent boundary layer, Phys. Fluids, 1983, 26: 641～652
[52]Delo, C. J., Kelso, R. M., Smits, A. J., Three-dimensional structure of a low-Reynolds-number turbulent boundary layer, J. Fluid Mech., 2004, 512: 47～83
[53]Chernyshenko, S. I., Baig, M. F., The mechanism of streak formation in near-wall turbulence, J. Fluid Mech., 2005, 544: 99～131
[54]Hutchins, N., Hambleton, W. T., Marusic, I., Inclined cross-stream stereo particle image velocimetry measurements in turbulent boundary layers, J. Fluid Mech., 2005, 541: 21～54
[55]Tomkins, C. D., Adrian, R. J., Spanwise structure and scale growth in turbulent boundary layers, J. Fluid Mech., 2003, 490: 37～74
[56]Townsend, A. A., The Structure of Turbulent Shear Flow, 2nd edn. Cambridge University Press, 1976
[57]Liu, Z., Adrian, R. J., Hanratty, T. J., Large-scale modes of turbulent channel flow: transport and structure, J. Fluid Mech., 2001, 448: 53～80
[58]Coceal, O., Dobre, A., Thomas, T. G., Belcher, S. E., Structure of turbulent flow over regular arrays of cubical roughness, J. Fluid Mech., 2007, 589: 375～409
[59]Poggi, D., Porporato, A., Ridolfi, L., Analysis of the small-scale structure of turbulence on smooth and rough walls, Phys. Fluids, 2003, 15(1): 35～46
[60]Adrian, R. J., Meinhart, C. D., Tomkins, C. D., Vortex organization in the outer region of the turbulent boundary layer, J. Fluid Mech., 2000, 422: 1～54
[61]Ganapathisubramani, B., Longmire, E. K., Marusic, I., Characteristics of vortex packets in turbulent boundary layers, J. Fluid Mech., 2003, 478: 35～46
[62]del Alamo, J. C., Jimenez, J., Zandonade, P., Moser, R. D., Scaling of the energy spectra of turbulent channels, J. Fluid Mech., 2004, 500: 135～144
[63]del Alamo, J. C., Jimenez,J., Spectra of the very large anisotropic scales in turbulent channels, Phys. Fluids Lett., 2003, 15(6): L41～44
[64]Guala, M., Hommema, S. E., Adrian, R. J., Large-scale and very-large-scale motions in turbulent pipe flow, J. Fluid Mech., 2006, 554: 521～542
[65]Kim, K. C., Adrian, R. J., Very large-scale motion in the outer layer, Phys. Fluids, 1999, 11(2): 417～422
[66]Acarlar, M. S., Smith, C. R., A Study of Hairpin Vortices in a Laminar Boundary Layer I-Hairpin Vortices generated by a Hemisphere protuberance, J. Fluid Mech., 1987, 175: 1～41
[67]Robinson, S. K., Coherent Motions in the Turbulent Boundary Layer, Ann. Rev. Fluid Mech., 1991, 23: 601～639
[68]Eckelmann, H., Nychas, S. G., Brodkey, R. S., Wallace, J. M., Vorticity and turbulence production in pattern recognized turbulent flow structures, Phys. Fluids, 1977, 20(10):225～231
[69]Johansson, A. V., Alfredsson, P. H., Kim, J., Evolution and dynamics of shear-layer structures in near-wall turbulence, J. Fluid Mech., 1991, 224: 579～599
[70]Skote, M., Haritonidis, J. H., Henningson, D. S., Varicose instabilities in turbulent boundary layers, Phys. Fluids, 2002, 14(7): 2309～2323
[71]Smith, C. R., A synthesized model of the near-wall behavior in turbulent boundary layers, Proc. Symp. Turbul., 1984, 8th, Rolla, Mo
[72]Black, T. J., An analytical study of the measured wall pressure field under supersonic turbulent boundary layers, NASA, 1968, CR-888
[73]Head, M. R., Bandyopadhyay, P., New aspects of turbulent boundary-layer structure, J. Fluid Mech., 1981, 107: 297～338
[74]Robinson, S. K., Kinematics of turbulent boundary layer structure: PhD dissertation, Stanford, Calif; Stanford Univ., 1990, Also, NASA TM. In press
[75]Elsinga, G. E., Adrian, R. J., van Oudheusden, B. W., Scarano, F., Tomographic-PIV investigation of a high Reynolds number turbulent boundary layer, 7th International Symposium on Particle Image Velocimetry, Rome, Italy, 11-14 September 2007a Adrian, R. J., Hairpin vortex organization in wall turbulence, Phys. Fluids, 2007, 19(4): 041301-1～16
[76]Kim, K., Sung, H. J., Effects of unsteady blowing through a spanwise slot on a turbulent boundary layer, J. Fluid Mech., 2006, 557: 423～450
[77]Elsinga,G. E., Kuik,D. J., van Oudheusden,B. W.,Scaran,F.,Investigation of the three-dimensional coherent structures in a turbulent boundary layer with Tomographic-PIV,AIAA 2007-1305,45th AIAA Aerospace Sciences Meeting and Exhibit, Reno, Nevada, 8 - 11 January 2007b
[78]Haidari, A. H., Smith, C. R., The generation and regeneration of single hairpin vortices, J. Fluid Mech., 1994, 211: 135～162
[79]Kang, Y-D, Choi, K-S, Chun, H. H., Direct intervention of hairpin structures for turbulent boundary-layer control, Phys. Fluids, 2008, 20(10): 101517-1～13
[80]Bajer, K., Basson, A. P., Gilbert, A. D., Vortex motion in a weak background shear flow, J. Fluid Mech., 2004, 509: 281～304
[81]Carlier, J., Stanislas, M., Experimental study of eddy structures in a turbulent boundary layer using particle image velocimetry, J. Fluid Mech., 2005, 535: 143～188
[82]del Alamo, J. C., Jimenez, J., Zandonade, P., Moser, R. D., Self-similar vortex clusters in the turbulent logarithmic region, J. Fluid Mech., 2006, 561: 329～358
[83]Ganapathisubramani, B., Hutchins, N., Hambleton, W. T., Longmire, E. K., Marusic, I., Investigation of large-scale coherence in a turbulent boundary layer using two-point correlations, J. Fluid Mech., 2005, 524: 57～80
[84]Ganapathisubramani, B., Clemens, N. T., Dolling, D. S., Large-scale motions in a supersonic turbulent boundary layer, J. Fluid Mech., 2006, 556: 271～282
[85]Zhou, J., Adrian, R. J., Balachandar, S., Autogeneration of near-wall vortical structures in channel flow, Phys. Fluids, 1996, 8: 288～290
[86]Kim, K., Sung, H. J., Adrian, R. J., Effects of background noise on generating coherent packets of hairpin vortices, Phys. Fluids, 2008, 20 105107-1～10
[87]Panton, R. L., Overview of the self-sustaining mechanisms of wall turbulence, Progress in Aerospace Sciences, 2001, 1～43
[88]Christensen, K. T., Adrian, R. J., Statistical evidence of hairpin vortex packets in wall turbulence, J. Fluid Mech., 2001, 431: 433～443
[89]Natrajan, V. K., Christensen, K. T., The role of coherent structures in subgrid-scale energy transfer within the log layer of wall turbulence, Phys. Fluids, 2006, 18(6): 065104
[90]Wu, Y., Christensen, K. T., Population trends of spanwise vortices in wall turbulence, J. Fluid Mech., 2006, 568: 55～76
[91]Kim, K., Adrian, R. J., Balachandar, S., Sureshkumar, R., Dynamics of Hairpin Vortices and Polymer-Induced Turbulent Drag Reduction, Phys. Rev. Lett., 2008, 100(13): 134504-1～4
[92]Rebbeck, H., Choi, K-S, A wind-tunnel experiment on real-time opposition control of turbulence, Phys. Fluids, 2006, 18: 035103
[93]Choi, K-S, NATURE, 2006, 440(6): 754
[94]Volino, R. J., Schultz, M. P., Flack, K. A., Vortex structure and heat transfer in the stagnation region of an impinging plane jet, J. Fluid Mech., 2007, 592: 263～293
[95]Acarlar, M. S., Smith, C. R., A Study of Hairpin Vortices in a Laminar Boundary Layer Part 2: Hairpin vortices generated by fluid injection, J. Fluid Mech., 1987, 175: 43～83
[96]Tufo, H. M., Fischer, P. F., Papka, M. E., Szymanski, M., Hairpin vortex formation, a case study for unsteady visualization, 41st CUG Conference, July 28, 1999
[97]Kang, Y-D, Direct intervention of hairpin vortex in boundary layer to reduce friction: [PhD Thesis], Nottinham, University of Nottingham, 2007
[98]Krueger, P. S., Ghari, M., The significance of vortex ring formation to the impulse and thrust of a starting jet, Phys. Fluids, 2003, 15(5): 1271～1281
[99]Victoria, S., Jacob, C., Pinhas, Z. B., The generation of streaks and hairpin vortices from a localized vortex disturbance embedded in unbounded uniform shear flow, J. Fluid Mech., 2005, 535: 65～100
[100]Cortelezzi, L., Karagozian, A. R., On the formation of the counter-rotating vortex pair in transverse jets, J. Fluid Mech., 2001, 446: 347～373
[101]Chang, Y. K., Vakilia, A. D., Dynamics of vortex rings in crossflow, Phys. Fluids, 1995, 7(7): 1583～1597
[102]Green, S. I., Fluid vortices, Springer, 1995
[103]Saffman, P. G., Baker, G. R., Vortex interactions, Ann. Rev. Fluid Mech., 1979, 11: 95～122
[104]Goldstein, J. C., Levinski, V., DNS of Hairpin Vortex Formation in Poiseuille Flow Due to Two-hole Suction,Texas Univ.at Austin Dept. of Aerospace Engineering and Engineering Mechanics, AFOSR International Conference on DNS/LES (3rd) held at Univ. of Texas, Arlington, TX on 5-9 Aug., 2001
[105]Loehrke, R. I., Nagib, H. M., Experiments on management of free-stream turbulence, AGARD-R-598, 1972
[106]Morel, T., Design of two-dimensional wind tunnel contractions, Trans ASME J. Fluids Eng., 1977, 99: 371～378
[107]Miller, D. S, Internal Flow Systems, Cranfield, UK: Br. Hydromech. Res. Assoc., 1978
[108]IDel’chik, I. E., Handbook of hydraulic resistance: coefficients of local resistance and of friction, AEC-TR-6630, 1966
[109]Ermt, L. P., Joubert, P. N., Low-Reynolds-number turbulent boundary layers, J. Fluid Mech., 1991, 230: 1～44
[110]Schlichting, H., Boundary layer theory, New York: McGraw-hill, 1968
[111]King, L. V., On the convection of heat from small cylinders in a stream of fluid: determination of the convection constants of small platinum wires, with applications to hot-wire anemometry, Philos Trans Roy Soc London A, 1914, 214: 373～432
[112]Hutchins, N., Choi, K-S, Accurate measurements of local skin friction coefficient using hot-wire anemometry, Progress in Aerospace Sciences, 2002, 38: 421～446
[113]Hutchins, N., An investigation of large-scale coherent structures in fully developed turbulent boundary layers, [PhD thesis], Nottingham; University of Nottingham, 2003
[114]Frank M. White, sixth edition, 471
[115]Taylor, G. I., Proc. R. Soc., London: Ser. A, 1935, 151: 421
[116]Chakraborty, P., Balachandar, S., Adrian, R. J., On the relationships between local vortex identification schemes, J. Fluid Mech., 2005, 535: 189～214
[117]Zhou, J., Adrian, R. J., Balachandar, S., Kendall, T. M., Mechanisms for generating coherent packets of hairpin vortices in channel flow,J. Fluid Mech., 1999, 387: 353～396
[118]Krogstad, P.A., Kaspersen, J. H., Rimestad, S., Convection Velocities in a Turbulent Boundary Layer, Phys. Fluids, 1998, 10(4): 949～957
[119]Johansson, A. V., Alfredsson, P. H., Eckelmann, H., On the Evolution of Shear-Layer Structures in Near-Wall Turbulence, The first European Turbulence, France: Ecully, 1987, 383～390
[120]Marusic, I., Hutchins, N., Experimental study of wall turbulence: Implications for control, Gad-el-Hak, M., Tsai, H. M., In Transition and Turbulence Control, World Scientific, 2005
[121]Zhang, X., An inclined rectangular jet in a turbulent boundary layer-vortex flow, Experiments in Fluids,2000,28: 344～354
[122]Smith, R. W., Effect of Reynolds Number on the Structure of Turbulent Boundary Layers, [Ph.D. Thesis], Department of Mechanical and Aerospace Engineering, Princeton University, January 1994
[2]Prandtl, L., Uber Flussigkeits bewegung bei sehr kleiner Reibung, Verhaldlg III Int. Math. Kong, (Heidelberg: Teubner) 1904,484～491; Also available in translation as: Motion of fluids with very little viscosity. NACA TM 1928,452: 484～491
[3]Roach, P. E. The generation of nearly isotropic turbulence by means of grids, Int J Heat Fluid Flow, 1987, 8(2): 82～92
[4]Spaid, F. W., Roos, F. W., Hicks, R. M. An experimental study of the turbulent boundary layer on atransport wing in subsonic and transonic flows, NASA TM, 1990, 102206
[5]Spalart, P. R., Direct numerical simulation of boundary layer upto Rθ= 1410, J. Fluid Mech., 1988, 187: 61～98
[6]Ramos, J. I., Sirignano, W. A., Study of turbulence in a motored four-stroke internal combustion engine, AIAA Journal, 1981, 19(5): 595～600
[7]Deng, G. B., Duvigneau,R., Queutey, P., Visonneau, M., Assessment of Turbulence Model for Ship Flow at Full Scale, Computational Mechanics WCCW VI in conjunction with APCOM'04, Beijing, China, Sept. 5～10, 2004
[8]Verhulst, F., Methods and Applications of Singular Perturbations: Boundary Layers and Multiple Timescale Dynamics, Springer, 2005, ISBN 0-387-22966-3
[9]Lumley, J. L.,A Century of Turbulence Flow, Turbulence and Combustion, 2001, 66: 241～286
[10]Tulaprkara, E. G., Hundred years of the boundary layer– Some aspects, Sˉadhanˉa, 2005, 30(4): 499～512
[11]Tani, I., History of Boundary Layer Theory,Ann. Rev. Fluid Mech., 1977, 9: 87～111
[12]White, F. M., Fluid Mechanics, 459～460
[13]von Karman, T., On laminar and turbulent friction, Z. Angew. Math. Mech., 1921, 1: 235～236
[14]White, F. M., Visous Fluid Flow, 416
[15]Millikan, C. B., A critical discussion of turbulent flows in channels and circular tubes, Proceedings of the Fifth International Congress of Applied Mechanics,Cambridge,1938,386～392
[16]Coles, D. E., The law of the wake in the turbulent boundary layer. J. Fluid Mech., 1956, 1: 97～160
[17]Schlichting, H., Gersten, K., Boundary layer theory, Berlin: Springer Verlag, 2000
[18]Corrsin, S., Kistler, A. L., Free-stream boundaries of turbulent flows, 1955, NACA TN3133
[19]Kolmogorov, A. N., A refinement of previous hypotheses concerning the local structure of turbulence in a viscous incompressible fluid at high Reynolds number, J. Fluid Mech., 1962, 13: 82～85
[20]Benzi, R., Ciliberto, S., Tripiccione, R., Baudet, C., Massaioli, F., Succi, S., Extended self-similarity in turbulent flows, Phys. Rev. E, 1993, 48(1): R29～R32
[21]She, Z-S, Leveque , E., Universal scaling laws in fully developed turbulence, Phys. Rev. Lett., 1994, 72(3): 336～339
[22]Kline, S. J., Reynolds, C., Schraubf, A., Runstadlepr, W., The structure of turbulent boundary layers, J. Fluid Mech., 1967, 30: 741～73
[23]Kim, H. T., Kline, S. J., Reynolds, W. C., The production of turbulence near a smooth wall, J. Fluid Mech., 1971, 50: 133～160
[24]Nychas, S. G., Hershey, H. C., Brodkey, R. S., A visual study of turbulent shear flow, J. Fluid Mech., 1973, 61: 513～540
[25]Xanthos, S., Gong, M., Andreopoulos, Y., Velocity and vorticity in weakly compressible isotropic turbulence under longitudinal expansive straining, J. Fluid Mech., 2007, 584: 301～335
[26]Cuypers, Y., Maurel, A., Petitjeans, P., Vortex Burst as a Source of Turbulence, Phys. Rev. Lett., 2003, 91(19): 194502
[27]Archer, P. J., Thomas, T. G., Coleman, G. N., Direct numerical simulation of vortex ring evolution from the laminar to the early turbulent regime, J. Fluid Mech., 2008, 598: 201～226
[28]Onsager, L., Statistical Hydrodynamics, Nuovo Cimento, 1949, 6(2): 279～287
[29]Wyngaard, J. C., Measurement of small-scale turbulence structure with hot wires, J. of Phys. E: Scientific Instruments, 1968, 2(1): 1105～1108
[30]Kaimal, J. C., Wyngaard, J. C., Haugen, D. A., Cote, O. R., Izumi, Y., Caughey, S. J., Readings, C. J., Turbulence Structure in the Convective Boundary Layer, Journal of the Atmospheric Sciences, 1976, 33(11): 2152～2169
[31]Blackwelder, R., On the role of phase information in conditional sampling, Phys. Fluids, 1977, 20(10): s232-242
[32]Antonia, R. A., Conditional Sampling in Turbulence Measurement, Ann. Rev. Fluid Mech., 1981, 13: 131～156
[33]Alfredsson, P. H., Johansson, A. V., On the detection of turbulence-generating events, J. Fluid Mech., 1984, 139: 325～345
[34]Patel, V. C., Rodi, W., Scheuerer, G., Turbulence models for near-wall and low Reynolds number flows - A review, AIAA Journal, 1985, 23(9): 1308～1319
[35]Flores, O., Jimenez, J., del Alamo, J. C., Vorticity organization in the outer layer of turbulent channels with disturbed walls, J. Fluid Mech., 2007,591: 145～154
[36]Bandyopadhyay, P. R., Watson, R. D., Structure of rough-wall turbulent boundary layers, Phys. Fluids, 1988, 31:1877～1883
[37]Park, S-H, Lee, I., Sung, H. J., Effect of local forcing on a turbulent boundary layer, Experiments in Fluids, 2001, 31: 384～393
[38]Choi, K-S, Near-wall structure of a turbulent boundary layer with riblets, J. Fluid Mech., 1989, 208: 417～458
[39]Rathnasingham, R., Breuer, K. S., System Identification and Active Control of a Turbulent Boundary Layer, 28th AIAA Fluid Dynamics Conference, June 29～July 2, 1997 Snowmass Village, CO AIAA 97–1793
[40]Jukes, T., Choi, K-S, Turbulent Boundary-Layer Control for Drag Reduction Using Surface Plasma, 2nd AIAA Flow Control Conference, Portland, Oregon, June 28-1, 2004, AIAA-2004-2216
[41]McComb, W. D., Allan, J., Greated, C. A., Effect of polymer additives on the small-scale structure of grid-generated turbulence, Phys. Fluids, 1977, 20(6): 873～879
[42]Wark, C. E., Nagib, H. M., Experimental investigation of coherent structures in turbulent boundary layers, J. Fluid Mech., 1991, 230: 183～208
[43]Tennekes, H., Lumley, J. L., A first course in turbulence, M.I.T. Press, Cambridge, Mass, 1972
[44]Kim, J., Moin, P., Moser, R., Turbulence statistics in fully developed channel flow at low Reynolds number, J. Fluid Mech., 1987, 177: 133～166
[45]Schoppa, W., Hussain, F., Coherent structure generation in near-wall turbulence, J. Fluid Mech., 2002, 453: 57～108
[46]Hinze, J. O., Turbulence, 2nd Edn, p. 579, New York: McGraw-Hill, 1975
[47]Hamilton, J. M., Kim, J., Waleffe, F., Regeneration mechanisms of near-wall turbulence structures, J. Fluid Mech., 1995, 287: 317～348
[48]Brandt, L., Henningson, D. S., Transition of streamwise streaks in zero-pressure-gradient boundary layers, J. Fluid Mech., 2002, 472: 229～261
[49]Hutchins, N., Marusic, I., Evidence of very long meandering features in the logarithmic region of turbulent boundary layers, J. Fluid Mech., 2007, 579: 1～28
[50]Cantwell, B. J., Organized motion in turbulent flow, Annu. Rev. Fluid Mech., 1981, 13: 457～515
[51]Smith, C. R., Schwartz, S. P., Observation of streamwise rotation in the near-wall region of a turbulent boundary layer, Phys. Fluids, 1983, 26: 641～652
[52]Delo, C. J., Kelso, R. M., Smits, A. J., Three-dimensional structure of a low-Reynolds-number turbulent boundary layer, J. Fluid Mech., 2004, 512: 47～83
[53]Chernyshenko, S. I., Baig, M. F., The mechanism of streak formation in near-wall turbulence, J. Fluid Mech., 2005, 544: 99～131
[54]Hutchins, N., Hambleton, W. T., Marusic, I., Inclined cross-stream stereo particle image velocimetry measurements in turbulent boundary layers, J. Fluid Mech., 2005, 541: 21～54
[55]Tomkins, C. D., Adrian, R. J., Spanwise structure and scale growth in turbulent boundary layers, J. Fluid Mech., 2003, 490: 37～74
[56]Townsend, A. A., The Structure of Turbulent Shear Flow, 2nd edn. Cambridge University Press, 1976
[57]Liu, Z., Adrian, R. J., Hanratty, T. J., Large-scale modes of turbulent channel flow: transport and structure, J. Fluid Mech., 2001, 448: 53～80
[58]Coceal, O., Dobre, A., Thomas, T. G., Belcher, S. E., Structure of turbulent flow over regular arrays of cubical roughness, J. Fluid Mech., 2007, 589: 375～409
[59]Poggi, D., Porporato, A., Ridolfi, L., Analysis of the small-scale structure of turbulence on smooth and rough walls, Phys. Fluids, 2003, 15(1): 35～46
[60]Adrian, R. J., Meinhart, C. D., Tomkins, C. D., Vortex organization in the outer region of the turbulent boundary layer, J. Fluid Mech., 2000, 422: 1～54
[61]Ganapathisubramani, B., Longmire, E. K., Marusic, I., Characteristics of vortex packets in turbulent boundary layers, J. Fluid Mech., 2003, 478: 35～46
[62]del Alamo, J. C., Jimenez, J., Zandonade, P., Moser, R. D., Scaling of the energy spectra of turbulent channels, J. Fluid Mech., 2004, 500: 135～144
[63]del Alamo, J. C., Jimenez,J., Spectra of the very large anisotropic scales in turbulent channels, Phys. Fluids Lett., 2003, 15(6): L41～44
[64]Guala, M., Hommema, S. E., Adrian, R. J., Large-scale and very-large-scale motions in turbulent pipe flow, J. Fluid Mech., 2006, 554: 521～542
[65]Kim, K. C., Adrian, R. J., Very large-scale motion in the outer layer, Phys. Fluids, 1999, 11(2): 417～422
[66]Acarlar, M. S., Smith, C. R., A Study of Hairpin Vortices in a Laminar Boundary Layer I-Hairpin Vortices generated by a Hemisphere protuberance, J. Fluid Mech., 1987, 175: 1～41
[67]Robinson, S. K., Coherent Motions in the Turbulent Boundary Layer, Ann. Rev. Fluid Mech., 1991, 23: 601～639
[68]Eckelmann, H., Nychas, S. G., Brodkey, R. S., Wallace, J. M., Vorticity and turbulence production in pattern recognized turbulent flow structures, Phys. Fluids, 1977, 20(10):225～231
[69]Johansson, A. V., Alfredsson, P. H., Kim, J., Evolution and dynamics of shear-layer structures in near-wall turbulence, J. Fluid Mech., 1991, 224: 579～599
[70]Skote, M., Haritonidis, J. H., Henningson, D. S., Varicose instabilities in turbulent boundary layers, Phys. Fluids, 2002, 14(7): 2309～2323
[71]Smith, C. R., A synthesized model of the near-wall behavior in turbulent boundary layers, Proc. Symp. Turbul., 1984, 8th, Rolla, Mo
[72]Black, T. J., An analytical study of the measured wall pressure field under supersonic turbulent boundary layers, NASA, 1968, CR-888
[73]Head, M. R., Bandyopadhyay, P., New aspects of turbulent boundary-layer structure, J. Fluid Mech., 1981, 107: 297～338
[74]Robinson, S. K., Kinematics of turbulent boundary layer structure: PhD dissertation, Stanford, Calif; Stanford Univ., 1990, Also, NASA TM. In press
[75]Elsinga, G. E., Adrian, R. J., van Oudheusden, B. W., Scarano, F., Tomographic-PIV investigation of a high Reynolds number turbulent boundary layer, 7th International Symposium on Particle Image Velocimetry, Rome, Italy, 11-14 September 2007a Adrian, R. J., Hairpin vortex organization in wall turbulence, Phys. Fluids, 2007, 19(4): 041301-1～16
[76]Kim, K., Sung, H. J., Effects of unsteady blowing through a spanwise slot on a turbulent boundary layer, J. Fluid Mech., 2006, 557: 423～450
[77]Elsinga,G. E., Kuik,D. J., van Oudheusden,B. W.,Scaran,F.,Investigation of the three-dimensional coherent structures in a turbulent boundary layer with Tomographic-PIV,AIAA 2007-1305,45th AIAA Aerospace Sciences Meeting and Exhibit, Reno, Nevada, 8 - 11 January 2007b
[78]Haidari, A. H., Smith, C. R., The generation and regeneration of single hairpin vortices, J. Fluid Mech., 1994, 211: 135～162
[79]Kang, Y-D, Choi, K-S, Chun, H. H., Direct intervention of hairpin structures for turbulent boundary-layer control, Phys. Fluids, 2008, 20(10): 101517-1～13
[80]Bajer, K., Basson, A. P., Gilbert, A. D., Vortex motion in a weak background shear flow, J. Fluid Mech., 2004, 509: 281～304
[81]Carlier, J., Stanislas, M., Experimental study of eddy structures in a turbulent boundary layer using particle image velocimetry, J. Fluid Mech., 2005, 535: 143～188
[82]del Alamo, J. C., Jimenez, J., Zandonade, P., Moser, R. D., Self-similar vortex clusters in the turbulent logarithmic region, J. Fluid Mech., 2006, 561: 329～358
[83]Ganapathisubramani, B., Hutchins, N., Hambleton, W. T., Longmire, E. K., Marusic, I., Investigation of large-scale coherence in a turbulent boundary layer using two-point correlations, J. Fluid Mech., 2005, 524: 57～80
[84]Ganapathisubramani, B., Clemens, N. T., Dolling, D. S., Large-scale motions in a supersonic turbulent boundary layer, J. Fluid Mech., 2006, 556: 271～282
[85]Zhou, J., Adrian, R. J., Balachandar, S., Autogeneration of near-wall vortical structures in channel flow, Phys. Fluids, 1996, 8: 288～290
[86]Kim, K., Sung, H. J., Adrian, R. J., Effects of background noise on generating coherent packets of hairpin vortices, Phys. Fluids, 2008, 20 105107-1～10
[87]Panton, R. L., Overview of the self-sustaining mechanisms of wall turbulence, Progress in Aerospace Sciences, 2001, 1～43
[88]Christensen, K. T., Adrian, R. J., Statistical evidence of hairpin vortex packets in wall turbulence, J. Fluid Mech., 2001, 431: 433～443
[89]Natrajan, V. K., Christensen, K. T., The role of coherent structures in subgrid-scale energy transfer within the log layer of wall turbulence, Phys. Fluids, 2006, 18(6): 065104
[90]Wu, Y., Christensen, K. T., Population trends of spanwise vortices in wall turbulence, J. Fluid Mech., 2006, 568: 55～76
[91]Kim, K., Adrian, R. J., Balachandar, S., Sureshkumar, R., Dynamics of Hairpin Vortices and Polymer-Induced Turbulent Drag Reduction, Phys. Rev. Lett., 2008, 100(13): 134504-1～4
[92]Rebbeck, H., Choi, K-S, A wind-tunnel experiment on real-time opposition control of turbulence, Phys. Fluids, 2006, 18: 035103
[93]Choi, K-S, NATURE, 2006, 440(6): 754
[94]Volino, R. J., Schultz, M. P., Flack, K. A., Vortex structure and heat transfer in the stagnation region of an impinging plane jet, J. Fluid Mech., 2007, 592: 263～293
[95]Acarlar, M. S., Smith, C. R., A Study of Hairpin Vortices in a Laminar Boundary Layer Part 2: Hairpin vortices generated by fluid injection, J. Fluid Mech., 1987, 175: 43～83
[96]Tufo, H. M., Fischer, P. F., Papka, M. E., Szymanski, M., Hairpin vortex formation, a case study for unsteady visualization, 41st CUG Conference, July 28, 1999
[97]Kang, Y-D, Direct intervention of hairpin vortex in boundary layer to reduce friction: [PhD Thesis], Nottinham, University of Nottingham, 2007
[98]Krueger, P. S., Ghari, M., The significance of vortex ring formation to the impulse and thrust of a starting jet, Phys. Fluids, 2003, 15(5): 1271～1281
[99]Victoria, S., Jacob, C., Pinhas, Z. B., The generation of streaks and hairpin vortices from a localized vortex disturbance embedded in unbounded uniform shear flow, J. Fluid Mech., 2005, 535: 65～100
[100]Cortelezzi, L., Karagozian, A. R., On the formation of the counter-rotating vortex pair in transverse jets, J. Fluid Mech., 2001, 446: 347～373
[101]Chang, Y. K., Vakilia, A. D., Dynamics of vortex rings in crossflow, Phys. Fluids, 1995, 7(7): 1583～1597
[102]Green, S. I., Fluid vortices, Springer, 1995
[103]Saffman, P. G., Baker, G. R., Vortex interactions, Ann. Rev. Fluid Mech., 1979, 11: 95～122
[104]Goldstein, J. C., Levinski, V., DNS of Hairpin Vortex Formation in Poiseuille Flow Due to Two-hole Suction,Texas Univ.at Austin Dept. of Aerospace Engineering and Engineering Mechanics, AFOSR International Conference on DNS/LES (3rd) held at Univ. of Texas, Arlington, TX on 5-9 Aug., 2001
[105]Loehrke, R. I., Nagib, H. M., Experiments on management of free-stream turbulence, AGARD-R-598, 1972
[106]Morel, T., Design of two-dimensional wind tunnel contractions, Trans ASME J. Fluids Eng., 1977, 99: 371～378
[107]Miller, D. S, Internal Flow Systems, Cranfield, UK: Br. Hydromech. Res. Assoc., 1978
[108]IDel’chik, I. E., Handbook of hydraulic resistance: coefficients of local resistance and of friction, AEC-TR-6630, 1966
[109]Ermt, L. P., Joubert, P. N., Low-Reynolds-number turbulent boundary layers, J. Fluid Mech., 1991, 230: 1～44
[110]Schlichting, H., Boundary layer theory, New York: McGraw-hill, 1968
[111]King, L. V., On the convection of heat from small cylinders in a stream of fluid: determination of the convection constants of small platinum wires, with applications to hot-wire anemometry, Philos Trans Roy Soc London A, 1914, 214: 373～432
[112]Hutchins, N., Choi, K-S, Accurate measurements of local skin friction coefficient using hot-wire anemometry, Progress in Aerospace Sciences, 2002, 38: 421～446
[113]Hutchins, N., An investigation of large-scale coherent structures in fully developed turbulent boundary layers, [PhD thesis], Nottingham; University of Nottingham, 2003
[114]Frank M. White, sixth edition, 471
[115]Taylor, G. I., Proc. R. Soc., London: Ser. A, 1935, 151: 421
[116]Chakraborty, P., Balachandar, S., Adrian, R. J., On the relationships between local vortex identification schemes, J. Fluid Mech., 2005, 535: 189～214
[117]Zhou, J., Adrian, R. J., Balachandar, S., Kendall, T. M., Mechanisms for generating coherent packets of hairpin vortices in channel flow,J. Fluid Mech., 1999, 387: 353～396
[118]Krogstad, P.A., Kaspersen, J. H., Rimestad, S., Convection Velocities in a Turbulent Boundary Layer, Phys. Fluids, 1998, 10(4): 949～957
[119]Johansson, A. V., Alfredsson, P. H., Eckelmann, H., On the Evolution of Shear-Layer Structures in Near-Wall Turbulence, The first European Turbulence, France: Ecully, 1987, 383～390
[120]Marusic, I., Hutchins, N., Experimental study of wall turbulence: Implications for control, Gad-el-Hak, M., Tsai, H. M., In Transition and Turbulence Control, World Scientific, 2005
[121]Zhang, X., An inclined rectangular jet in a turbulent boundary layer-vortex flow, Experiments in Fluids,2000,28: 344～354
[122]Smith, R. W., Effect of Reynolds Number on the Structure of Turbulent Boundary Layers, [Ph.D. Thesis], Department of Mechanical and Aerospace Engineering, Princeton University, January 1994