| Citation: |
LI H X, XU D. Methods and progress of experimental research on passive scalar turbulent mixing[J]. Journal of Experiments in Fluid Mechanics, 2024, 38(4): 90-103. DOI: 10.11729/syltlx20230124
|
Turbulent mixing plays a vital role in daily life and engineering applications. Extensive research in turbulent mixing is crucial for various subjects, including turbulent theories, turbulent combustion, and chemical engineering. For the experimental studies of turbulent mixing, the development of sensors and non-intrusive laser-based measurement techniques furthers exploring and understanding the multi-scale nonlinear process in turbulent mixing. This review focuses on the Rayleigh scattering technique and laser-induced fluorescence technique for passive scalar field measurements. Potential ways to improve the spatial resolution of laser-induced fluorescence are introduced and discussed for measurements of turbulent mixing in two dimensions. Then an experimental perspective on small-scale mixing is presented, covering topics of the scaling law of mixing in the viscous-convective regime, the probability density function of scalar fluctuation fields, and the fractal dimension of the mixing interface. This work aims to introduce fundamental experimental methods and progress on the passive scalar turbulent mixing, together with the corresponding theoretical basis.
| [1] |
DIMOTAKIS P E. Turbulent mixing[J]. Annual Review of Fluid Mechanics, 2005, 37: 329–356. doi: 10.1146/annurev.fluid.36.050802.122015
|
| [2] |
刘亚明, 柳朝晖, 贺铸, 等. 湍流被动标量研究的最新进展[J]. 力学进展, 2005, 35(4): 549–558. DOI: 10.6052/1000-0992-2005-4-J2004-125
LIU Y M, LIU Z H, HE Z, et al. Recent progress in statistics of turbulent passive scalar[J]. Advances in Mechanics, 2005, 35(4): 549–558. doi: 10.6052/1000-0992-2005-4-J2004-125
|
| [3] |
VILLERMAUX E. Mixing versus stirring[J]. Annual Review of Fluid Mechanics, 2019, 51: 245–273. doi: 10.1146/annurev-fluid-010518-040306
|
| [4] |
PAUL E L, ATIEMO-OBENG V A, KRESTA S M. Handbook of industrial mixing: science and practice[M]. Hoboken, NJ: Wiley-Interscience, 2004.
|
| [5] |
ISSAKHOV A A, BAITUREYEVA A R. Modeling of a passive scalar transport from thermal power plants to atmospheric boundary layer[J]. International Journal of Environmental Science and Technology, 2019, 16(8): 4375–4392. doi: 10.1007/s13762-019-02273-y
|
| [6] |
HE X Z, SHANG X D, TONG P E. Test of the anomalous scaling of passive temperature fluctuations in turbulent Rayleigh–Bénard convection with spatial inhomogeneity[J]. Journal of Fluid Mechanics, 2014, 753: 104–130. doi: 10.1017/jfm.2014.325
|
| [7] |
张晓航, 许春晓, 张兆顺, 等. 无剪切湍流混合层中被动标量扩散的实验研究[J]. 流体力学实验与测量, 2003, 17(4): 22–27. DOI: 10.3969/j.issn.1672-9897.2003.04.004
ZHANG X H, XU C X, ZHANG Z S, et al. Experimental study on the passive scalar diffusion in shearless turbulent mixing layer[J]. Journal of Experiments in Fluid Mechanics, 2003, 17(4): 22–27. doi: 10.3969/j.issn.1672-9897.2003.04.004
|
| [8] |
张晓航, 许春晓, 张兆顺. Sc数对湍流被动标量扩散的影响[J]. 工程力学, 2004, 21(3): 36–39. DOI: 10.3969/j.issn.1000-4750.2004.03.007
ZHANG X H, XU C X, ZHANG Z S. Effect of Sc number on turbulent diffusion of passive scalar[J]. Engineering Mechanics, 2004, 21(3): 36–39. doi: 10.3969/j.issn.1000-4750.2004.03.007
|
| [9] |
CRIMALDI J P. Planar laser induced fluorescence in aqueous flows[J]. Experiments in Fluids, 2008, 44(6): 851–863. doi: 10.1007/s00348-008-0496-2
|
| [10] |
MILLER P L, DIMOTAKIS P E. Reynolds number dependence of scalar fluctuations in a high Schmidt number turbulent jet[J]. Physics of Fluids A: Fluid Dynamics, 1991, 3(5): 1156–1163. doi: 10.1063/1.858043
|
| [11] |
MILLER P L, DIMOTAKIS P E. Stochastic geometric properties of scalar interfaces in turbulent jets[J]. Physics of Fluids A: Fluid Dynamics, 1991, 3(1): 168–177. doi: 10.1017/S0022112096001425
|
| [12] |
MILLER P L, DIMOTAKIS P E. Measurements of scalar power spectra in high Schmidt number turbulent jets[J]. Journal of Fluid Mechanics, 1996, 308: 129–146. doi: 10.1017/s0022112096001425
|
| [13] |
PAPAVASSILIOU D V, HANRATTY T J. Transport of a passive scalar in a turbulent channel flow[J]. International Journal of Heat and Mass Transfer, 1997, 40(6): 1303–1311. doi: 10.1016/s0017-9310(96)00202-5
|
| [14] |
DIZECHI M, MARSCHALL E. Viscosity of some binary and ternary liquid mixtures[J]. Journal of Chemical & Engineering Data, 1982, 27(3): 358–363. doi: 10.1021/je00029a039
|
| [15] |
BRAHAMI Y. Active scalar mixing in turbulent jet flows[D]. Rouen: Normandie Université, 2020.
|
| [16] |
ABARZHI S I, SREENIVASAN K R. Turbulent mixing and beyond[J]. Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, 2010, 368(1916): 1539–1546. doi: 10.1098/rsta.2010.0021
|
| [17] |
SREENIVASAN K R, ABARZHI S I. Acceleration and turbulence in Rayleigh-Taylor mixing[J]. Philosophical Transactions Series A: Mathematical, Physical and Engineering Sciences, 2013, 371(2003): 20130267. doi: 10.1098/rsta.2013.0267
|
| [18] |
ABARZHI S I. Self-similar interfacial mixing with variable acceleration[J]. Physics of Fluids, 2021, 33(12): 122110. doi: 10.1063/5.0064120
|
| [19] |
ANDREWS M J, DALZIEL S B. Small Atwood number Rayleigh-Taylor experiments[J]. Philosophical Transactions Series A: Mathematical, Physical and Engineering Sciences, 2010, 368(1916): 1663–1679. doi: 10.1098/rsta.2010.0007
|
| [20] |
ZHANG G, XU A G, ZHANG D J, et al. Delineation of the flow and mixing induced by Rayleigh–Taylor instability through tracers[J]. Physics of Fluids, 2021, 33(7): 076105. doi: 10.1063/5.0051154
|
| [21] |
江荣宝, 黄熙龙, 邹立勇, 等. 液-液斜界面R-T失稳特征的实验研究[J]. 高压物理学报, 2018, 32: 80-86.
JIANG B R, HUANG X L, ZOU L Y, et al. Experimental investigation on the characteristics of unstability at liquid-liquid tilted interface induced by Rayleigh-Taylor instability[J]. Chinese Journal of High Pressure Physics, 2018, 32: 80-86. doi: 10.11858/gywlxb.20180512
|
| [22] |
BALAKUMAR B J, ORLICZ G C, TOMKINS C D, et al. Simultaneous particle-image velocimetry–planar laser-induced fluorescence measurements of Richtmyer–Meshkov instability growth in a gas curtain with and without reshock[J]. Physics of Fluids, 2008, 20(12): 124103. doi: 10.1063/1.3041705
|
| [23] |
BALAKUMAR B J, ORLICZ G C, RISTORCELLI J R, et al. Turbulent mixing in a Richtmyer–Meshkov fluid layer after reshock: velocity and density statistics[J]. Journal of Fluid Mechanics, 2012, 696: 67–93. doi: 10.1017/jfm.2012.8
|
| [24] |
MANSOOR M M, DALTON S M, MARTINEZ A A, et al. The effect of initial conditions on mixing transition of the Richtmyer–Meshkov instability[J]. Journal of Fluid Mechanics, 2020, 904: A3. doi: 10.1017/jfm.2020.620
|
| [25] |
黄熙龙, 廖深飞, 邹立勇, 等. 扩散型气柱界面R-M失稳中混合率的实验研究[J]. 力学学报, 2016, 48(5): 1073–1079. DOI: 10.6052/0459-1879-16-108
HUANG X L, LIAO S F, ZOU L Y, et al. Experimental investigation of mixing rate in r-m instability of diffuse gas cylinder interface[J]. Chinese Journal of Theoretical and Applied Mechanics, 2016, 48(5): 1073–1079. doi: 10.6052/0459-1879-16-108
|
| [26] |
XIAO M J, HU Z X, DAI Z H, et al. Experimentally consistent large-eddy simulation of re-shocked Richtmyer–Meshkov turbulent mixing[J]. Physics of Fluids, 2022, 34(12): 125125. doi: 10.1063/5.0129595
|
| [27] |
丛洲洋, 郭旭, 司延. 反射激波诱导界面不稳定性研究进展[J]. 中国科学 (物理学 力学 天文学), 2020, 50(10): 14-35.
CONG Z Y, GUO X, SI Y. Advances in interfacial instability induced by reshock[J]. Scientia Sinica (Physica, Mechanica & Astronomica), 2020, 50(10): 14-35. doi: 10.1360/SSPMA-2020-0099
|
| [28] |
LIANG Y, LUO X S. Review on hydrodynamic instabilities of a shocked gas layer[J]. Science China Physics, Mechanics & Astronomy, 2023, 66(10): 104701. doi: 10.1007/s11433-023-2162-0
|
| [29] |
SREENIVASAN K R. Turbulent mixing: a perspective[J]. Proceedings of the National Academy of Sciences of the United States of America, 2019, 116(37): 18175–18183. doi: 10.1073/pnas.1800463115
|
| [30] |
RAUWENDAAL C. Mixing in polymer processing[M]. New York: M. Dekker, 1991.
|
| [31] |
ECKART C. An analysis of the stirring and mixing processes in incompressible fluids[J]. Journal of Marine Research, 1948, 7: 265–275.
|
| [32] |
CORRSIN S. On the spectrum of isotropic temperature fluctuations in an isotropic turbulence[J]. Journal of Applied Physics, 1951, 22(4): 469–473. doi: 10.1063/1.1699986
|
| [33] |
KOLMOGOROV A N. Dissipation of energy in the locally isotropic turbulence[J]. Proceedings of the Royal Society of London Series A: Mathematical and Physical Sciences, 1991, 434(1890): 15–17. doi: 10.1098/rspa.1991.0076
|
| [34] |
KOLMOGOROV A N. The local structure of turbulence in incompressible viscous fluid for very large Reynolds numbers[J]. Proceedings of the Royal Society of London Series A: Mathematical and Physical Sciences, 1991, 434(1890): 9–13. doi: 10.1098/rspa.1991.0075
|
| [35] |
BATCHELOR G K. Small-scale variation of convected quantities like temperature in turbulent fluid Part 1. General discussion and the case of small conductivity[J]. Journal of Fluid Mechanics, 1959, 5(1): 113. doi: 10.1017/s002211205900009x
|
| [36] |
方乐, 崔桂香, 许春晓, 等. 标量湍流的能量传输特性[J]. 计算物理, 2006, 23(6): 692–698. DOI: 10.19596/j.cnki.1001-246x.2006.06.011
FANG L, CUI G X, XU C X, et al. Energy transfer in scalar turbulence[J]. Chinese Journal of Computational Physics, 2006, 23(6): 692–698. doi: 10.19596/j.cnki.1001-246x.2006.06.011
|
| [37] |
WARHAFT Z. Passive scalars in turbulent flows[J]. Annual Review of Fluid Mechanics, 2000, 32: 203–240. doi: 10.1146/annurev.fluid.32.1.203
|
| [38] |
COOK A W, CABOT W, MILLER P L. The mixing transition in Rayleigh–Taylor instability[J]. Journal of Fluid Mechanics, 2004, 511: 333–362. doi: 10.1017/s0022112004009681
|
| [39] |
THORNBER B, DRIKAKIS D, YOUNGS D L, et al. Growth of a Richtmyer-Meshkov turbulent layer after reshock[J]. Physics of Fluids, 2011, 23(9): 095107. doi: 10.1063/1.3638616
|
| [40] |
REESE D T, AMES A M, NOBLE C D, et al. Simultaneous direct measurements of concentration and velocity in the Richtmyer–Meshkov instability[J]. Journal of Fluid Mechanics, 2018, 849: 541–575. doi: 10.1017/jfm.2018.419
|
| [41] |
MOHAGHAR M, CARTER J, PATHIKONDA G, et al. The transition to turbulence in shock-driven mixing: effects of Mach number and initial conditions[J]. Journal of Fluid Mechanics, 2019, 871: 595–635. doi: 10.1017/jfm.2019.330
|
| [42] |
GIBSON C H. Fine structure of scalar fields mixed by turbulence II: spectral theory[J]. Physics of Fluids, 1968, 11(11): 2316–2327. doi: 10.1063/1.1691821
|
| [43] |
ZWIRNER L, KHALILOV R, KOLESNICHENKO I, et al. The influence of the cell inclination on the heat transport and large-scale circulation in liquid metal convection[J]. Journal of Fluid Mechanics, 2020, 884: A18. doi: 10.1017/jfm.2019.935
|
| [44] |
KRAICHNAN R H. Small-scale structure of a scalar field convected by turbulence[J]. Physics of Fluids, 1968, 11(5): 945–953. doi: 10.1063/1.1692063
|
| [45] |
DONZIS D A, SREENIVASAN K R, YEUNG P K. The batchelor spectrum for mixing of passive scalars in isotropic turbulence[J]. Flow, Turbulence and Combustion, 2010, 85(3): 549–566. doi: 10.1007/s10494-010-9271-6
|
| [46] |
CLAY M P. Strained turbulence and low-diffusivity turbulent mixing using high per-formance computing[D] Georgia: Georgia Institute of Technology, 2017.
|
| [47] |
DASI L P, SCHUERG F, WEBSTER D R. The geometric properties of high-Schmidt-number passive scalar iso-surfaces in turbulent boundary layers[J]. Journal of Fluid Mechanics, 2007, 588: 253–277. doi: 10.1017/s0022112007007525
|
| [48] |
MOHAGHAR M, DASI L P, WEBSTER D R. Scalar power spectra and turbulent scalar length scales of high-Schmidt-number passive scalar fields in turbulent boundary layers[J]. Physical Review Fluids, 2020, 5(8): 084606. doi: 10.1103/physrevfluids.5.084606
|
| [49] |
IWANO K, HOSOI J, SAKAI Y, et al. Power spectrum of high Schmidt number scalar in a turbulent jet at a moderate Reynolds number[J]. Experiments in Fluids, 2021, 62(6): 129. doi: 10.1007/s00348-021-03216-5
|
| [50] |
TALBOT B, MAZELLIER N, RENOU B, et al. Time-resolved velocity and concentration measurements in variable-viscosity turbulent jet flow[J]. Experiments in Fluids, 2009, 47(4): 769–787. doi: 10.1007/s00348-009-0729-z
|
| [51] |
BUDZINSKI J M, BENJAMIN R F, JACOBS J W. Influence of initial conditions on the flow patterns of a shock-accelerated thin fluid layer[J]. Physics of Fluids, 1994, 6(11): 3510–3512. doi: 10.1063/1.868447
|
| [52] |
CRIMALDI J P. The effect of photobleaching and velocity fluctuations on single-point LIF measurements[J]. Experiments in Fluids, 1997, 23(4): 325–330. doi: 10.1007/s003480050117
|
| [53] |
COPPETA J, ROGERS C. Dual emission laser induced fluorescence for direct planar scalar behavior measurements[J]. Experiments in Fluids, 1998, 25(1): 1–15. doi: 10.1007/s003480050202
|
| [54] |
FERRIER A J, FUNK D R, ROBERTS P J W. Application of optical techniques to the study of plumes in stratified fluids[J]. Dynamics of Atmospheres and Oceans, 1993, 20(1-2): 155–183. doi: 10.1016/0377-0265(93)90052-9
|
| [55] |
SAKAKIBARA J, ADRIAN R J. Whole field measurement of temperature in water using two-color laser induced fluorescence[J]. Experiments in Fluids, 1999, 26(1): 7–15. doi: 10.1007/s003480050260
|
| [56] |
SOMEYA S, BANDO S, SONG Y C, et al. DeLIF measurement of pH distribution around dissolving CO2 droplet in high pressure vessel[J]. International Journal of Heat and Mass Transfer, 2005, 48(12): 2508–2515. doi: 10.1016/j.ijheatmasstransfer.2004.12.042
|
| [57] |
PANCHUK-VOLOSHINA N, HAUGLAND R P, BISHOP-STEWART J, et al. Alexa dyes, a series of new fluorescent dyes that yield exceptionally bright, photostable conjugates[J]. The Journal of Histochemistry and Cytochemistry, 1999, 47(9): 1179–1188. doi: 10.1177/002215549904700910
|
| [58] |
LOZANO A, YIP B, HANSON R K. Acetone: a tracer for concentration measurements in gaseous flows by planar laser-induced fluorescence[J]. Experiments in Fluids, 1992, 13(6): 369–376. doi: 10.1007/BF00223244
|
| [59] |
SCHULZ C, SICK V. Tracer-LIF diagnostics: quantitative measurement of fuel concentration, temperature and fuel/air ratio in practical combustion systems[J]. Progress in Energy and Combustion Science, 2005, 31(1): 75–121. doi: 10.1016/j.pecs.2004.08.002
|
| [60] |
BERLMAN I B. Handbook of fluorescence spectra of aromatic molecules[M]. 2d ed. New York: Academic Press, 1971.
|
| [61] |
黄真理, 周维虎, 曲兆松. 三维激光诱导荧光(3DLIF)技术及测量水体标量场设备研究[J]. 实验流体力学, 2017, 31(5): 1–14. DOI: 10.11729/syltlx20160173
HUANG Z L, ZHOU W H, QU Z S. Study on three dimensional laser-induced fluorescence (3DLIF) techniques and its instrument[J]. Journal of Experiments in Fluid Mechanics, 2017, 31(5): 1–14. doi: 10.11729/syltlx20160173
|
| [62] |
KONG G, BUIST K A, PETERS E A J F, et al. Dual emission LIF technique for pH and concentration field measurement around a rising bubble[J]. Experimental Thermal and Fluid Science, 2018, 93: 186–194. doi: 10.1016/j.expthermflusci.2017.12.032
|
| [63] |
RAFFEL M, WILLERT C E, SCARANO F, et al. Particle image velocimetry: A practical guide[M]. Cham: Springer International Publishing, 2018. doi: 10.1103/PhysRevE.56.1753
|
| [64] |
GUILKEY J E, KERSTEIN A R, MCMURTRY P A, et al. Long-tailed probability distributions in turbulent-pipe-flow mixing[J]. Physical Review E, 1997, 56(2): 1753–1758. doi: 10.1103/physreve.56.1753
|
| [65] |
DEUSCH S, DRACOS T. Time resolved 3D passive scalar concentration-field imaging by laser induced fluorescence (LIF) in moving liquids[J]. Measurement Science and Technology, 2001, 12(2): 188–200. doi: 10.1088/0957-0233/12/2/310
|
| [66] |
READY J F. Industrial applications of lasers[M]. 2nd ed. San Diego: Academic Press, 1997.
|
| [67] |
雷明明, 田兴志. 直角刀口法测量激光光束质量[J]. 激光与红外, 2008, 038: 74–77. DOI: 10.3969/j.issn.1001-5078.2008.01.022
LEI M M, TIAN X Z. Measurement of the laser beam quality using right-angle knife-edge method[J]. LASER & INFRARED, 2008, 038: 74–77. doi: 10.3969/j.issn.1001-5078.2008.01.022
|
| [68] |
PITTS W M, KASHIWAGI T. The application of laser-induced Rayleigh light scattering to the study of turbulent mixing[J]. Journal of Fluid Mechanics, 1984, 141: 391–429. doi: 10.1017/s0022112084000902
|
| [69] |
ZHAO F Q, HIROYASU H. The applications of laser Rayleigh scattering to combustion diagnostics[J]. Progress in Energy and Combustion Science, 1993, 19(6): 447–485. doi: 10.1016/0360-1285(93)90001-u
|
| [70] |
闫博, 李猛, 陈力, 等. 基于滤波瑞利散射技术的带压燃烧场温度测量实验研究[J]. 实验流体力学, 2019, 33(4): 27–32. DOI: 10.11729/syltlx20180168
YAN B, LI M, CHEN L, et al. Experimental study on temperature measurement of high pressure combustion based on filtered Rayleigh scattering technology[J]. Journal of Experiments in Fluid Mechanics, 2019, 33(4): 27–32. doi: 10.11729/syltlx20180168
|
| [71] |
王海青, 林伟, 仝毅恒, 等. 基于激光的燃烧场温度诊断方法综述[J]. 气体物理, 2020, 5(1): 42–55. DOI: 10.19527/j.cnki.2096-1642.0752
WANG H Q, LIN W, TONG Y H, et al. Review of laser-based temperature diagnosis methods for combustion field[J]. Physics of Gases, 2020, 5(1): 42–55. doi: 10.19527/j.cnki.2096-1642.0752
|
| [72] |
高南, 刘玄鹤. 免标定热线风速测量方法的初步研究[J]. 实验流体力学, 2023, 37(5): 1–8. DOI: 10.11729/syltlx20230004
GAO N, LIU X H. A preliminary study on calibration-free hot-wire anemometry method[J]. Journal of Experiments in Fluid Mechanics, 2023, 37(5): 1–8. doi: 10.11729/syltlx20230004
|
| [73] |
MCKEON B, COMTE-BELLOT G, FOSS J, et al. Velocity, vorticity, and Mach Number[M]//TROPEA C, YARIN A L, FOSS J F. Springer Handbook of Experimental Fluid Mechanics. Heidelberg: Springer Berlin Heidelberg, 2007: 215-471.
|
| [74] |
沈熊. 激光测速技术(LDV)诞生50周年启示[J]. 实验流体力学, 2014, 28(6): 51–55. DOI: 10.11729/syltlx20140011
SHEN X. A historical review for the 50 th anniversary of laser Doppler velocimetry[J]. Journal of Experiments in Fluid Mechanics, 2014, 28(6): 51–55. doi: 10.11729/syltlx20140011
|
| [75] |
王洪平, 高琪, 魏润杰, 等. 基于层析PIV的湍流边界层展向涡研究[J]. 实验流体力学, 2016, 30(2): 59–66. DOI: 10.11729/syltlx20150086
WANG H P, GAO Q, WEI R J, et al. Study of spanwise vortices in turbulent boundary layer flow based on tomographic PIV[J]. Journal of Experiments in Fluid Mechanics, 2016, 30(2): 59–66. doi: 10.11729/syltlx20150086
|
| [76] |
田海平, 伊兴睿, 钟山, 姜楠, 张山鹰. 基于Stereo-PIV技术的三维发卡涡结构定量测量研究[J]. 力学学报, 2020, 52: 1666–1677. DOI: 10.6052/0459-1879-20-203
TIAN H P, YI X R, ZHONG S, et al. Experimental study on quantitative measurement of three-dimensional structure of harpin vortex by Stereo-PIV[J]. Chinese Journal of Theoretical and Applied Mechanics, 2020, 52: 1666–1677. doi: 10.6052/0459-1879-20-203
|
| [77] |
CHEN J, ODIER P, RIVERA M, et al. Laboratory measurement of entrainment and mixing in oceanic overflows[C]//Proceedings of ASME/JSME 2007 5th Joint Fluids Engineering Conference. 2009: 1283-1292. doi: 10.1115/FEDSM2007-37673
|
| [78] |
HU H, SAGA T, KOBAYASHI T, et al. Simultaneous velocity and concentration measurements of a turbulent jet mixing flow[J]. Annals of the New York Academy of Sciences, 2002, 972(1): 254–259. doi: 10.1111/j.1749-6632.2002.tb04581.x
|
| [79] |
XU D, CHEN J. Experimental study of stratified jet by simultaneous measurements of velocity and density fields[J]. Experiments in Fluids, 2012, 53(1): 145–162. doi: 10.1007/s00348-012-1275-7
|
| [80] |
LI H X, FISCHER A, AVILA M, et al. Measurement error of tracer-based velocimetry in single-phase turbulent flows with inhomogeneous refractive indices[J]. Experimental Thermal and Fluid Science, 2022, 136: 110681. doi: 10.1016/j.expthermflusci.2022.110681
|
| [81] |
PRASAD R R, SREENIVASAN K R. Quantitative three-dimensional imaging and the structure of passive scalar fields in fully turbulent flows[J]. Journal of Fluid Mechanics, 1990, 216: 1–34. doi: 10.1017/s0022112090000325
|
| [82] |
NYE J O, BRODKEY R S. The scalar spectrum in the viscous-convective subrange[J]. Journal of Fluid Mechanics, 1967, 29(1): 151–163. doi: 10.1017/s0022112067000680
|
| [83] |
TAVOULARIS S, CORRSIN S. Experiments in nearly homogenous turbulent shear flow with a uniform mean temperature gradient. Part 1[J]. Journal of Fluid Mechanics, 1981, 104: 311–347. doi: 10.1017/s0022112081002930
|
| [84] |
CASTAING B, GUNARATNE G, HESLOT F, et al. Scaling of hard thermal turbulence in Rayleigh-Bénard convection[J]. Journal of Fluid Mechanics, 1989, 204: 1. doi: 10.1017/s0022112089001643
|
| [85] |
DUBIEF Y, TERRAPON V E. Heat transfer enhancement and reduction in low-Rayleigh number natural convection flow with polymer additives[J]. Physics of Fluids, 2020, 32(3): 033103. doi: 10.1063/1.5143275
|
| [86] |
HE X Z, FUNFSCHILLING D, NOBACH H, et al. Transition to the ultimate state of turbulent Rayleigh-Bénard convection[J]. Physical Review Letters, 2012, 108(2): 024502. doi: 10.1103/PhysRevLett.108.024502
|
| [87] |
PUMIR A, SHRAIMAN B, SIGGIA E. Exponential tails and random advection[J]. Physical Review Letters, 1991, 66(23): 2984–2987. doi: 10.1103/PhysRevLett.66.2984
|
| [88] |
KERSTEIN A, MCMURTRY P. Mean-field theories of random advection[J]. Physical Review E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics, 1994, 49(1): 474–482. doi: 10.1103/physreve.49.474
|
| [89] |
GOLLUB J P, CLARKE J, GHARIB M, et al. Fluctuations and transport in a stirred fluid with a mean gradient[J]. Physical Review Letters, 1991, 67(25): 3507–3510. doi: 10.1103/physrevlett.67.3507
|
| [90] |
WARHAFT Z. Probability distribution of a passive scalar in grid-generated turbulence[J]. Physical Review Letters, 1991, 67(25): 3503–3506. doi: 10.1103/PhysRevLett.67.3503
|
| [91] |
SREENIVASAN K R, PRASAD R R, MENEVEAU C, et al. The fractal geometry of interfaces and the multifractal distribution of dissipation in fully turbulent flows[J]. Pure and Applied Geophysics, 1989, 131(1): 43–60. doi: 10.1007/BF00874479
|
| [92] |
VILLERMAUX E, INNOCENTI C. On the geometry of turbulent mixing[J]. Journal of Fluid Mechanics, 1999, 393: 123–147. doi: 10.1017/s0022112099005674
|
| [93] |
CATRAKIS H J, DIMOTAKIS P E. Mixing in turbulent jets: scalar measures and isosurface geometry[J]. Journal of Fluid Mechanics, 1996, 317: 369–406. doi: 10.1017/s002211209600078x
|
| [1] | ZHANG Bin, ZHOU Genshui, GAO Debao, DU Xinming, FAN Xiaobing, LIU Jianhua. Vortex evolution of the flow around an underwater vehicle in density-stratified flow[J]. Journal of Experiments in Fluid Mechanics, 2024, 38(2): 31-39. DOI: 10.11729/syltlx20230137 |
| [2] | WANG Yuanyuan, WANG Chengyue, MANG Shanshan, SHEN Yunian, CHEN Zhihua. Research on the vortex dynamics of two-dimensional jellyfish-like flapping wings based on particle image velocimetry[J]. Journal of Experiments in Fluid Mechanics. DOI: 10.11729/syltlx20230080 |
| [3] | ZHANG Yong, DING Junfei, LIU Yiqun, LIANG Xiaoyi, TIAN Haiping. Research on trichromatic mask for 3D PIV particle image extraction using a single color camera from three views[J]. Journal of Experiments in Fluid Mechanics. DOI: 10.11729/syltlx20240012 |
| [4] | LU Xintao, ZHAO Hang, SHE Wenxuan, TU Han, GAO Qi, WEI Runjie, ZHANG Fang, Chen Shuang. Study on MHz high-speed PIV technique[J]. Journal of Experiments in Fluid Mechanics. DOI: 10.11729/syltlx20230144 |
| [5] | JIN Yuanzhong, ZHENG Borui, YU Minghao, LIU Yuanpeng, ZHANG Qian, SUN Zhengzhong, YU Tao. Experimental study on flow control of asymmetric vortex over the leeward region of the head of the slender body by sliding discharge plasma actuation[J]. Journal of Experiments in Fluid Mechanics, 2022, 36(5): 43-51. DOI: 10.11729/syltlx20210101 |
| [6] | LI Xiaohui, WANG Hongwei, HUANG Zhan, ZHAO Junbo. Research advances of tomographic particle image velocimetry[J]. Journal of Experiments in Fluid Mechanics, 2021, 35(1): 86-96. DOI: 10.11729/syltlx20190160 |
| [7] | Ding Junfei, Xu Shengming, Shi Shengxian. Light field volumetric particle image velocimetry[J]. Journal of Experiments in Fluid Mechanics, 2016, 30(6): 50-58. DOI: 10.11729/syltlx20160141 |
| [8] | Wang Hongwei, Huang Zhan. Research on particle image velocimetry based on optical flow[J]. Journal of Experiments in Fluid Mechanics, 2015, (3): 68-75. DOI: 10.11729/syltlx20140115 |
| [9] | RONG Zhen, CHEN Fang, LIU Hong. Application of particle image velocimetry to Mach 4.0 flows[J]. Journal of Experiments in Fluid Mechanics, 2012, 26(6): 53-58. DOI: 10.3969/j.issn.1672-9897.2012.06.012 |
| [10] | SHEN Gong-xin. On PIV to face new century[J]. Journal of Experiments in Fluid Mechanics, 2000, 14(2): 1-15. DOI: 10.3969/j.issn.1672-9897.2000.02.001 |
Supported by: Beijing Renhe Information Technology Co., Ltd. 
DownLoad: