Thirty years of turbulence study in China

doi:10.1007/s10483-019-2427-9

摘要/Abstract

摘要：

This paper provides a comprehensive introduction to the major progress in transition and turbulence studies in China over the past thirty years. Despite the author's best efforts, there are some unavoidable omissions. We expect that with the continued deepening of turbulence research, Chinese scholars will make increasing contributions in this field, which will certainly have strong influence on the establishment of a China School of Turbulence.

关键词: uniform convergence, parabolic equations, non-uniform mesh, turbulence, wall bounded flow, transition

Abstract:

Key words: uniform convergence, parabolic equations, non-uniform mesh, turbulence, wall bounded flow, transition

中图分类号:

Bohua SUN. Thirty years of turbulence study in China[J]. Applied Mathematics and Mechanics (English Edition), 2019, 40(2): 193-214.

参考文献

[1] CHOU, P. Y. On an extension of Reynolds' method of finding apparent stress and the nature of turbulence. Chinese Journal of Physics, 4, 1-33(1940)
[2] CHOU, P. Y. On velocity correlations and the solutions of the equations of turbulent fluctuation. Quarterly of Applied Mathematics, 3, 38-54(1945)
[3] CHEN, S. Y. and ZHOU, P. Y. The application of quasi-similarity conditions in turbulence modeling theory. Advances in Hydrodynamics, 2(2), 1-14(1987)
[4] ZHOU, P. Y. and CHEN, S. Y. On the theory of turbulence for incompressible fluids. Sadhana, 10(3/4), 403-417(1987)
[5] ZHOU, P. Y., HUANG, Y. N., and MENG, Q. G. The pseudo-similarity theory of the plane turbulent mixing layer. Acta Mechanica Sinica, 22(1), 1-8(1990)
[6] ZHOU, P. Y., LIN, J. Z., and WEI, Z. L. The experimental results of 2-d free shear turbulent flows and the comparison with the theoretical computation. Journal of Hydrodynamics, Ser. B, 3, 1-9(1991)
[7] LIN, J. Z. and HUANG, Y. N. The pseudo-similarity theory of turbulence and its application to a channel flow. Journal of Hydraulic Engineering, 12, 72-77(1994)
[8] LI, Y. G., QIN, R. X., and ZHOU, P. Y. Laser double-frequency lock-in displacement sensor with application to gravitational radiation detection. Experimental Gravitational Physics, World Scientific, Singapore (1988)
[9] WANG, X. H., HUANG, Y. N., and ZHOU, P. Y. Statistical theory of homogeneous isotropic turbulence for incompressible fluids. Science in China Series A-Mathematics, Physics, Astronomy and Technological Science, 37(2), 209-220(1994)
[10] LIN, J. Z., HUANG, Y. N., and ZHOU, P. Y. The new method of solving velocity correlation functions and application to the plane turbulent wake. Acta Mechanica Sinica, 9(2), 102-109(1993)
[11] LIN, J. Z., HUANG, Y. N., and ZHOU, P. Y. An approximate method for solving turbulent velocity correlation functions in channel flows. Chinese Science Bulletin, 40(14), 1167-1172(1995)
[12] MENG, Q. G., HUANG, Y. N., and ZHOU, P. Y. The statistical theory of the plane turbulent mixing layer flow (in Chinese). Journal of Hydrodynamics, 10(4), 443-450(1995)
[13] FAN, M., HUANG, Y. N., and ZHOU, P. Y. The solution for incompressible plane turbulent jet by using the method of successive substitution (in Chinese). Journal of Hydrodynamics, 11(4), 465-470(1996)
[14] TSAI, S. T. and LIN, D. M. A note on a new theory of turbulence. Applied Mathematics and Mechanics (English Edition), 12(1), 101-105(1991) https://doi.org/10.1007/BF02018074
[15] SHI, C. C., HUANG, Y. N., ZHU, Z. X., SU, W. D., and DONG, Y. F. Chaotic phenomena produced by the spherical vortices in the Beltrami flows. Chinese Physics Letters, 9(10), 515-518(1992)
[16] HUANG, Y. N. and HU, X. Superposition about the 3D vortex solutions of the fluid dynamic equation. Applied Mathematics and Mechanics (English Edition), 21(12), 1359-1370(2000) https://doi.org/10.1007/BF02459214
[17] HUANG, Y. N. New development of Prof. Zhou's statistical theory of turbulence (in Chinese). Acta Scientiarum Naturalium, Universitatis Pekinensis, 34(2/3), 151-158(1998)
[18] HUANG, Y. N. and LUO, X. P. On orientation averages for vortex models of turbulence. Physics of Fluids, 11(8), 2381-2386(1999)
[19] SAFFMAN, P. G. and PULLIN, D. I. Calculation of velocity structure functions for vortex models of isotropic turbulence. Physics of Fluids, 8(11), 3072-3084(1996)
[20] HUANG, Y. N. and HU, X. The tensor denotation of Beltrami spherical vortices and their symmetry analysis. Applied Mathematics and Mechanics (English Edition), 23(1), 13-17(2002) https://doi.org/10.1007/BF02437725
[21] LEE, C. B. and LIAN, Q. X. The closed characteristics of the Reynolds equation. Acta Aeronautica et Astronautica Sinica, 14(5), 335-336(1993)
[22] YANG, K., XIA, Z. H., SHI, Y. P., and CHEN, S. Y. Effect of oscillation structures on inertialrange intermittence and topology in turbulent field. Communications in Computational Physics, 19(1), 251-272(2016)
[23] WANG, J. C., SHI, Y. P., WANG, L. P., XIAO, Z. L., HE, X. T., and CHEN, S. Y. Scaling and statistics in three-dimensional compressible turbulence. Physical Review Letters, 108(21), 214505(2012)
[24] WANG, J. C., YANG, Y. T., SHI, Y. P., XIAO, Z. L., HE, X. T., and CHEN, S. Y. Cascade of kinetic energy in three-dimensional compressible turbulence. Physical Review Letters, 110(21), 214505(2013)
[25] WU, T., GENG, C. H., YAO, Y. C., XU, C. X., and HE, G. W. Characteristics of space-time energy spectra in turbulent channel flows. Physical Review Fluids, 2(8), 084609(2017)
[26] HE, G. W., JIN, G. D., and YANG, Y. Space-time correlations and dynamic coupling in turbulent flows. Annual Review of Fluid Mechanics, 49, 51-70(2017)
[27] HE, G. W. and ZHANG, J. B. Elliptic model for space-time correlations in turbulent shear flows. Physical Review E, 73(5), 055303(2006)
[28] HE, G. W., JIN, G. D., and ZHAO, X. Scale-similarity model for Lagrangian velocity correlations in isotropic and stationary turbulence. Physical Review E, 80(6), 066313(2009)
[29] ZHAO, X. and HE, G. W. Space-time correlations of fluctuating velocities in turbulent shear flows. Physical Review E, 79(4), 046316(2009)
[30] HE, X. Z., HE, G. W., and TONG, P. Small-scale turbulent fluctuations beyond Taylor's frozenflow hypothesis. Physical Review E, 81(6), 065303(2010)
[31] GENG, C. H., HE, G. W., WANG, Y. S., XU, C. X., LOZANO-DURAN, A., and WALLACE, J. M. Taylor's hypothesis in turbulent channel flow considered using a transport equation analysis. Physics of Fluids, 27(2), 025111(2015)
[32] HE, G. W., RUBINSTEIN, R., and WANG, L. P. Effects of subgrid-scale modeling on time correlations in large eddy simulation. Physics of Fluids, 14(7), 2186-2193(2002)
[33] YANG, Y., HE, G. W., and WANG, L. P. Effects of subgrid-scale modeling on Lagrangian statistics in large-eddy simulation. Journal of Turbulence, 9, N8(2008)
[34] HE, G. W., WANG, M., and LELE, S. K. On the computation of space-time correlations by large-eddy simulation. Physics of Fluids, 16(11), 3859-3867(2004)
[35] GUO, L., LI, D., ZHANG, X., and HE, G. W. LES prediction of space-time correlations in turbulent shear flows. Acta Mechanica Sinica, 28(4), 993-998(2012)
[36] YAO, H. D. and HE, G. W. A kinematic subgrid scale model for large-eddy simulation of turbulence-generated sound. Journal of Turbulence, 10, N19(2009)
[37] JIN, G. D., HE, G. W., and WANG, L. P. Large-eddy simulation of turbulent collision of heavy particles in isotropic turbulence. Physics of Fluids, 22(5), 055106(2010)
[38] YANG, Y., PULLIN, D. I., and BERMEJO-MORENO, I. Multi-scale geometric analysis of Lagrangian structures in isotropic turbulence. Journal of Fluid Mechanics, 654, 233-270(2010)
[39] YANG, Y. and PULLIN, D. I. On Lagrangian and vortex-surface fields for flows with Taylor Green and Kida-Pelz initial conditions. Journal of Fluid Mechanics, 661, 446-481(2010)
[40] YANG, Y. and PULLIN, D. I. Evolution of vortex-surface fields in viscous Taylor-Green and Kida-Pelz flows. Journal of Fluid Mechanics, 685, 146-164(2011)
[41] ZHAO, Y. M., YANG, Y., and CHEN, S. Y. Vortex reconnection in the late transition in channel flow. Journal of Fluid Mechanics, 802, R4(2016)
[42] ZHAO, Y. M., YANG, Y., and CHEN, S. Y. Evolution of material surfaces in the temporal transition in channel flow. Journal of Fluid Mechanics, 793, 840-876(2016)
[43] YANG, Y. and PULLIN, D. I. Geometric study of Lagrangian and Eulerian structures in turbulent channel flow. Journal of Fluid Mechanics, 674, 67-92(2011)
[44] YANG, Y. and PULLIN, D. I. On Lagrangian and vortex-surface fields for flows with TaylorGreen and Kida-Pelz initial conditions. Journal of Fluid Mechanics, 661, 446-481(2010)
[45] YANG, Y. and PULLIN, D. I. Evolution of vortex-surface fields in viscous Taylor-Green and Kida-Pelz flows. Journal of Fluid Mechanics, 685, 146-164(2011)
[46] ZHAO, Y., YANG, Y., and CHEN, S. Evolution of material surfaces in the temporal transition in channel flow. Journal of Fluid Mechanics, 793, 840-876(2016)
[47] ZHAO, Y., XIONG, S., YANG, Y., and CHEN, S. Sinuous distortion of vortex surfaces in the lateral growth of turbulent spots. Physical Review Fluids, 3(7), 074701(2018)
[48] KOLMOGOROV, A. N. The local structure of turbulence in incompressible viscous fluid for very large Reynolds numbers. Mathematics and Its Applications (Soviet Series) (ed. TIKHOMIROV, V. M.), Vol. 25, Springer, Dordrecht (1991)
[49] KOLMOGOROV, A. N. Dissipation of energy in the locally isotropic turbulence. Proceedings:Mathematical and Physical Sciences, 434(1890), 15-17(1991)
[50] QIAN, J. Scaling exponents of the second-order structure function of turbulence. Journal of Physics A:Mathematical and General, 31(14), 3193-3204(1998)
[51] QIAN, J. Normal and anomalous scaling of turbulence. Physical Review E, 58(6), 7325(1998)
[52] QIAN, J. Closure approach to high-order structure functions of turbulence. Physical Review Letters, 84(4), 646-654(2000)
[53] MCCOMB, W. D. Homogeneous, Isotropic Turbulence:Phenomenology, Renormalization and Statistical Closures, Oxford University Press, Oxford (2014)
[54] SHE, Z. S., CHEN, X., and HUSSAIN, F. Quantifying wall turbulence via a symmetry approach:a lie group theory. Journal of Fluid Mechanics, 827, 322-356(2017)
[55] CHEN, X., HUSSAIN, F., and SHE, Z. S. Quantifying wall turbulence via a symmetry approach, part 2, Reynolds stresses. Journal of Fluid Mechanics, 850, 401-438(2018)
[56] CHEN, X. and SHE, Z. S. Analytic prediction for planar turbulent boundary layers. Science China Physics, Mechanics and Astronomy, 59, 114711(2016)
[57] SHE, Z. S., WU, Y., CHEN, X., and HUSSAIN, F. A multi-state description of roughness effects in turbulent pipe flow. New Journal of Physics, 14(9), 093054(2012)
[58] ZHANG, Y. S., BI, W. T., HUSSAIN, F., LI, X. L., and SHE, Z. S. Mach-number-invariant mean-velocity profile of compressible turbulent boundary layers. Physical Review Letters, 109(5), 054502(2012)
[59] WU, B., BI, W. T., HUSSAIN, F., and SHE, Z. S. On the invariant mean velocity profile for compressible turbulent boundary layers. Journal of Turbulence, 18(182), 186-202(2017)
[60] LUO, J. S., WANG, X. J., and ZHOU, H. Inherent mechanism of breakdown in laminar-turbulent transition of plane channel flows. Science in China Series G:Physics Mechanics and Astronomy, 48(2), 228-236(2005)
[61] TANG, H. T., LUO, J. S., and ZHOU, H. Mechanism of breakdown in laminar-turbulent transition of incompressible boundary layer on a flat plate. Transactions of Tianjin University, 13(2), 79-87(2007)
[62] HUANG, Z. F., WEI, C., and ZHOU, H. The mechanism of breakdown in laminar-turbulent transition of a supersonic boundary layer on a flat plate-temporal mode. Science in China, 48(5), 614-625(2005)
[63] CAO, W., HUANG, Z. F., and ZHOU, H. Study of the mechanism of breakdown in laminarturbulent transition of a supersonic boundary layer on a flat plate. Applied Mathematics and Mechanics (English Edition), 27(4), 425-434(2006) https://doi.org/10.1007/s10483-006-0401-1
[64] DONG, M. and ZHOU, H. A simulation on bypass transition and its key mechanism. Science China (Physics, Mechanics and Astronomy), 56(4), 775-784(2013)
[65] ZHANG, Y. M. and ZHOU, H. Numerical study of local boundary layer receptivity to freestream vortical disturbances. Applied Mathematics and Mechanics (English Edition), 26(5), 547-554(2005) https://doi.org/10.1007/BF02466327
[66] GAO, J., LUO, J. S., and WU, X. S. Receptivity of hypersonic boundary layer due to fast-slow acoustics interaction. Acta Mechanica Sinica, 31(6), 899-909(2015)
[67] REN, J. and FU, S. Study of the discrete spectrum in a Mach 4.5 Görtler flow. Flow Turbulence and Combustion, 94(2), 339-357(2015)
[68] JIANG, X. Y. and LEE, C. B. Review of research on the receptivity of hypersonic boundary layer. Journal of Experiments in Fluid Mechanics, 31(2), 1-11(2017)
[69] REN, J. and FU, S. Secondary instabilities of Görtler vortices in high-speed boundary layer flows. Journal of Fluid Mechanics, 781, 388-421(2015)
[70] REN, J., FU, S., and HANIFI, A. Stabilization of the hypersonic boundary layer by finiteamplitude streaks. Physics of Fluids, 28(2), 754-203(2016)
[71] SU, C. H. and ZHOU, H. Transition prediction for supersonic and hypersonic boundary layers on a cone with angle of attack. Science in China Series G:Physics, Mechanics and Astronomy, 52(8), 1223-1232(2009)
[72] SU, C. H. and ZHOU, H. Transition prediction of the supersonic boundary layer on a cone under the consideration of receptivity to slow acoustic waves. Science China Physics, Mechanics and Astronomy, 54(10), 1875-1882(2011)
[73] SU, C. H. The reliability of the improved eN method for the transition prediction of boundary layers on a flat plate. Science China Physics, Mechanics and Astronomy, 55(5), 837-843(2012)
[74] SU, C. H. Physical implication of two problems in transition prediction of boundary layers based on linear stability theory. Science China Physics, Mechanics and Astronomy, 57(5), 950-962(2014)
[75] LI, X., FU, D. X., and MA, Y. W. Direct numerical simulation of hypersonic boundary layer transition over a blunt cone. AIAA Journal, 46(11), 2899-2913(2008)
[76] LIANG, X., LI, X. L., FU, D. X., and MA, Y. W. Effects of wall temperature on boundary layer stability over a blunt cone at Mach 7.99. Computers and Fluids, 39(2), 359-371(2010)
[77] SU, C. H. and ZHOU, H. The variation of transition location in response to the variation of the amplitudes of initial disturbances. Science China Physics, Mechanics and Astronomy, 53(6), 1109-1115(2010)
[78] LIU, J. X. and LUO, J. S. Effect of disturbances at inlet on hypersonic boundary layer transition on a blunt cone at small angle of attack. Applied Mathematics and Mechanics (English Edition), 31(5), 535-544(2010) https://doi.org/10.1007/s10483-010-0501-z
[79] LI, J. and LUO, J. S. Applications of parabolized stability equation for predicting transition position in boundary layers. Applied Mathematics and Mechanics (English Edition), 33(6), 679-686(2012) https://doi.org/10.1007/s10483-012-1579-7
[80] ZHANG, Y. M. and ZHOU, H. PSE as applied to problems of transition in compressible boundary layers. Applied Mathematics and Mechanics (English Edition), 29(7), 833-840(2008) https://doi.org/10.1007/s10483-008-0701-8
[81] ZHANG, Y. M. and ZHOU, H. PSE as applied to problems of secondary instability in supersonic boundary layers. Applied Mathematics and Mechanics (English Edition), 29(1), 1-8(2008) https://doi.org/10.1007/s10483-008-0101-7
[82] ZHANG, Y. M. and SU, C. H. Self-consistent parabolized stability equation (PSE) method for compressible boundary layer. Applied Mathematics and Mechanics (English Edition), 36(7), 835-846(2015) https://doi.org/10.1007/s10483-015-1951-9
[83] YU, G. T., GAO, J., and LUO, J. S. Stability analysis method considering non-parallelism:EPSE method and its application. Applied Mathematics and Mechanics (English Edition), 37(1), 27-36(2016) https://doi.org/10.1007/s10483-016-2013-9
[84] GUO, L. L., TANG, D. B., and LIU, J. X. Evolution analysis of TS wave and high-order harmonic waves in boundary layers. Transactions of Nanjing University of Aeronautics & Astronautics, 23, 8-14(2006)
[85] TANG, D. B., MA, Q. R., and CHENG, G. W. Study of compressible nonparallel flow stability for boundary layers. Acta Aeronautica et Astronautica Sinica, 23(2), 166-169(2002)
[86] XIA, H., TANG, D. B., and LU, C. G. Nonparallel stability analysis of three dimensional disturbance wave in boundary layers. Acta Mechanica Sinica, 34(5), 688-695(2002)
[87] GUO, X., TANG, D. B., and SHEN, Q. Boundary layer stability with multiple modes in hypersonic flows. Modern Physics Letters B, 23, 321-324(2009)
[88] LIU, J. X., TANG, D. B., and YANG, Y. Z. On nonlinear-evolution of C-type instability in nonparallel boundary layers. Chinese Journal of Aeronautics, 20(4), 313-319(2007)
[89] TANG, D. B. Boundary Layer Transition, Science Press, Beijing (2015)
[90] LEE, C. B. and CHEN, S. Y. A review of recent progress in the study of transition in hypersonic boundary layer. National Science Review, nwy052(2018)
[91] ZHANG, C. H., TANG, Q., and LEE, C. B. Hypersonic boundary-layer transition on a flared cone. Acta Mechanica Sinica, 29(1), 48-54(2013)
[92] ZHANG, C. H. and LEE, C. B. Rayleigh-scattering visualization of the development of secondmode waves. Journal of Visualization, 20(1), 1-6(2016)
[93] ZHANG, C. H., ZHU, Y. D., CHEN, X., YUAN, H. J., WU, J. Z., CHEN, S. Y., LEE, C. B., and GAD-EL-HAK, M. Transition in hypersonic boundary layers. AIP Advances, 5(10), 107137(2015)
[94] ZHU, Y. D., ZHANG, C. H., CHEN, X., YUAN, H. J., WU, J. Z., CHEN, S. Y., LEE, C. B., and GAD-EL-HAK, M. Transition in hypersonic boundary layers:role of dilatational waves. AIAA Journal, 54, 3039-3049(2016)
[95] ZHU, Y. D., CHEN, X., WU, J. Z., CHEN, S. Y., LEE, C. B., and GAD-EL-HAK, M. Aerodynamic heating in transitional hypersonic boundary layers:role of second-mode instability. Physics of Fluids, 30(1), 011701(2018)
[96] ZHU, Y. D., LEE, C. B., and CHEN, X. Newly identified principle for aerodynamic heating in hypersonic flows. Journal of Fluid Mechanics, 855, 152-180(2018)
[97] SUN, B. H. and ORAN, E. S. New principle for aerodynamic heating. National Science Review, 5, 606-607(2018)
[98] CHEN, X., ZHU, Y. D., and LEE, C. B. Interactions between second mode and low-frequency waves in a hypersonic boundary layer. Journal of Fluid Mechanics, 820, 693-735(2017)
[99] LI, X. L., MA, Y. W., and FU, D. X. High efficient method for incompressible N-S equations and analysis of two-dimensional turbulent channel flow (in Chinese). Acta Mechanica Sinica, 33(5), 577-587(2001)
[100] LI, X. L., MA, Y. W., and FU, D. X. Scaling law in two-dimensional turbulent channel flow (in Chinese). Acta Mechanica Sinica, 34(4), 604-608(2002)
[101] LI, X. L., FU, D. X., and MA, Y. W. Direct numerical simulation of a spatially evolving supersonic turbulent boundary layer at Ma=6. Chinese Physics Letters, 23(6), 1519-1522(2006)
[102] LI, X. L., FU, D. X., and MA, Y. W. Assessment of the compressible turbulence model by using the DNS data (in Chinese). Chinese Journal of Theoretical and Applied Mechanics, 44, 222-229(2012)
[103] DENG, X. G. and ZHANG, H. X. Developing high-order weighted compact nonlinear schemes. Journal of Computational Physics, 165(1), 22-44(2000)
[104] MA, Y. W. and FU, D. X. Fourth order accurate compact scheme with group velocity control (GVC). Science in China Series A:Mathematics, 44(9), 1197-1204(2001)
[105] DONG, M., LUO, J. S., and CAO, W. Numerical investigation of the evolution of disturbances in supersonic sharp cone boundary layers. Applied Mathematics and Mechanics (English Edition), 27(6), 713-719(2006) https://doi.org/10.1007/s10483-006-0601-1
[106] DONG, M. and LUO, J. S. Mechanism of transition in a hypersonic sharp cone boundary layer with zero angle of attack. Applied Mathematics and Mechanics (English Edition), 28(8), 1019-1028(2007) https://doi.org/10.1007/s10483-007-0804-2
[107] DONG, M. and ZHOU, H. Inflow boundary condition for DNS of turbulent boundary layers on supersonic blunt cones. Applied Mathematics and Mechanics (English Edition), 29(8), 985-998(2008) https://doi.org/10.1007/s10483-008-0802-3
[108] DONG, M. and LUO, J. S. The influence of the turbulent statistical characteristics by cone effect in a supersonic boundary layer (in Chinese). Chinese Journal of Theoretical and Applied Mechanics, 40(3), 394-401(2008)
[109] DONG, M. Direct numerical simulation of a spatially evolving hypersonic blunt cone turbulent boundary layer at Mach 6(in Chinese). Acta Aerodynamica Sinica, 27(2), 199-205(2009)
[110] DONG, M. and ZHOU, H. Improvement of turbulent mode in the calculation of aerodynamic heat in hypersonic turbulent boundary layer (in Chinese). Scientia Sinica Physica, Mechanica and Astronomica, 40(2), 231-241(2010)
[111] LI, Q. B. and FU, S. High-order accurate gas-kinetic scheme and turbulence simulation (in Chinese). Scientia Sinica Physica, Mechanica and Astronomica, 44(3), 278-284(2014)
[112] LI, Q. B., TAN, S., FU, S., and XU, K. Numerical simulation of compressible turbulence with gas-kinetic BGK scheme. 13th Asian Congress of Fluid Mechanics, Dhaka, Bangladesh, 12-17(2010)
[113] TAN, S., LI, Q. B., FU, S., and ZENG, S. Engineering simulation of turbulence with gas-kinetic BGK scheme. AIP Conference Proceedings, 1376, 78-80(2011)
[114] FU, S. and LI, Q. B. Numerical simulation of compressible mixing layers. International Journal of Heat and Fluid Flow, 27(5), 895-901(2006)
[115] FU, S. and GUO, Y. Study of wall-parameter-free low-Reynolds-number nonlinear eddy-viscosity model (in Chinese). Acta Mechanica Sinica, 33(2), 145-152(2001)
[116] ZHANG, G. H. and FU, S. Second-moment closure modelling of the compressible homogeneous turbulent shear flow (in Chinese). Acta Mechanica Sinica, 32(2), 141-150(2000)
[117] KRAICHNAN, R. H. and CHEN, S. Y. Is there a statistical mechanics of turbulence? Physica D:Nonlinear Phenomena, 37(1-3), 160-172(1989)
[118] MENEVEAU, C. Statistics of turbulence subgrid-scale stresses:necessary conditions and experimental tests. Physics of Fluids, 6(2), 815-833(1994)
[119] SHI, Y. P., XIAO, Z. L., and CHEN, S. Y. Constrained subgrid-scale stress model for large eddy simulation. Physics of Fluids, 20(1), 011701(2008)
[120] MENEVEAU, C. Germano identity-based subgrid-scale modeling:a brief survey of variations on a fertile theme. Physics of Fluids, 24(12), 121301(2012)
[121] CHEN, S. Y., XIA, Z. H., PEI, S. Y., WANG, J. C., YANG, Y. T., XIAO, Z. L., and SHI, Y. P. Reynolds-stress-constrained large-eddy simulation of wall-bounded turbulent flows. Journal of Fluid Mechanics, 703, 1-28(2012)
[122] CHEN, S. Y., CHEN, Y. C., XIA, Z. H., QU, K., SHI, Y. P., XIAO, Z. L., LIU, Q. H., CAI, Q. D., LIU, F., LEE, C. B., ZHANG, R. K., and CAI, J. S. Constrained large-eddy simulation and detached eddy simulation of flow past a commercial aircraft at 14 degrees angle of attack. Science China Physics, Mechanics and Astronomy, 56(2), 270-276(2013)
[123] CHEN, S. Y., WANG, M. R., and XIA, Z. H. Multiscale fluid mechanics and modeling. Procedia IUTAM, 10, 100-114(2014)
[124] LI, J. C. and XIE, Z. T. Large-eddy simulation for canopy turbulent flow (in Chinese). Acta Mechanica Sinica, 31(4), 406-415(1999)
[125] LI, J. C. Large eddy simulation of complex turbulent flows:physical aspects and research trends. Acta Mechanica Sinica, 17(4), 289-301(2001)
[126] CUI, G. X., SHI, R. F., WANG, Z. S., XU, C. X., and ZHANG, Z. S. Large eddy simulation of city micro-atmospheric environment. Science in China Series G:Physics, Mechanics and Astronomy, 51(8), 933-944(2008)
[127] CUI, G. X., XU, C. X., FANG, L., SHAO, L., and ZHANG, Z. S. A new subgrid eddy-viscosity model for large-eddy simulation of anisotropic turbulence. Journal of Fluid Mechanics, 582, 377-397(2007)
[128] LU, X. Y. and DALTON, C. Calculation of the timing of vortex formation from an oscillating cylinder. Journal of Fluids and Structures, 10(5), 527-541(1996)
[129] LU, X. Y. and SATO, J. A numerical study of flow past a rotationally oscillating circular cylinder. Journal of Fluids and Structures, 10(8), 829-849(1996)
[130] LU, X. Y., DALTON, C., and ZHANG, J. F. Application of large eddy simulation to an oscillating flow past a circular cylinder. Journal of Fluids Engineering, 119(3), 519-525(1997)
[131] ZHOU, Y. and ANTONIA, R. A. A study of turbulent vortices in the near wake of a cylinder. Journal of Fluid Mechanics, 253, 643-661(1993)
[132] ZHOU, Y. and ANTONIA, R. A. Critical points in a turbulent near wake. Journal of Fluid Mechanics, 275, 59-81(1994)
[133] ZHANG, H. J., ZHOU, Y., and ANTONIA, R. A. Longitudinal and spanwise vortical structures in a turbulent near wake. Physics of Fluids, 12(11), 2954-2964(2000)
[134] RINOSHIKA, A. and ZHOU, Y. Orthogonal wavelet multi-resolution analysis of a turbulent cylinder wake. Journal of Fluid Mechanics, 524, 229-248(2005)
[135] WANG, H. F., ZHOU, Y., CHAN, C. K., and LAM, K. S. Effect of initial conditions on interaction between a boundary layer and a wall-mounted finite-length-cylinder wake. Physics of Fluids, 18(6), 065106(2006)
[136] XU, S. J., ZHOU, Y., and WANG, M. H. A symmetric binary-vortex street behind a longitudinally oscillating cylinder. Journal of Fluid Mechanics, 556, 27-43(2006)
[137] ALAM, M. D. M. and ZHOU, Y. Turbulent wake of an inclined cylinder with water running. Journal of Fluid Mechanics, 589, 261-303(2007)
[138] HU, J. C. and ZHOU, Y. Flow structure behind two staggered circular cylinders, part 2, heat and momentum transport. Journal of Fluid Mechanics, 607, 81-107(2008)
[139] HU, J. C. and ZHOU, Y. Flow structure behind two staggered circular cylinders, part 1, downstream evolution and classification. Journal of Fluid Mechanics, 607, 51-80(2008)
[140] ZHOU, T., WANG, H., RAZALI, S. M., ZHOU, Y., and CHENG, L. Three-dimensional vorticity measurements in the wake of a yawed circular cylinder. Physics of Fluids, 22(1), 015108(2010)
[141] BAI, Y., JIA, Y. X., LEE, C. B., and ZHU, Y. D. Experimental study of a periodical flapping flag. Acta Physica Sinica, 65(12), 178-184(2016)
[142] ZHANG, M. M., CHENG, L., and ZHOU, Y. Closed-loop-controlled vortex shedding and vibration of a flexibly supported square cylinder under different schemes. Physics of Fluids, 16(5), 1439-1448(2004)
[143] WANG, H. F. and ZHOU, Y. The finite-length square cylinder near wake. Journal of Fluid Mechanics, 638, 453-490(2009)
[144] ALAM, M. M., ZHOU, Y., and WANG, X. W. The wake of two side-by-side square cylinders. Journal of Fluid Mechanics, 669, 432-471(2011)
[145] XIA, Z. H., SHI, Y. P., CAI, Q. D., and GAI, J. Dissipation function in turbulent plane Poiseuille and Couette flows subject to spanwise rotations. Applied Mathematics and Mechanics (English Edition), 40(2), 185-192(2019) https://doi.org/10.1007/s10483-019-2422-6
[146] DONG, G. J. and LU, X. Y. Characteristics of flow over traveling wavy foils in a side-by-side arrangement. Physics of Fluids, 19(5), 057107(2007)
[147] LU, X. Y. and LIAO, Q. Dynamic responses of a two-dimensional flapping foil motion. Physics of Fluids, 18(9), 098104(2006)
[148] LU, X. Y. and YIN, X. Z. Propulsive performance of a fish-like travelling wavy wall. Acta Mechanica, 175(1-4), 197-215(2005)
[149] LEE, C. B. and WU, J. Z. Transition in wall-bounded flows. Applied Mechanics Reviews, 61(3), 030802(2008)
[150] LEE, C. B. New features of CS solitons and the formation of vortices. Physics Letters A, 247(6), 397-402(1998)
[151] LEE, C. B. and WANG, S. Study of the shock motion in a hypersonic shock system/turbulent boundary layer interaction. Experiments in Fluids, 19(3), 143-149(1995)
[152] LEE, C. B., HONG, Z. X., KACHANOV, Y. S., BORODULIN, V., and GAPONENKO, V. A study in transitional flat plate boundary layers:measurement and visualization. Experiments in Fluids, 28(3), 243-251(2000)
[153] LEE, C. B. Possible universal transitional scenario in a at plate boundary layer:measurement and visualization. Physical Review E, 62(3), 3659-3670(2000)
[154] HAMA, F. R. and NUTANT, J. Detailed flow-field observations in the transition process in a thick boundary layer. Procecdings of 1963 Heat Transfer and Fluid Mechanics, Stanford University Press, Stanford (1963)
[155] LEE, C. B. CS-soliton:its feature and importance (in Chinese). Experiments and Measurements in Fluid Mechanics, 17(3), 57-60(2003)
[156] LEE, C. B. and LI, R. Q. Dominant structure for turbulent production in a transitional boundary layer. Journal of Turbulence, 8, N55(2007)
[157] LEE, C. B. On the formation of the streamwise vortex in a transitional boundary layer. Acta Physica Sinica, 50(1), 182-184(2001)
[158] ZHAO, Y. M., YANG, Y., and CHEN, S. Y. Evolution of material surfaces in the temporal transition in channel flow. Journal of Fluid Mechanics, 793, 840-876(2016)
[159] LIAN, Q. X. A visual study of the coherent structure of the turbulent boundary layer in flow with adverse pressure gradient. Journal of Fluid Mechanics, 215, 101-124(1990)
[160] LIAN, Q. X. A kind of fast changing coherent structure in a turbulent boundary layer. Acta Mechanica Sinica, 15(3), 193-200(1999)
[161] GUO, H., LIAN, Q. X., LI, Y., and WANG, H. W. A visual study on complex flow structures and flow breakdown in a boundary layer transition. Experiments in Fluids, 37(3), 311-322(2004)
[162] GUO, H., LI, X. H., WANG, H. W., and FENG, Y. L. Experimental study on boundary-layer transition control by spanwise discrete suction. Journal of Experiments in Fluid Mechanics, 28(6), 13-19(2014)
[163] GONG, A. L., LI, R. Q., and LEE, C. B. On the generation of low-frequency signals in a transitional boundary layer. Acta Physica Sinica, 51(5), 1068-1074(2002)
[164] MENG, Q. G., LI, R. Q., and LEE, C. B. A link between the turbulent cascade and the dynamics of transition. Acta Physica Sinica, 53(8), 2621-2624(2004)
[165] MENG, Q. G., CAI, Q. D., and LEE, C. B. Limitation for the energy spectrum analysis for the understanding of the turbulent cascade. Acta Physica Sinica, 53(9), 3090-3093(2004)
[166] LI, R. Q. and LEE, C. B. A link between chaos dynamics and the onset of turbulence in a transitional boundary layer. Acta Physica Sinica, 51(8), 1743-1749(2002)
[167] LI, R. Q. and LEE, C. B. Problems in the paper "a link between chaos dynamics and the onset of turbulence in a transitional boundary layer". Acta Physica Sinica, 54(1), 1743-1749(2005)
[168] GAO, Q., ORTIZ-DUENAS, C., and LONGMIRE, E. Circulation signature of vortical structures in turbulent boundary layers. 16th Australasian Fluid Mechanics Conference (AFMC), The University of Queensland, Brisbane, 135-141(2007)
[169] GAO, Q., ORTIZ-DUENAS, C., and LONGMIRE, E. Analysis of vortex populations in turbulent wall-bounded flows. Journal of Fluid Mechanics, 678, 87-123(2011)
[170] GAO, Q., ORTIZ-DUENAS, C., and LONGMIRE, E. Evolution of coherent structures in turbulent boundary layers based on moving tomographic PIV. Experiments in Fluids, 54(12), 1625(2013)
[171] WANG, J. J., ZHANG, C., and PAN, C. Effects of roughness elements on bypass transition induced by a circular cylinder wake. Journal of Visualization, 14(1), 53-61(2011)
[172] ZHANG, C., PAN, C., and WANG, J. J. Evolution of vortex structure in boundary layer transition induced by roughness elements. Experiments in Fluids, 51(5), 1343-1352(2011)
[173] HE, G. S., WANG, J. J., and PAN, C. Initial growth of a disturbance in a boundary layer influenced by a circular cylinder wake. Journal of Fluid Mechanics, 718, 116-130(2013)
[174] PAN, C., WANG, J. J., and HE, G. S. Experimental investigation of wake-induced bypass transition control by surface roughness. Chinese Physics Letters, 29(10), 104704(2012)
[175] PAN, C., WANG, J. J., and ZHANG, C. Identification of Lagrangian coherent structures in the turbulent boundary layer. Science in China Series G:Physics, Mechanics and Astronomy, 52(2), 248-257(2009)
[176] PAN, C., WANG, J. J., ZHANG, P. F., and FENG, L. H. Coherent structures in bypass transition induced by a cylinder wake. Journal of Fluid Mechanics, 603, 367-389(2008)
[177] HE, G. S., PAN, C., FENG, L. H., GAO, Q., and WANG, J. J. Evolution of Lagrangian coherent structures in a cylinder-wake disturbed at plate boundary layer. Journal of Fluid Mechanics, 792, 274-306(2016)
[178] FENG, L. H., WANG, J. J., and PAN, C. Proper orthogonal decomposition analysis of vortex dynamics of a circular cylinder under synthetic jet control. Physics of Fluids, 23(1), 014106(2011)
[179] WANG, J. J., PAN, C., and ZHANG, P. F. On the instability and reproduction mechanism of a laminar streak. Journal of Turbulence, 10, N26(2009)
[180] ZHANG, Z., SUN, Z. L., and YAN, D. C. Experimental research on the mechanism of reverse transition in turbulent boundary layer. Acta Scientiarum Naturalium-Universitatis Pekinensis, 42(3), 305-309(2006)
[181] FAN, Q. L., WANG, L. T., ZHANG, H. Q., GUO, Y. C., and LIN, W. Y. Coherent structures in turbulent round jets. Advances in Mechanics, 32, 109-118(2002)
[182] FAN, Q. L., ZHANG, H. Q., GUO, Y. C., and WANG, X. L. Particle-vortex interactions in turbulent shear flows. Advances in Mechanics, 31, 611-620(2001)
[183] WANG, J. J. and XIA, K. Q. Advances in experimental investigation of Rayleigh-Benard turbulent convection. Advances in Mechanics, 29, 557-566(1999)
[184] WANG, S. F., JIANG, F., NIU, Z. N., and WU, Z. Z. An experimental study on turbulent coherent structures near a sheared air-water interface. Acta Mechanica Sinica, 15(4), 289-298(1999)
[185] ZHONG, H. J., CHEN, S. Y., and LEE, C. B. Experimental study of freely falling thin disks:transition from planar zigzag to spiral. Physics of Fluids, 23(1), 011702(2011)
[186] LEE, C. B., SU, Z., ZHONG, H., CHEN, S., ZHOU, M., and WU, J. Experimental investigation of freely falling thin disks, part 2, transition of three-dimensional motion from zigzag to spiral. Journal of Fluid Mechanics, 732, 77-104(2013)
[187] JIA, L. C., ZHU, Y. D., JIA, Y. X., YUAN, H. J., and LEE, C. B. Image pre-processing method for near-wall PIV measurements over moving curved interfaces. Measurement Science and Technology, 28(3), 035201(2017)
[188] JIA, L. C., ZOU, T. D., ZHU, Y. D., and LEE, C. B. Rotor boundary layer development with inlet guide vane (IGV) wake impingement. Physics of Fluids, 30(4), 040911(2018)
[189] LI, C. and ZHANG, Y. C. Effect of glow discharge on hypersonic flat plate boundary layer. Applied Mathematics and Mechanics (English Edition), 40(2), 249-260(2019) https://doi.org/10.1007/s10483-019-2424-9
[190] ZHANG, Y. C. and LI, C. Transition control of Mach 6.5 hypersonic flat plate boundary layer. Applied Mathematics and Mechanics (English Edition), 40(2), 283-292(2019) https://doi.org/10.1007/s10483-019-2423-8
[191] ZHU, Y. D., YUAN, H. J., ZHANG, C. H., and LEE, C. B. Image-preprocessing method for nearwall particle image velocimetry (PIV) image interrogation with very large in-plane displacement. Measurement Science and Technology, 24(12), 125302(2013)
[192] ZHU, Y. D. Experimental and numerical study of flow structures of the second-mode instability. Applied Mathematics and Mechanics (English Edition), 40(2), 273-282(2019) https://doi.org/10.1007/s10483-019-2430-9
[193] YI, S. H., TIAN, L. F., ZHAO, Y. X., and HE, L. The new advance of the experimental research on compressible turbulence based on the NPLS technique. Advances in Mechanics, 41, 379-390(2011)
[194] HUANG, N. and ZHENG, X. J. A laboratory test of the electrification phenomenon in windblown sand flux. Chinese Science Bulletin, 46(5), 417-420(2001)
[195] ZHENG, X. J., HUANG, N., and ZHOU, Y. H. Laboratory measurement of electrification of wind-blown sands and simulation of its effect on sand saltation movement. Journal of Geophysical Research:Atmospheres, 108(D10), 4322(2003)
[196] ZHENG, X. J., ZHANG, R., and HUANG, H. J. Theoretical modeling of relative humidity on contact electrification of sand particles. Scientific Reports, 4, 4399(2014)
[197] ZHENG, X. J. and WANG, P. Numerical simulation on stochastic movement of sands in windblown sand. Journal of Desert Research, 26(2), 184-188(2006)
[198] BO, T. L. and ZHENG, X. J. Numerical simulation of the evolution and propagation of aeolian dune fields toward a desert-oasis zone. Geomorphology, 180, 24-32(2013)
[199] CHEN, X. R., DENG, X. Y., WANG, Y. K., LIU, P. Q., and GU, Z. F. Influence of nose perturbations on behaviors of asymmetric vortices over slender body. Acta Mechanica Sinica, 18(6), 581-593(2002)