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The velocity time series of round air jets are acquired with the hot-wire anemometer. We compute the largest Lyapunov exponent and the turbulent incoherent perturbation of the velocity signals at 939 ≤ Re ≤ 3758 using an analytical method of chaotic time series which is based on the invariant of the largest Lyapunov exponent. The results show that the largest Lyapunov exponent increases with exit Reynolds number, and decreases with the distance away from nozzle exit. The reciprocal of the largest Lyapunov exponent is positively correlated with correlation time. The incoherent perturbation of turbulence increases either with exit Reynolds number or with the distance away from nozzle exit. The incoherent perturbation of turbulence is negatively correlated with Kolmogorov scale.
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Keywords:
- turbulent jets /
- chaos /
- the largest Lyapunov exponent /
- incoherent perturbation
[1] Brandstater A, Swift J, Swinney H L, Wolf A 1983 Phys. Rev. Lett. 51 1442
[2] Finn J M, del-Castillo-Negrete D 2001 Chaos 11 816
[3] Zhang J, Liu N S, Lu X Y 2009 Phys. Rev. E 79 045306
[4] Qian J 1993 J. China Univ. Sci. Technol. 23 91 (in Chinese) [钱俭 1993 中国科学技术大学学报 23 91]
[5] Xiao N, Jin N D 2007 Acta Phys. Sin. 56 5149 (in Chinese) [肖楠, 金宁德 2007 56 5149]
[6] McMackin L, Voelz D G, Fender J S 1995 Proc. SPIE Int. Soc. Opt. Eng. 2580 183
[7] Zhou H L, Lu Z M, Ren X T, Xie X L 1999 Acta Mech. Sin. 31 603 (in Chinese) [周慧良, 卢志明, 任逍涛, 谢锡麟 1999 力学学报 31 603]
[8] Zhang F, Liu H, Xu J, Tang C 2012 Appl. Mech. Mater. 121 3919
[9] Zhang Z S, Cui G X, Xu C X 2005 Theory and Modeling of Turbulence (Beijing: Tsinghua University Press) p130 (in Chinese) [张兆顺, 崔桂香, 许春晓 2005 湍流理论与模拟 (北京: 清华大学出版社) 第130页]
[10] Hussain A K M F 1986 J. Fluid Mech. 173 303
[11] Liu H F, Zhao Y Y, Dai Z H, Gong X, Yu Z H 2001 Acta Phys. Sin. 50 2311 (in Chinese) [刘海峰, 赵艳艳, 代正华, 龚欣, 于遵宏 2001 50 2311]
[12] Liu H F, Dai Z H, Li W F, Gong X, Yu Z H 2005 Phys. Lett. A 341 119
[13] Jayawardena A W, Xu P, Li W K 2008 Chaos 18 023115
[14] Moriya N 2010 Nucl. Instrum. Methods Phys. Res. A 618 306
[15] Yao T L, Liu H F, Xu J L, Li W F 2012 Acta Phys. Sin. 61 060603 (in Chinese) [姚天亮, 刘海峰, 许建良, 李伟锋 2012 61 060603]
[16] Takens F 1981 Dynamical System and Turbulence, Lecture Notes in Mathematics (Berlin: Springer-Verlag) p366
[17] Rosenstein M T, Collins J J, de Luca C J 1993 Physica D 65 117
[18] Liu B Z, Peng J H 2005 Nonlinear Dynamics (Beijing: Higher Education Press) p399 (in Chinese) [刘秉正, 彭建华 2005 非线性动力学 (北京: 高等教育出版社) 第399页]
[19] Yang J Q, Liu B Z, Peng J H, Ma Z J 1999 Space Med. Med. Eng. 12 185 (in Chinese) [杨健群, 刘秉正, 彭建华, 马治家 1999 航天医学与医学工程 12 185]
[20] Liu C, Zhou W X, Yuan W K 2010 Physica A 389 2675
[21] Crow S C, Champagne F H 1971 J. Fluid Mech. 48 547
[22] Liepmann D, Gharib M 1992 J. Fluid Mech. 245 643
[23] Lü J H, Lu J A, Chen S H 2002 Chaotic Time Series Analysis and Applications (Wuhan: Wuhan University Press) p31 (in Chinese) [吕金虎, 陆君安, 陈士华 2002 混沌时间序列分析及其应用 (武汉: 武汉大学出版社) 第31页]
[24] Pope S B 2000 Turbulent Flows (Cambridge: Cambridge University Press) p184
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[1] Brandstater A, Swift J, Swinney H L, Wolf A 1983 Phys. Rev. Lett. 51 1442
[2] Finn J M, del-Castillo-Negrete D 2001 Chaos 11 816
[3] Zhang J, Liu N S, Lu X Y 2009 Phys. Rev. E 79 045306
[4] Qian J 1993 J. China Univ. Sci. Technol. 23 91 (in Chinese) [钱俭 1993 中国科学技术大学学报 23 91]
[5] Xiao N, Jin N D 2007 Acta Phys. Sin. 56 5149 (in Chinese) [肖楠, 金宁德 2007 56 5149]
[6] McMackin L, Voelz D G, Fender J S 1995 Proc. SPIE Int. Soc. Opt. Eng. 2580 183
[7] Zhou H L, Lu Z M, Ren X T, Xie X L 1999 Acta Mech. Sin. 31 603 (in Chinese) [周慧良, 卢志明, 任逍涛, 谢锡麟 1999 力学学报 31 603]
[8] Zhang F, Liu H, Xu J, Tang C 2012 Appl. Mech. Mater. 121 3919
[9] Zhang Z S, Cui G X, Xu C X 2005 Theory and Modeling of Turbulence (Beijing: Tsinghua University Press) p130 (in Chinese) [张兆顺, 崔桂香, 许春晓 2005 湍流理论与模拟 (北京: 清华大学出版社) 第130页]
[10] Hussain A K M F 1986 J. Fluid Mech. 173 303
[11] Liu H F, Zhao Y Y, Dai Z H, Gong X, Yu Z H 2001 Acta Phys. Sin. 50 2311 (in Chinese) [刘海峰, 赵艳艳, 代正华, 龚欣, 于遵宏 2001 50 2311]
[12] Liu H F, Dai Z H, Li W F, Gong X, Yu Z H 2005 Phys. Lett. A 341 119
[13] Jayawardena A W, Xu P, Li W K 2008 Chaos 18 023115
[14] Moriya N 2010 Nucl. Instrum. Methods Phys. Res. A 618 306
[15] Yao T L, Liu H F, Xu J L, Li W F 2012 Acta Phys. Sin. 61 060603 (in Chinese) [姚天亮, 刘海峰, 许建良, 李伟锋 2012 61 060603]
[16] Takens F 1981 Dynamical System and Turbulence, Lecture Notes in Mathematics (Berlin: Springer-Verlag) p366
[17] Rosenstein M T, Collins J J, de Luca C J 1993 Physica D 65 117
[18] Liu B Z, Peng J H 2005 Nonlinear Dynamics (Beijing: Higher Education Press) p399 (in Chinese) [刘秉正, 彭建华 2005 非线性动力学 (北京: 高等教育出版社) 第399页]
[19] Yang J Q, Liu B Z, Peng J H, Ma Z J 1999 Space Med. Med. Eng. 12 185 (in Chinese) [杨健群, 刘秉正, 彭建华, 马治家 1999 航天医学与医学工程 12 185]
[20] Liu C, Zhou W X, Yuan W K 2010 Physica A 389 2675
[21] Crow S C, Champagne F H 1971 J. Fluid Mech. 48 547
[22] Liepmann D, Gharib M 1992 J. Fluid Mech. 245 643
[23] Lü J H, Lu J A, Chen S H 2002 Chaotic Time Series Analysis and Applications (Wuhan: Wuhan University Press) p31 (in Chinese) [吕金虎, 陆君安, 陈士华 2002 混沌时间序列分析及其应用 (武汉: 武汉大学出版社) 第31页]
[24] Pope S B 2000 Turbulent Flows (Cambridge: Cambridge University Press) p184
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