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分析了含有外尺度的Von-Karman湍流空间相关函数模型, 并利用光纤湍流空间传感阵列的实测数据, 根据拟合算法获得了大气光学湍流空间外尺度的值及日变化, 对模型的适用性进行了实验验证. 将空间相关函数理论与空间多点同步测量的数据相结合, 尽可能清晰地展现了几种适合用相关函数描述的湍涡尺度. 结果表明, 在1.8 m的草地上, 大气光学湍流的外尺度呈现出白天较大、夜间较小的日变化趋势, 正午前后均值约为0.44 m, 夜间约为0.3 m. 有三点需要说明: 其一, 当两点间距恰好等于外尺度时, 其空间相关系数为0.26, 当两点间距超过外尺度之后, 仍具有一定的相关性; 其二, 积分尺度代表了湍涡尺度的平均值, 该值略小于外尺度; 其三, 湍涡的最大尺度所对应的湍流空间相关性为0, 其值略大于外尺度. 不难发现: 湍涡三种尺度的日变化与湍流强度的日变化趋势非常相似. 以空间布点探测的方法获取湍流特征尺度, 结果直观, 而且能够直接验证湍流空间相关函数模型, 所以可在一定程度上促进湍流空间结构特性的研究.In this article, the Von-Karman model of turbulence spatial correlation function which contains the parameter of outer scale is analyzed. Then, the experimental data of air refractive index variation obtained from a high quality fiber optical turbulence sensing array are used to evaluate the outer scale of atmospheric optical turbulence as well as its diurnal variation through the algorithm of nonlinear fitting. The results validate the suitability of the Von-Karman model. By combining the theory of correlation function with the spatially distributed and simultaneously measured data, three kinds of turbulence spatial scales described by correlation function are revealed as clearly as possible. Results show that the values of outer scale in atmospheric optical turbulence 1.8 m above the grassland tend to be larger in the daytime and smaller in the night. The mean value around noon is 0.44 m, while in the night it becomes 0.3 m. Here, three of the important views should be noted. Firstly, when the displacement of two points is just equal to the outer scale, their correlation coefficient is 0.26, and when it exceeds the outer scale, there is still a certain value of correlation coefficient. Secondly, the integral scale represents the averaged value of scale in the vortex of optical turbulence. And, it is slightly smaller than the outer scale. Thirdly, when the distance of two points equals the biggest scale of vortex in optical turbulence, the correlation coefficient tends to zero, and the value of biggest scale is slightly bigger than the outer scale. It is easy to find that the diurnal variation tendencies of the three spatial scales are similar to that of intensity in optical turbulence. The method of obtaining the characteristic scales by spatially arranged and simultaneously measured optical turbulence is direct, and the results can be considered as the evidence to prove the models of correlation function including the Von-Karman model. So, it promotes the research on the property of spatial structure to a certain extent.
[1] Arkadi Z, Ephim G, Norman S K 2010 Opt. Commun. 283 1229
[2] Lukin V P, Nosov V V, Torgaev A V 2014 Appl. Opt. 53 B196
[3] Yi X, Liu Z J, Yue P 2012 Opt. Express 20 4232
[4] Lutomirski R F, Yura H T 1971 Appl. Opt. 10 1652
[5] Lukin V P 2005 Proc. SPIE 5981 598101
[6] Taylor G I 1938 Proc. R. Soc. A 164 476
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[8] Kulikov V A, Andreeva M S, Koryabin A V, Shmalhausen V I 2012 Appl. Opt. 51 8505
[9] Obukhov A M 1971 Boundary-Layer Meteorol. 2 7
[10] Coulman C E, Vernin J, Coqueugniot Y, Caccia J L 1988 Appl. Opt. 27 155
[11] Frank D E 1998 Radio Sci. 33 895
[12] Wang Q, Mei H P, Qian X M, Rao R Z 2015 Acta Phys. Sin. 64 114212 (in Chinese) [王倩, 梅海平, 钱仙妹, 饶瑞中 2015 物理学报 64 114212]
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[14] Mei H P 2007 Ph. D. Dissertation (Hefei: Hefei Institutes of Physical Science, Chinese Academy of Sciences) (in Chinese) [梅海平 2007 博士学位论文(合肥: 中国科学院合肥物质科学研究院)]
[15] Xiao S M 2014 Ph. D. Dissertation (Hefei: Hefei Institutes of Physical Science, Chinese Academy of Sciences) (in Chinese) [肖树妹 2014 博士学位论文(合肥: 中国科学院合肥物质科学研究院)]
[16] Rao R Z 2012 Modern Atmospheric Optics (Beijing: Science Press) pp155-159 (in Chinese) [饶瑞中 2012 现代大气光学(北京: 科学出版社)第155159页]
[17] Tian Y J, Yang Q S, Yang N, Li B, Chen B, Yang J B 2013 J. Vib. Eng. 26 90 (in Chinese) [田玉基, 杨庆山, 杨娜, 李波, 陈波, 杨靖波 2013 振动工程学报 26 90]
[18] Consortini A, Ronchi L 1972 Appl. Opt. 11 1205
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[1] Arkadi Z, Ephim G, Norman S K 2010 Opt. Commun. 283 1229
[2] Lukin V P, Nosov V V, Torgaev A V 2014 Appl. Opt. 53 B196
[3] Yi X, Liu Z J, Yue P 2012 Opt. Express 20 4232
[4] Lutomirski R F, Yura H T 1971 Appl. Opt. 10 1652
[5] Lukin V P 2005 Proc. SPIE 5981 598101
[6] Taylor G I 1938 Proc. R. Soc. A 164 476
[7] Liu S D, Liang F M, Liu S K, Xin G J 2008 Atmospheric Turbulence (Beijing: Peking University Press) p47 (in Chinese) [刘式达, 梁福明, 刘式适, 辛国君 2008 大气湍流 (北京: 北京大学出版社) 第47页]
[8] Kulikov V A, Andreeva M S, Koryabin A V, Shmalhausen V I 2012 Appl. Opt. 51 8505
[9] Obukhov A M 1971 Boundary-Layer Meteorol. 2 7
[10] Coulman C E, Vernin J, Coqueugniot Y, Caccia J L 1988 Appl. Opt. 27 155
[11] Frank D E 1998 Radio Sci. 33 895
[12] Wang Q, Mei H P, Qian X M, Rao R Z 2015 Acta Phys. Sin. 64 114212 (in Chinese) [王倩, 梅海平, 钱仙妹, 饶瑞中 2015 物理学报 64 114212]
[13] Tatarskii V I (translated by Silverman R A) 1961 Wave Propagation in a Turbulent Medium (New York: McGraw-Hill Book company) pp7, 8
[14] Mei H P 2007 Ph. D. Dissertation (Hefei: Hefei Institutes of Physical Science, Chinese Academy of Sciences) (in Chinese) [梅海平 2007 博士学位论文(合肥: 中国科学院合肥物质科学研究院)]
[15] Xiao S M 2014 Ph. D. Dissertation (Hefei: Hefei Institutes of Physical Science, Chinese Academy of Sciences) (in Chinese) [肖树妹 2014 博士学位论文(合肥: 中国科学院合肥物质科学研究院)]
[16] Rao R Z 2012 Modern Atmospheric Optics (Beijing: Science Press) pp155-159 (in Chinese) [饶瑞中 2012 现代大气光学(北京: 科学出版社)第155159页]
[17] Tian Y J, Yang Q S, Yang N, Li B, Chen B, Yang J B 2013 J. Vib. Eng. 26 90 (in Chinese) [田玉基, 杨庆山, 杨娜, 李波, 陈波, 杨靖波 2013 振动工程学报 26 90]
[18] Consortini A, Ronchi L 1972 Appl. Opt. 11 1205
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