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In 2000, Nikishov et al. presented an analytical model for the power spectrum of oceanic turbulence, in which the stable stratification of seawater is assumed, i.e., the eddy diffusivity of temperature is equal to that of salinity, and the eddy diffusivity ratio is equal to unity. Until now, all previous studies on the light propagation through oceanic turbulence were based on the Nikishov's power spectrum model. However, the eddy diffusivity of temperature and eddy diffusivity of salt are different from each other in most of underwater environments. Very recently, Elamassie et al. established a more reasonable power spectrum model of underwater turbulent fluctuations as an explicit function of eddy diffusivity ratio. The characteristic parameters such as the spatial coherence length of optical wave in turbulent medium play an important role in characterizing the strength of turbulence, the phase correction techniques in light propagation, etc. In the present paper, based on the Elamassie's power spectrum model of oceanic turbulence, the analytical formulae of the wave structure function, the spatial coherence length of optical wave and the Fried parameter in oceanic turbulence are derived, and the correctness of each of these formulae is verified. It is shown numerically that the results obtained by using the Elamassie's power spectrum model are quite different from those obtained by using the Nikishov's power spectrum model. If the Nikishov's power spectrum model is adopted, the strength of turbulence is underestimated when oceanic turbulence is dominated by the temperature fluctuations, while the strength of turbulence is overestimated when oceanic turbulence is dominated by the salinity fluctuations. If the Elamassie's power spectrum model is adopted, it is shown that the Kolmogorov five-thirds power law of the wave structure function is also valid for oceanic turbulence in the inertial range, and 2.1 times the spatial coherence length of optical wave is the Fried parameter, which are in agreement with those in atmospheric turbulence. In addition, based on the Elamassie's power spectrum model, the semi-analytical formula of the short-term beam spreading of Gaussian beams is derived in this paper, and its correctness is also verified. It is shown that the difference in short-term beam spreading is very large, whether the stable stratification of seawater is assumed or not. The results obtained in this paper are very useful for applications in optical communication, imaging and sensing systems involving turbulent underwater channels.
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Keywords:
- oceanic turbulence /
- wave structure function /
- spatial coherence length and Fried parameter /
- short-term beam spreading
[1] Andrews L C, Phillips R L 2012 Appl. Phys. 51 2678
[2] Rao R Z 2012 Modern Atmospheric Optics (Beijing:Science Press) pp368–411 (in Chinese) [饶瑞中 2012 现代大气光学 (北京: 科学出版社) 第 368–411 页]
[3] Nikishov V V, Nikishov V I 2000 Int. J. Fluid Mech. Res. 27 82
[4] Lu L, Ji X L, Baykal Y 2014 Opt. Express 22 027112
[5] Pu H, Ji X L 2016 J. Opt. 18 105704
[6] Hou W L 2009 Opt. Lett. 34 2688
[7] Hou W L, Woods S, Jarosz E, Goode W, Weidemann A 2012 Appl. Phys. 51 2678
[8] Hou W L, Jarosz E, Woods S, Goode W, Weidemann A 2013 Opt. Express 21 4367
[9] Gökçe M C, Baykal Y 2018 Opt. Commun. 410 830
[10] Baykal Y 2016 Appl. Opt. 55 1228
[11] Gökçe M C, Baykal Y 2018 Opt. Commun. 413 196
[12] Baykal Y 2016 Opt. Commun. 375 15
[13] Korotkova O, Farwell N, Shchepakina E 2012 Waves in Random and Complex Media 22 260
[14] Yang T, Ji X L, Li X Q 2015 Acta Phys. Sin. 64 204206 (in Chinese) [杨婷, 季小玲, 李晓庆 2015 物理学报 64 204206]
[15] Liu Y X, Chen Z Y, Pu J X 2017 Acta Phys. Sin. 66 124205 (in Chinese) [刘永欣, 陈子阳, 蒲继雄 2017 物理学报 66 124205]
[16] Wu T, Ji X L, Luo Y J 2018 Acta Phys. Sin. 67 054206 (in Chinese) [吴彤, 季小玲, 罗燏娟 2018 物理学报 67 054206]
[17] Elamassie M, Uysal M, Baykal Y, Abdallah M, Qaraqe K 2017 J. Opt. Soc. Am. A 34 1969
[18] Cui L Y, Cao L 2015 Optik 126 4704
[19] Lu L, Wang Z Q, Zhang P F, Zhang J H, Ji X L, Fan C Y, Qiao C H 2016 Optik 127 5341
[20] Yang Y Q, Yu L, Wang Q, Zhang Y X 2017 Appl. Opt. 56 7046
[21] Jackson P R, Rehmann C R 2003 J. Phys. Oceanogr. 33 1592
[22] Lu W, Liu L R, Sun J F 2006 J. Opt. A: Pure Appl. Opt. 8 1052
[23] Fried D L 1966 J. Opt. Soc. Am. 56 1372
[24] Yura H T 1973 J. Opt. Soc. Am. 63 567
[25] Andrews L C, Phillips R L, Sasiela R J, Parenti R 2005 Proc. SPIE 5793 28
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[1] Andrews L C, Phillips R L 2012 Appl. Phys. 51 2678
[2] Rao R Z 2012 Modern Atmospheric Optics (Beijing:Science Press) pp368–411 (in Chinese) [饶瑞中 2012 现代大气光学 (北京: 科学出版社) 第 368–411 页]
[3] Nikishov V V, Nikishov V I 2000 Int. J. Fluid Mech. Res. 27 82
[4] Lu L, Ji X L, Baykal Y 2014 Opt. Express 22 027112
[5] Pu H, Ji X L 2016 J. Opt. 18 105704
[6] Hou W L 2009 Opt. Lett. 34 2688
[7] Hou W L, Woods S, Jarosz E, Goode W, Weidemann A 2012 Appl. Phys. 51 2678
[8] Hou W L, Jarosz E, Woods S, Goode W, Weidemann A 2013 Opt. Express 21 4367
[9] Gökçe M C, Baykal Y 2018 Opt. Commun. 410 830
[10] Baykal Y 2016 Appl. Opt. 55 1228
[11] Gökçe M C, Baykal Y 2018 Opt. Commun. 413 196
[12] Baykal Y 2016 Opt. Commun. 375 15
[13] Korotkova O, Farwell N, Shchepakina E 2012 Waves in Random and Complex Media 22 260
[14] Yang T, Ji X L, Li X Q 2015 Acta Phys. Sin. 64 204206 (in Chinese) [杨婷, 季小玲, 李晓庆 2015 物理学报 64 204206]
[15] Liu Y X, Chen Z Y, Pu J X 2017 Acta Phys. Sin. 66 124205 (in Chinese) [刘永欣, 陈子阳, 蒲继雄 2017 物理学报 66 124205]
[16] Wu T, Ji X L, Luo Y J 2018 Acta Phys. Sin. 67 054206 (in Chinese) [吴彤, 季小玲, 罗燏娟 2018 物理学报 67 054206]
[17] Elamassie M, Uysal M, Baykal Y, Abdallah M, Qaraqe K 2017 J. Opt. Soc. Am. A 34 1969
[18] Cui L Y, Cao L 2015 Optik 126 4704
[19] Lu L, Wang Z Q, Zhang P F, Zhang J H, Ji X L, Fan C Y, Qiao C H 2016 Optik 127 5341
[20] Yang Y Q, Yu L, Wang Q, Zhang Y X 2017 Appl. Opt. 56 7046
[21] Jackson P R, Rehmann C R 2003 J. Phys. Oceanogr. 33 1592
[22] Lu W, Liu L R, Sun J F 2006 J. Opt. A: Pure Appl. Opt. 8 1052
[23] Fried D L 1966 J. Opt. Soc. Am. 56 1372
[24] Yura H T 1973 J. Opt. Soc. Am. 63 567
[25] Andrews L C, Phillips R L, Sasiela R J, Parenti R 2005 Proc. SPIE 5793 28
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