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Based on the Longuet-Higgins wave model theory, a modified phase modulation method of simulating freak waves is improved in this paper. The method can generate freak waves at assigned time and place, and their waveforms can not only maintain the frequency spectrum structure of the target spectrum and also satisfy the wave series statistics to a great extent. Then, the electromagnetic backscattering model of freak and background wave is established by the finite difference time domain method and the two-scale method. After averaging relative deviation and analyzing the error of the root mean square deviation within the measurement uncertainties, considering the computational efficiency, we use the two-scale model method to calculate the electromagnetic scattering coefficient of freak wave. Numerical results show that the normalized radar cross section (NRCS) of freak wave is much smaller than that of background wave. On the other hand, we analyze the electromagnetic scattering properties of freak waves under the different polarization modes, incident angles and incident frequencies. We find that in the condition of grazing incidence, the backscatter coefficient of freak wave increases with the increase of the incident frequency, but the increase amplitude is reduced, which meets the rough surface scattering theory. When the incident frequency is fixed and the incident〉is small, the backscatter coefficient calculation results of freak wave are similar under the condition of different polarizations VV's and HH's, but the backscatter coefficient of freak wave decreases obviously with the increase of incident angle, which is caused by the radar electromagnetic wave that is parallel to the sea surface and contacts it gradually. In addition, we find that the backscatter coefficient calculation result of freak waves under the VV polarization is much higher than under HH polarization from the two groups of experimental figures. According to the result of datum analysis, a conclusion is drawn that we can determine where the freak wave is when the NRCS difference of synthetic aperture radar (SAR) image is smaller than -11.8 dB. In the practical engineering application, the characteristic parameters are difficult to observe, while the difference in electromagnetic scattering coefficient between freak wave and background wave can be calculated from the SAR image of sea surface. This conclusion provides a reference standard for predicting the freak waves in engineering application, through which we can calculate the characteristic parameters of freak wave, determine its position, and study the electromagnetic scattering characteristics under the different polarization modes, incident angles and incident frequencies in future researches.
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Keywords:
- freak waves /
- phase modulation /
- electromagnetic backscattering /
- indicator
[1] Kharif C, Pelinovsky E, Slunyaev A 2009 Rogue Waves in the Ocean (Berlin:Deblik)
[2] Didenkulova I I, Slunyaev A V, Pelinovsky E N, et al. 2006 Natural Hazards and Earth System Sciences 6 1007
[3] Kharif C, Pelinovsky E 2003 Europ. J. Mech. 22 603
[4] Kim N, Kim C H 2003 Int. J. Offshore and Polar Engineering 13 38
[5] Pei Y G, Zhang N C, Zhang Y Q 2007 Acta Oceanol. Sin. 29 172 (in Chinese)[裴玉国, 张宁川, 张运秋 2007 海洋学报 29 172]
[6] Pei Y G, Zhang N C, Zhang Y Q 2007 China Ocean Engineer. 21 515
[7] Huang G X 2002 Ph. D. Dissertation (Dalian:Dalian University of Technology) (in Chinese)[黄国兴 2002 博士学位论文 (大连:大连理工大学)]
[8] Liu X X, Zhang N C, Pei Y G, Zhang Y Q 2007 Numerical Simulation of Freak Waves in Three-Dimensional Wave Field (Beijing:China Ocean Press) pp908-914 (in Chinese)[刘晓霞, 张宁川, 裴玉国, 张运秋 2007 中国环境资源与水利水电工程 (北京:海洋出版社) 第908–914页]
[9] Zhao X Z, Sun Z C, Liang S X 2009 China Ocean Engineer. 23 429
[10] Liu Z Q, Zhang N C, Yu Y X 2011 Acta Oceanol. Sin. 30 19
[11] Zhang Y Q, Zhang N C 2007 Acta Oceanol. Sin. 26 116
[12] Zhang Y Q, Zhang N C, Pei Y G 2007 China Ocean Engineer. 21 207
[13] Onorato M, Osborne A R, Serio M 2004 Phys. Rev. E 70 67302
[14] Longuet-Higgins M S 1952 J. Marine Res. 11 245
[15] Wu G K, Ji G R, Ji T T, Ren H X 2014 Acta Phys. Sin. 63 134203 (in Chinese)[吴庚坤, 姬光荣, 姬婷婷, 任红霞 2014 物理学报 63 134203]
[16] Guo L X, Wang Y H, Wu Z S 2005 Acta Phys. Sin. 54 5130 (in Chinese)[郭立新, 王运华, 吴振森 2005 物理学报 54 5130]
[17] Yang J L, Guo L X, Wan J W 2007 Acta Phys. Sin. 56 2106 (in Chinese)[杨俊岭, 郭立新, 万建伟 2007 物理学报 56 2106]
[18] Ulaby F 1982 Microwave Remote Sensing (Vol. 2) (London:Addison-Wesbey Publishing)
[19] Wang Y H, Guo L X, Wu Z S 2006 Acta Phys. Sin. 55 209 (in Chinese)[王运 华, 郭立新, 吴振森 2006 物理学报55 209]
[20] Zhang Y D 2004 Ph. D. Dissertation (Xi'an:Xidian University) (in Chinese)[张 延冬 2004 博士学位论文 (西安:西安电子科技大学)]
[21] Vladimir K, Daniele H 2003 J. Geophys. Res. 108 8054
[22] Xie T, He C, William P, Kuang H L 2010 Chin. Phys. B 19 024101
[23] Xu D L, Yu D Y 2001 Theory of Random Waves (Beijing:Higher Education Press) pp200-204 (in Chinese)[徐德伦, 于定勇 2001 随机海浪理论(北京:高 等教育出版社)第200–215页]
[24] Ge D B, Yan Y B 2005 Finite-Difference Time-Domain Method for Electromagnetic Waves (Xi'an:Xidian University Press) (in Chinese)[葛德彪, 闫 玉波 2005 电磁波时域有限差分方法(西安:西安电子科技大学出版社)]
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[1] Kharif C, Pelinovsky E, Slunyaev A 2009 Rogue Waves in the Ocean (Berlin:Deblik)
[2] Didenkulova I I, Slunyaev A V, Pelinovsky E N, et al. 2006 Natural Hazards and Earth System Sciences 6 1007
[3] Kharif C, Pelinovsky E 2003 Europ. J. Mech. 22 603
[4] Kim N, Kim C H 2003 Int. J. Offshore and Polar Engineering 13 38
[5] Pei Y G, Zhang N C, Zhang Y Q 2007 Acta Oceanol. Sin. 29 172 (in Chinese)[裴玉国, 张宁川, 张运秋 2007 海洋学报 29 172]
[6] Pei Y G, Zhang N C, Zhang Y Q 2007 China Ocean Engineer. 21 515
[7] Huang G X 2002 Ph. D. Dissertation (Dalian:Dalian University of Technology) (in Chinese)[黄国兴 2002 博士学位论文 (大连:大连理工大学)]
[8] Liu X X, Zhang N C, Pei Y G, Zhang Y Q 2007 Numerical Simulation of Freak Waves in Three-Dimensional Wave Field (Beijing:China Ocean Press) pp908-914 (in Chinese)[刘晓霞, 张宁川, 裴玉国, 张运秋 2007 中国环境资源与水利水电工程 (北京:海洋出版社) 第908–914页]
[9] Zhao X Z, Sun Z C, Liang S X 2009 China Ocean Engineer. 23 429
[10] Liu Z Q, Zhang N C, Yu Y X 2011 Acta Oceanol. Sin. 30 19
[11] Zhang Y Q, Zhang N C 2007 Acta Oceanol. Sin. 26 116
[12] Zhang Y Q, Zhang N C, Pei Y G 2007 China Ocean Engineer. 21 207
[13] Onorato M, Osborne A R, Serio M 2004 Phys. Rev. E 70 67302
[14] Longuet-Higgins M S 1952 J. Marine Res. 11 245
[15] Wu G K, Ji G R, Ji T T, Ren H X 2014 Acta Phys. Sin. 63 134203 (in Chinese)[吴庚坤, 姬光荣, 姬婷婷, 任红霞 2014 物理学报 63 134203]
[16] Guo L X, Wang Y H, Wu Z S 2005 Acta Phys. Sin. 54 5130 (in Chinese)[郭立新, 王运华, 吴振森 2005 物理学报 54 5130]
[17] Yang J L, Guo L X, Wan J W 2007 Acta Phys. Sin. 56 2106 (in Chinese)[杨俊岭, 郭立新, 万建伟 2007 物理学报 56 2106]
[18] Ulaby F 1982 Microwave Remote Sensing (Vol. 2) (London:Addison-Wesbey Publishing)
[19] Wang Y H, Guo L X, Wu Z S 2006 Acta Phys. Sin. 55 209 (in Chinese)[王运 华, 郭立新, 吴振森 2006 物理学报55 209]
[20] Zhang Y D 2004 Ph. D. Dissertation (Xi'an:Xidian University) (in Chinese)[张 延冬 2004 博士学位论文 (西安:西安电子科技大学)]
[21] Vladimir K, Daniele H 2003 J. Geophys. Res. 108 8054
[22] Xie T, He C, William P, Kuang H L 2010 Chin. Phys. B 19 024101
[23] Xu D L, Yu D Y 2001 Theory of Random Waves (Beijing:Higher Education Press) pp200-204 (in Chinese)[徐德伦, 于定勇 2001 随机海浪理论(北京:高 等教育出版社)第200–215页]
[24] Ge D B, Yan Y B 2005 Finite-Difference Time-Domain Method for Electromagnetic Waves (Xi'an:Xidian University Press) (in Chinese)[葛德彪, 闫 玉波 2005 电磁波时域有限差分方法(西安:西安电子科技大学出版社)]
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