| 间歇湍流的分形特征——分数维及分数阶导数的应用 |
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| 引用本文： | 刘式达,付遵涛,刘式适.间歇湍流的分形特征——分数维及分数阶导数的应用[J].地球物理学报,2014,57(9):2751-2755. |
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| 作者姓名： | 刘式达 付遵涛 刘式适 |
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| 作者单位： | 北京大学物理学院大气与海洋科学系, 气候与海-气实验室, 北京 100871 |
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| 基金项目： | 国家自然科学基金（40975027）资助. |
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| 摘 要： | 分数维由Mandelbrot创立已有30年，分数阶导数在1695年由L’Hospital提出已有400年的历史.本文用物理学中的间歇湍流问题说明分数维及分数阶导数的物理意义.由于间歇湍流涡旋不完全充满空间，所以其维数为2
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| 关 键 词： | 分数阶导数 分数维 间歇湍流 扩散 |
| 收稿时间： | 2013-09-16 |
Fractal behaviors of intermittent turbulence —Applications of fractional dimension and fractional derivatives |
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| LIU Shi-Da,FU Zun-Tao,LIU Shi-Kuo.Fractal behaviors of intermittent turbulence —Applications of fractional dimension and fractional derivatives[J].Chinese Journal of Geophysics,2014,57(9):2751-2755. |
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| Authors: | LIU Shi-Da FU Zun-Tao LIU Shi-Kuo |
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| Institution: | Department of Atmospheric and Oceanic Sciences and Laboratory for Climate and Ocean-Atmosphere Studies, School of Physics, Peking University, Beijing 100871, China |
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| Abstract: | Fractional dimension was coined by Mandelbrot 30 years ago and the fractional derivatives proposed in 1695 by L 'Hospital has a history of more than 400 years. In this paper, intermittent turbulence problems in physics have been applied to illustrate the physical significance of fractal dimension and fractional derivatives. Due to incomplete occupation of the intermittent turbulent eddies in the space, so the dimension of intermittent turbulence is 2
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| Keywords: | Fractional derivatives Fractal dimension Intermittent turbulence Diffusion |
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