海洋中示踪物等值线的分形长度及其与混合效率的关系*

doi:10.11978/2023020

热带海洋学报 ›› 2024, Vol. 43 ›› Issue (1): 1-15.doi: 10.11978/2023020CSTR: 32234.14.2023020

• 海洋水文学 • 下一篇

海洋中示踪物等值线的分形长度及其与混合效率的关系*

钱钰坤¹^,²(), 刘统亚³^,⁴, 张华¹^,⁵, 彭世球¹^,²^,⁵()

1.热带海洋环境国家重点实验室, 中国科学院南海海洋研究所, 广东广州 511458
2.中国科学院应用海洋重点实验室, 中国科学院南海海洋研究所, 广东广州 511458
3.卫星海洋环境动力学国家重点实验室, 自然资源部第二海洋研究所, 浙江杭州 310012
4.南方海洋科学与工程广东省实验室(珠海), 广东珠海 519000
5.中国科学院大学, 北京 100049

收稿日期:2023-05-12 修回日期:2023-06-08 出版日期:2024-01-10 发布日期:2024-01-19
作者简介:
钱钰坤(1983—), 男, 广西柳州市人, 博士, 从事海洋数值模拟与混合参数化研究。email: qianyukun@scsio.ac.cn
*感谢南海海洋研究所的高性能计算中心为本文数值模拟提供的技术支持。
基金资助:
国家重点研发项目(2022YFC3105004); 国家自然科学基金项目(41976023); 国家自然科学基金项目(41931182); 国家自然科学基金项目(42106008); 国家自然科学基金项目(42376028); 热带海洋环境国家重点实验室自主研究项目(LTOZZ2102); 热带海洋环境国家重点实验室开放课题(LTO2107)

Fractal lengths of tracer contours in the ocean and its relationship with mixing efficiency

QIAN Yukun¹^,²(), LIU Tongya³^,⁴, ZHANG Hua¹^,⁵, PENG Shiqiu¹^,²^,⁵()

1. State Key Laboratory of Tropical Oceanography, South China Sea Institute of Oceanology, Chinese Academy of Sciences, Guangzhou 511458, China
2. Key Laboratory of Science and Technology on Operational Oceanography, South China Sea Institute of Oceanology, Chinese Academy of Sciences, Guangzhou 511458, China
3. State Key Laboratory of Satellite Ocean Environment Dynamics, Second Institute of Oceanography, Ministry of Natural Resources, Hangzhou 310012, China
4. Southern Marine Science and Engineering Guangdong Laboratory (Zhuhai), Zhuhai 519000, China
5. University of Chinese Academy of Sciences, Beijing 100049, China

Received:2023-05-12 Revised:2023-06-08 Online:2024-01-10 Published:2024-01-19
Supported by:
National Key Research and Development Program of China(2022YFC3105004); National Natural Science Foundation of China(41976023); National Natural Science Foundation of China(41931182); National Natural Science Foundation of China(42106008); National Natural Science Foundation of China(42376028); Independent Research Project Program of State Key Laboratory of Tropical Oceanography(LTOZZ2102); Open Project of the State Key Laboratory of Tropical Oceanography(LTO2107)

摘要/Abstract

摘要：

涡致混合扩散是物理海洋研究中的热点和难点问题。本文基于“有效扩散”理论, 研究示踪物等值线在海表地转湍流的多尺度搅拌作用下, 发生拉伸、扭曲、变形、折叠等改变其几何拓扑结构的现象, 并探讨了等值线分形长度的变化与混合效率的关系。研究结果表明, 在地转流场的搅拌下, 示踪物的等值线会被迅速拉长, 并产生丰富的精细结构。这种分形式的增长可达原长度的10~20倍, 是混合效率提高的主要原因; 而涡丝和锋面伴随的梯度增强虽然也有贡献, 但为次要因素。另一方面, 在示踪物模拟过程中, 小尺度扩散会通过不可逆混合对示踪物进行均匀化, 从而抹平等值线的精细结构, 抑制等值线的增长, 限制混合效率的提高。基于“数盒子”算法计算了等值线的分形维度, 其数值在1.4到1.6之间, 介于一维和二维之间。但由于地转湍流数据分辨率的限制, 无法考虑更小尺度(次中尺度过程)的搅拌作用, 可能低估了等值线的分形长度和混合效率。本研究将海洋混合与等值线几何特征联系了起来, 初步得到了分形长度和混合效率两者的经验关系式, 未来可以利用图像识别等成熟遥感技术将海洋示踪物等值线的几何特征直接转换为混合效率, 为诊断分析海洋混合及其参数化提供了一种新的思路。

关键词: 海洋混合, 地转湍流, 分形几何, 有效扩散, 等值线

Abstract:

Quantifying eddy mixing in the ocean is a hot and tough problem in the area of physical oceanography. Based on the theory of effective diffusivity, the present study investigated the stirring effects of geostrophic turbulence that led to stretching, distorting, deforming, and folding of tracer contours. These changes are then related to the efficiency of turbulent mixing. Results show that under the stirring effect of geostrophic turbulence, the length of tracer contour can be quickly elongated and fine-scale tracer filaments and fronts are also generated. This fractal elongation of tracer contour, about 10~20 times longer than the original length, is the dominant contributor to the mixing efficiency, whereas the gradient enhancement associated with filament and front generations only plays a secondary role. On the other hand, fine-scale features are smoothed out by small-scale diffusivity which eventually suppresses the increase of contour length and the generation of tracer filaments. This imposes an upper bound of the mixing efficiency when the stirring and smoothing effects are in a dynamical balance. Through a ‘box-counting’ method, the fractal dimension of tracer contour is also found between 1.4~1.6, indicating a geometric dimension lies somewhere between 1D and 2D. Due to the limitation of data resolution, contour length and thus mixing efficiency may be underestimated. Finally, the present study made an empirical relation between the fractal dimension and mixing efficiency, providing an opportunity for estimating mixing efficiency through a well-developed pattern recognition technique in remote sensing, and a new way of diagnosing ocean mixing and its parameterization.

Key words: oceanic mixing, geostrophic turbulence, fractal geometry, effective diffusivity, contour

钱钰坤, 刘统亚, 张华, 彭世球. 海洋中示踪物等值线的分形长度及其与混合效率的关系*[J]. 热带海洋学报, 2024, 43(1): 1-15.

QIAN Yukun, LIU Tongya, ZHANG Hua, PENG Shiqiu. Fractal lengths of tracer contours in the ocean and its relationship with mixing efficiency[J]. Journal of Tropical Oceanography, 2024, 43(1): 1-15.

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参考文献 38

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纬度范围	a±stderr	b±stderr	R
60°S—45°S	7.93±0.05	−6.65±0.07	3070.05
45°S—30°S	10.18±0.01	−9.42±0.01	195.92
30°S—15°S	10.23±0.01	−9.50±0.01	220.11
15°S—0°	10.18±0.01	−9.42±0.02	429.19
0°—15°N	10.17±0.01	−9.44±0.02	382.90
15°N—30°N	10.09±0.01	−9.42±0.02	309.17
30°N—45°N	9.27±0.02	−8.05±0.04	1346.88
45°N—60°N	9.32±0.03	−8.13±0.04	1759.98

海洋中示踪物等值线的分形长度及其与混合效率的关系*

Fractal lengths of tracer contours in the ocean and its relationship with mixing efficiency

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