基于Omega方程的南海垂向流速诊断与对比研究

洪坤强; 谢玲玲; 黄家辉

doi:10.12284/hyxb20250109

基于Omega方程的南海垂向流速诊断与对比研究

doi: 10.12284/hyxb20250109

洪坤强^1,,
谢玲玲^{1, 2, 3},
黄家辉^{1, 4, ,}

1.
广东海洋大学海洋与气象学院近海海洋变化与灾害预警实验室，广东湛江 524088
2.
广东省高等学校陆架及深远海气候资源与环境重点实验室，广东湛江 524088
3.
粤西热带海洋生态环境野外观测研究站，广东湛江 524088
4.
自然资源部湛江海洋中心，广东湛江 524005

基金项目: 国家自然科学基金面上项目（42276019）；国家重点研发课题（2024YFC2817003）；广东省科技计划项目（2024B1212040008）。

详细信息

作者简介:
洪坤强（2002—），男，河南省固始县人，研究方向为海洋中小尺度过程。E-mail：hongkq_gdou@163.com

通讯作者:
黄家辉，男，研究方向为海洋中小尺度过程。E-mail：Iron_man1224@163.com

中图分类号: P731
计量
- 文章访问数: 165
- HTML全文浏览量: 41
- PDF下载量: 16
- 被引次数: 0
出版历程
- 收稿日期: 2025-07-11
- 修回日期: 2025-11-05
- 网络出版日期: 2025-12-04
- 刊出日期: 2025-12-31

A comparative study on Omega equation-based vertical velocity diagnosis for the South China Sea

Hong Kunqiang^1
,,
Xie Lingling^{1, 2, 3},
Huang Jiahui^{1, 4
, ,}

1.
Laboratory of Coastal Ocean Variation and Disaster Prediction, College of Oceanology and Meteorology, Guangdong Ocean University, Zhanjiang 524088, China
2.
Guangdong Key Laboratory of Climate, Resource and Environment in Continental Shelf Sea and Deep Ocean, Zhanjiang 524088, China
3.
Guangdong Western Tropical Marine Ecological and Environmental Field Observation Research Station, Zhanjiang 524088, China
4.
Zhanjiang Marine Center, Ministry of Natural Resources, Zhanjiang 524005, China

摘要

摘要: 本文基于OFES（Ocean general circulation model For the Earth Simulator）模式0.1° × 0.1°高分辨率温盐和三维流场数据，分析Omega方程在南海垂向流速诊断中的适用性和南海垂向流速的时空变化特征。结果表明，Omega方程诊断垂向流速w_Omega与OFES模式垂向流速w_OFEES在南海海盆大部分区域量级相当，约为 O （10⁻⁵ m/s），南海北部陆架区则小一个量级。w_Omega和w_OFEES的空间相关系数r^s在台湾西南部（R1区）和越南以东（R2区）较大，在菲律宾西（R3区）、南海南部（R4区）以及海南岛东北部（R5区）较小。季节变化上，R1、R2和R4区r^s冬季大、夏季小，R3和R5区r^s无明显季节特征。R1和R2区是Omega方程的适用区，其w_Omega与w_OFEES的时间相关系数r^t较大。各区域中形变项（$ {S}_{{\mathrm{DEF}}} $）的贡献率均超过50%，整体大于平流项（$ {S}_{{\mathrm{ADV}}} $），并呈现出“上层$ {S}_{{\mathrm{ADV}}} $主导，下层$ {S}_{{\mathrm{DEF}}} $增强”的共同垂向结构，其临界深度在20～70 m之间。对比eSQG（effective Surface Quasi-Geostrophy）诊断垂向流速结果，Omega方程明显更适用于南海垂向流速的诊断。
- 南海 /
- 垂向流速 /
- Omega方程 /
- OFES /
- 时空变化 /
- eSQG
Abstract: Based on 0.1° × 0.1° high-resolution temperature, salinity, and three-dimensional velocity data from the Ocean general circulation model For the Earth Simulator (OFES), this study analyzes the applicability of the Omega equation for diagnosing vertical velocity in the South China Sea (SCS) and the spatiotemporal variation characteristics of vertical velocity in the SCS. The results show that the vertical velocity diagnosed by the Omega equation (w_Omega) and the OFES model vertical velocity (w_OFES) are of comparable magnitude in most areas of the SCS basin, approximately O(10⁻⁵ m/s), while w_Omega is one order of magnitude smaller than w_OFES on the northern continental shelf of the SCS. The spatial correlation coefficient (r^s) between w_Omega and w_OFES is larger in the region southwestern of Taiwan (R1) and east of Vietnam (R2), and smaller in the western Philippines (R3), the southern SCS (R4), and the northeastern region of Hainan Island (R5). In terms of seasonal variation, r^s is larger in winter and smaller in summer in regions R1, R2, and R4, while regions R3 and R5 show no significant seasonal characteristics in r^s. Regions R1 and R2 are applicable areas for the Omega equation, where the temporal correlation coefficient r^t between w_Omega and w_OFES is larger. In all regions, the contribution of the deformation term ($ {S}_{{\mathrm{DEF}}} $) exceeds 50%, generally greater than the contribution of the advection term ($ {S}_{{\mathrm{ADV}}} $), and they exhibit a common vertical structure of “$ {S}_{{\mathrm{ADV}}} $ dominance in the upper layer and $ {S}_{{\mathrm{DEF}}} $ enhancement in the lower layer”, with the critical depth ranging from 20−70 m. Comparing the results of vertical velocity diagnosed by effective Surface Quasi-Geostrophy (eSQG) and the Omega equation, the Omega equation is significantly better adapted for diagnosing vertical velocity in the SCS.
- South China Sea /
- vertical velocity /
- Omega equation /
- OFES /
- spatio-temporal variation /
- eSQG

HTML全文

图 1 全年、夏季和冬季平均的EKE与N²水平分布

Fig. 1 2D distribution (x−y) of mean EKE and N² in whole year, summer and winter

下载: 全尺寸图片幻灯片

图 2 全年、夏季和冬季R1区100 m层w_Omega、w_OFES和Δw的水平分布

黑色线表示100 m等深线

Fig. 2 2D distribution (x−y) of w_Omega, w_OFES and Δw at 100 m in the R1 region in whole year, summer and winter

Black lines denote the 100 m isobath

下载: 全尺寸图片幻灯片

图 6 全年、夏季和冬季R5区50 m层w_Omega、w_OFES和Δw的水平分布

黑色线表示50 m等深线

Fig. 6 2D distribution (x−y) of w_Omega, w_OFES and Δw at 100 m in the R5 region in whole year, summer and winter.

Black lines denote the 50 m isobath

下载: 全尺寸图片幻灯片

图 3 全年、夏季和冬季R2区100 m层w_Omega、w_OFES和Δw的水平分布

Fig. 3 2D distribution (x−y) of w_Omega, w_OFES and Δw at 100 m in the R2 region in whole year, summer and winter

下载: 全尺寸图片幻灯片

图 4 全年、夏季和冬季R3区100 m层w_Omega、w_OFES和Δw的水平分布

Fig. 4 2D distribution (x−y) of w_Omega, w_OFES and Δw at 100 m in the R3 region in whole year, summer and winter

下载: 全尺寸图片幻灯片

图 5 全年、夏季和冬季R4区100 m层w_Omega、w_OFES和Δw的水平分布

黑色线表示100 m等深线

Fig. 5 2D distribution (x−y) of w_Omega, w_OFES and Δw at 100 m in the R4 region in whole year, summer and winter

Black lines denote the 100 m isobath

下载: 全尺寸图片幻灯片

图 7 全年、夏季和冬季R1～R5区w_Omega和w_OFES的均方根（RMS）剖面图

Fig. 7 Profile of root mean square of w_Omega and w_OFES in the R1 to R5 regions in whole year, summer and winter

下载: 全尺寸图片幻灯片

图 8 R1～R5区w_Omega和w_OFES的空间相关系数r^s随时间和深度的变化及其时间平均

Fig. 8 Correlation r^s as a function of time and depth between the w_Omega and w_OFES in the R1 to R5 regions and their temporal averaged correlation values

下载: 全尺寸图片幻灯片

图 9 R1～R5区w_Omega和w_OFES的时间相关系数r^t的水平分布

Fig. 9 2D distribution (x−y) of temporal correlation r^t of w_Omega and w_OFES in the R1 to R5 regions

下载: 全尺寸图片幻灯片

图 10 南海区域平均海表高度异常（SLA）时间序列对比

蓝线表示OFES模式结果，红线表示CMEMS卫星高度计数据

Fig. 10 Comparison of the regional mean sea level anomaly (SLA) time series in the South China Sea

The blue line represents the OFES simulation, and the red line represents the CMEMS satellite altimetry data

下载: 全尺寸图片幻灯片

图 11 南海年平均SSH与ADT的空间分布对比

a. OFES模式输出的年平均SSH；b. CMEMS提供的年平均ADT

Fig. 11 Spatial comparison of the annual mean SSH and ADT in the South China Sea

a. Annual mean SSH from the OFES simulation; b. annual mean ADT from CMEMS

下载: 全尺寸图片幻灯片

图 12 全年、夏季和冬季R1～R5区$ {S}_{{\mathrm{DEF}}} $和$ {S}_{{\mathrm{ADV}}} $剖面图

Fig. 12 Profile of $ {S}_{{\mathrm{DEF}}} $ and $ {S}_{{\mathrm{ADV}}} $ in the R1 to R5 regions in whole year, summer and winter

下载: 全尺寸图片幻灯片

表 1 全年、夏季和冬季R1～R5区w_Omega和w_OFES的空间相关系数r^s

Tab. 1 Spatial correlation r^s of w_Omega and w_OFES in the R1 to R5 regions in whole year, summer and winter

	全年	夏季	冬季
R1 (100 m)	0.45（p < 0.01）	0.52（p < 0.01）	0.64（p < 0.01）
R2 (100 m)	0.73（p < 0.01）	0.70（p < 0.01）	0.77（p < 0.01）
R3 (100 m)	0.61（p < 0.01）	0.51（p < 0.01）	0.55（p < 0.01）
R4 (100 m)	0.66（p < 0.01）	0.20（p < 0.01）	0.60（p < 0.01）
R5 (50 m)	0.15（P = 0.02）	0.41（p < 0.01）	0.09（P = 0.20）

下载: 导出CSV

表 2 全年、夏季和冬季R1～R5区w_eSQG和w_OFES的空间相关系数r^s

Tab. 2 Spatial correlation r^s of w_eSQG and w_OFES in the R1 to R5 regions in whole year, summer and winter

	全年	夏季	冬季
R1 (100 m)	0.30（p < 0.01）	0.32（p < 0.01）	0.04（p = 0.15）
R2 (100 m)	0.41（p < 0.01）	0.49（p < 0.01）	0.35（p < 0.01）
R3 (100 m)	0.18（p < 0.01）	0.14（p < 0.01）	0.42（p < 0.01）
R4 (100 m)	0.64（p < 0.01）	0.69（p < 0.01）	0.51（p < 0.01）
R5 (50 m)	0.14（p < 0.01）	0.27（p < 0.01）	0.07（p = 0.16）

下载: 导出CSV

表 3 R1～R5区w_Omega（w_eSQG）和w_OFES的时间相关系数r^t超过0.4的比例

Tab. 3 The proportion of regions R1～R5 where the temporal correlation coefficient (r^t) between w_Omega (w_eSQG) and w_OFES exceeds 0.4

	w_Omega和w_OFES的r^t_Omega>0.4	w_eSQG和w_OFES的r^t_eSQG>0.4
R1 (100 m)	81%	73%
R2 (100 m)	87%	55%
R3 (100 m)	2%	0
R4 (100 m)	33%	10%
R5 (50 m)	9%	7%

下载: 导出CSV

参考文献(58)

[1]	Freilich M A, Mahadevan A. Decomposition of vertical velocity for nutrient transport in the upper ocean[J]. Journal of Physical Oceanography, 2019, 49(6): 1561−1575. doi: 10.1175/JPO-D-19-0002.1
[2]	Boyd P W, Claustre H, Levy M, et al. Multi-faceted particle pumps drive carbon sequestration in the ocean[J]. Nature, 2019, 568(7752): 327−335. doi: 10.1038/s41586-019-1098-2
[3]	Pascual A, Ruiz S, Buongiorno Nardelli B, et al. Net primary production in the Gulf Stream sustained by quasi-geostrophic vertical exchanges[J]. Geophysical Research Letters, 2015, 42(2): 441−449. doi: 10.1002/2014GL062569
[4]	黄小龙, 经志友, 郑瑞玺, 等. 南海西部夏季上升流锋面的次中尺度特征分析[J]. 热带海洋学报, 2020, 39(3): 1−9. Huang Xiaolong, Jing Zhiyou, Zheng Ruixi, et al. Analysis of submesoscale characteristics of summer upwelling fronts in the western South China Sea[J]. Journal of Tropical Oceanography, 2020, 39(3): 1−9.
[5]	Chen Ke, Gaube P, Pallàs-Sanz E. On the vertical velocity and nutrient delivery in warm core rings[J]. Journal of Physical Oceanography, 2020, 50(6): 1557−1582. doi: 10.1175/JPO-D-19-0239.1
[6]	Estrada-Allis S N, Barceló-Llull B, Pallàs-Sanz E, et al. Vertical velocity dynamics and mixing in an anticyclone near the canary islands[J]. Journal of Physical Oceanography, 2019, 49(2): 431−451. doi: 10.1175/JPO-D-17-0156.1
[7]	Lin Hongyang, Liu Zhiyu, Hu Jianyu, et al. Characterizing meso- to submesoscale features in the South China Sea[J]. Progress in Oceanography, 2020, 188: 102420. doi: 10.1016/j.pocean.2020.102420
[8]	Rousselet L, Doglioli A M, de Verneil A, et al. Vertical motions and their effects on a biogeochemical tracer in a cyclonic structure finely observed in the Ligurian Sea[J]. Journal of Geophysical Research: Oceans, 2019, 124(6): 3561−3574. doi: 10.1029/2018JC014392
[9]	Legal C, Klein P, Treguier A M, et al. Diagnosis of the vertical motions in a mesoscale stirring region[J]. Journal of Physical Oceanography, 2007, 37(5): 1413−1424. doi: 10.1175/JPO3053.1
[10]	Wang Liju, Xie Lingling, Zheng Quanan, et al. Tropical cyclone enhanced vertical transport in the northwestern South China Sea I: mooring observation analysis for Washi (2005)[J]. Estuarine, Coastal and Shelf Science, 2020, 235: 106599. doi: 10.1016/j.ecss.2020.106599
[11]	Allen J T, Smeed D A, Nurser A J G, et al. Diagnosis of vertical velocities with the QG omega equation: an examination of the errors due to sampling strategy[J]. Deep Sea Research Part I: Oceanographic Research Papers, 2001, 48(2): 315−346. doi: 10.1016/S0967-0637(00)00035-2
[12]	Lindstrom S S, Pandolph Watts D. Vertical motion in the Gulf Stream near 68°W[J]. Journal of Physical Oceanography, 1994, 24(11): 2321−2333. doi: 10.1175/1520-0485(1994)024<2321:VMITGS>2.0.CO;2
[13]	Lapeyre G, Klein P. Dynamics of the upper oceanic layers in terms of surface quasigeostrophy theory[J]. Journal of Physical Oceanography, 2006, 36(2): 165−176. doi: 10.1175/JPO2840.1
[14]	Klein P, Isern-Fontanet J, Lapeyre G, et al. Diagnosis of vertical velocities in the upper ocean from high resolution sea surface height[J]. Geophysical Research Letters, 2009, 36(12): L12603.
[15]	Ponte A L, Klein P, Capet X, et al. Diagnosing surface mixed layer dynamics from high-resolution satellite observations: numerical insights[J]. Journal of Physical Oceanography, 2013, 43(7): 1345−1355. doi: 10.1175/JPO-D-12-0136.1
[16]	Barceló-Llull B, Pallàs-Sanz E, Sangrà P, et al. Ageostrophic secondary circulation in a subtropical intrathermocline eddy[J]. Journal of Physical Oceanography, 2017, 47(5): 1107−1123. doi: 10.1175/JPO-D-16-0235.1
[17]	Hu Jianyu, Gan Jianping, Sun Zhenyu, et al. Observed three-dimensional structure of a cold eddy in the southwestern South China Sea[J]. Journal of Geophysical Research: Oceans, 2011, 116(C5): C05016.
[18]	Rixen M, Allen J T, Pollard R T, et al. Along or across front ocean survey strategy? The estimation of quasi-geostrophic vertical velocities and temperature fluxes[J]. Geophysical Research Letters, 2003, 30(5): 1264.
[19]	Pietri A, Capet X, d’Ovidio F, et al. Skills and limitations of the adiabatic omega equation: how effective is it to retrieve oceanic vertical circulation at mesoscale and submesoscale?[J]. Journal of Physical Oceanography, 2021, 51(3): 931−954. doi: 10.1175/JPO-D-20-0052.1
[20]	Xie Lingling, Pallàs-Sanz E, Zheng Quanan, et al. Diagnosis of 3D vertical circulation in the upwelling and frontal zones east of Hainan Island, China[J]. Journal of Physical Oceanography, 2017, 47(4): 755−774. doi: 10.1175/JPO-D-16-0192.1
[21]	Buongiorno Nardelli B, Mulet S, Iudicone D. Three-dimensional ageostrophic motion and water mass subduction in the Southern Ocean[J]. Journal of Geophysical Research: Oceans, 2018, 123(2): 1533−1562. doi: 10.1002/2017JC013316
[22]	Sutcliffe R C. A contribution to the problem of development[J]. Quarterly Journal of the Royal Meteorological Society, 1947, 73(317/318): 370−383.
[23]	Hoskins B J, Draghici I, Davies H C. A new look at the ω-equation[J]. Quarterly Journal of the Royal Meteorological Society, 1978, 104(439): 31−38.
[24]	Tintoré J, Gomis D, Alonso S, et al. Mesoscale dynamics and vertical motion in the Alborán Sea[J]. Journal of Physical Oceanography, 1991, 21(6): 811−823. doi: 10.1175/1520-0485(1991)021<0811:MDAVMI>2.0.CO;2
[25]	Viúdez Á, Haney R L, Tintoré J. Circulation in the Alboran see as determined by quasi-synoptic hydrographic observations. Part II: mesoscale ageostrophic motion diagnosed through density dynamical assimilation[J]. Journal of Physical Oceanography, 1996, 26(5): 706−724. doi: 10.1175/1520-0485(1996)026<0706:CITASA>2.0.CO;2
[26]	Pollard R T, Regier L A. Vorticity and vertical circulation at an ocean front[J]. Journal of Physical Oceanography, 1992, 22(6): 609−625. doi: 10.1175/1520-0485(1992)022<0609:VAVCAA>2.0.CO;2
[27]	Sanz E P, Viúdez Á. Diagnosing mesoscale vertical motion from horizontal velocity and density data[J]. Journal of Physical Oceanography, 2005, 35(10): 1744−1762. doi: 10.1175/JPO2784.1
[28]	Giordani H, Planton S. Modeling and analysis of ageostrophic circulation over the Azores oceanic front during the SEMAPHORE experiment[J]. Monthly Weather Review, 2000, 128(7): 2270−2287. doi: 10.1175/1520-0493(2000)128<2270:MAAOAC>2.0.CO;2
[29]	Giordani H, Prieur L, Caniaux G. Advanced insights into sources of vertical velocity in the ocean[J]. Ocean Dynamics, 2006, 56(5/6): 513−524.
[30]	谭可易. 南海西北陆架海温盐锋三维结构及季节变化研究[D]. 湛江: 广东海洋大学, 2020. Tan Keyi. Seasonal variation of three-dimensional structure of thermal and salinity fronts in the northwestern South China Sea[D]. Zhanjiang: Guangdong Ocean University, 2020.
[31]	杨潇霄, 曹海锦, 经志友. 南海上层海洋次中尺度过程空间差异和季节变化特征[J]. 热带海洋学报, 2021, 40(5): 10−24. Yang Xiaoxiao, Cao Haijin, Jing Zhiyou. Spatial and seasonal differences of the upper-ocean submesoscale processes in the South China Sea[J]. Journal of Tropical Oceanography, 2021, 40(5): 10−24.
[32]	张雨辰, 张新城, 张金超, 等. 南海亚中尺度过程的时空特征与垂向热量输运研究[J]. 中国海洋大学学报, 2020, 50(12): 1−11. Zhang Yuchen, Zhang Xincheng, Zhang Jinchao, et al. Spatiotemporal characteristics and vertical heat transport of submesoscale processes in the South China Sea[J]. Periodical of Ocean University of China, 2020, 50(12): 1−11.
[33]	Zhu Yaohua, Wang Dingqi, Wang Yonggang, et al. Vertical velocity and transport in the South China Sea[J]. Acta Oceanologica Sinica, 2022, 41(7): 13−25. doi: 10.1007/s13131-021-1954-4
[34]	Zhang Zhiwei, Zhang Yuchen, Qiu Bo, et al. Spatiotemporal characteristics and generation mechanisms of submesoscale currents in the northeastern South China Sea revealed by numerical simulations[J]. Journal of Geophysical Research: Oceans, 2020, 125(2): e2019JC015404. doi: 10.1029/2019JC015404
[35]	郑曼立. 南海西北陆架水体及营养盐三维输运与季节变化研究[D]. 湛江: 广东海洋大学, 2019. Zheng Manli. Seasonal variability of 3D volume and nutrient transports in the northwestern South China Sea[D]. Zhanjiang: Guangdong Ocean University, 2019.
[36]	Lu Wenfang, Yan Xiaohai, Han Lu, et al. One-dimensional ocean model with three types of vertical velocities: a case study in the South China Sea[J]. Ocean Dynamics, 2017, 67(2): 253−262. doi: 10.1007/s10236-016-1029-9
[37]	黄家辉, 谢玲玲, 李强, 等. eSQG方法在南海垂向流速诊断中的应用研究[J]. 海洋学报, 2022, 44(12): 55−69. Huang Jiahui, Xie Lingling, Li Qiang, et al. Application of eSQG method in vertical velocity diagnosis in the South China Sea[J]. Haiyang Xuebao, 2022, 44(12): 55−69.
[38]	Chelton D B, Schlax M G, Samelson R M. Global observations of nonlinear mesoscale eddies[J]. Progress in Oceanography, 2011, 91(2): 167−216. doi: 10.1016/j.pocean.2011.01.002
[39]	Qiu Bo, Chen Shuiming, Klein P, et al. Reconstructability of three-dimensional upper-ocean circulation from SWOT sea surface height measurements[J]. Journal of Physical Oceanography, 2016, 46(3): 947−963. doi: 10.1175/JPO-D-15-0188.1
[40]	Qiu Bo, Chen Shuiming, Klein P, et al. Reconstructing upper-ocean vertical velocity field from sea surface height in the presence of unbalanced motion[J]. Journal of Physical Oceanography, 2020, 50(1): 55−79. doi: 10.1175/JPO-D-19-0172.1
[41]	Viúdez Á, Tintoré J, Haney R L. About the nature of the generalized omega equation[J]. Journal of the Atmospheric Sciences, 1996, 53(5): 787−795. doi: 10.1175/1520-0469(1996)053<0787:ATNOTG>2.0.CO;2
[42]	乐洲, 黄科, Mantravadi V S. 2000−2015年夏秋季孟加拉湾湾口区涡流相互作用能量学特征[J]. 热带海洋学报, 2020, 39(2): 11−24. Le Zhou, Huang Ke, Mantravadi V S. Energy characteristics of eddy-mean flow interaction in the estuary of Bay of Bengal in summer and autumn during 2000−2015[J]. Journal of Tropical Oceanography, 2020, 39(2): 11−24.
[43]	Böning C W, Budich R G. Eddy dynamics in a primitive equation model: sensitivity to horizontal resolution and friction[J]. Journal of Physical Oceanography, 1992, 22(4): 361−381. doi: 10.1175/1520-0485(1992)022<0361:EDIAPE>2.0.CO;2
[44]	Li Jianing, Dong Jihai, Yang Qingxuan, et al. Spatial-temporal variability of submesoscale currents in the South China Sea[J]. Journal of Oceanology and Limnology, 2019, 37(2): 474−485. doi: 10.1007/s00343-019-8077-1
[45]	Zhang Jinchao, Zhang Zhiwei, Qiu Bo, et al. Seasonal modulation of submesoscale kinetic energy in the upper ocean of the northeastern South China Sea[J]. Journal of Geophysical Research: Oceans, 2021, 126(11): e2021JC017695. doi: 10.1029/2021JC017695
[46]	杨少磊. 越南冷涡及其上升流的观测与研究[D]. 青岛: 中国海洋大学, 2008. Yang Shaolei. Observations and research on vietnam cold eddies and eddy-induced upwelling current[D]. Qingdao: Ocean University of China, 2008.
[47]	郑全安, 谢玲玲, 郑志文, 等. 南海中尺度涡研究进展[J]. 海洋科学进展, 2017, 35(2): 131−158. Zheng Quanan, Xie Lingling, Zheng Zhiwen, et al. Progress in research of mesoscale eddies in the South China Sea[J]. Advances in Marine Science, 2017, 35(2): 131−158.
[48]	Xie Lingling, Zheng Quanan. New insight into the South China Sea: Rossby normal modes[J]. Acta Oceanologica Sinica, 2017, 36(7): 1−3. doi: 10.1007/s13131-017-1077-0
[49]	王晓慧. 南海地区Argo轨迹资料处理与应用研究[D]. 长沙: 国防科技大学, 2017. Wang Xiaohui. Research on processing and application of Argo trajectory data in South China Sea[D]. Changsha: National University of Defense Technology, 2017.
[50]	吴日升, 李立. 南海上升流研究概述[J]. 台湾海峡, 2003, 22(2): 269−277. Wu Risheng, Li Li. Summarization of study on upwelling system in the South China Sea[J]. Journal of Oceanography in Taiwan Strait, 2003, 22(2): 269−277.
[51]	经志友, 齐义泉, 华祖林. 南海北部陆架区夏季上升流数值研究[J]. 热带海洋学报, 2008, 27(3): 1−8. Jing Zhiyou, Qi Yiquan, Hua Zulin. Numerical study on summer upwelling over northern continental shelf of South China Sea[J]. Journal of Tropical Oceanography, 2008, 27(3): 1−8.
[52]	Liu Sumin, Hong Bo, Wang Guifen, et al. Physical structure and phytoplankton community off the eastern Hainan coast during summer 2015[J]. Acta Oceanologica Sinica, 2020, 39(11): 103−114. doi: 10.1007/s13131-020-1668-z
[53]	Lu Yuanzheng, Cen Xianrong, Guo Shuangxi, et al. Spatial variability of diapycnal mixing in the South China Sea inferred from density overturn analysis[J]. Journal of Physical Oceanography, 2021, 51(11): 3417−3434. doi: 10.1175/JPO-D-20-0241.1
[54]	Wang Xiaowei, Peng Shiqiu, Liu Zhiyu, et al. Tidal mixing in the South China Sea: an estimate based on the internal tide energetics[J]. Journal of Physical Oceanography, 2016, 46(1): 107−124. doi: 10.1175/JPO-D-15-0082.1
[55]	陈更新. 南海中尺度涡的时空特征研究[D]. 青岛: 中国科学院海洋研究所, 2010. Chen Gengxin. A study on the spatiotemporal characteristics of mesoscale eddies in the South China Sea[D]. Qingdao: The Institute of Oceanology, Chinese Academy of Sciences, 2010.
[56]	兰健, 洪洁莉, 李丕学. 南海西部夏季冷涡的季节变化特征[J]. 地球科学进展, 2006, 21(11): 1145−1152. Lan Jian, Hong Jieli, Li Pixue. Seasonal variability of cool-core eddy in the Western South China Sea[J]. Advances in Earth Science, 2006, 21(11): 1145−1152.
[57]	Masumoto Y, Sasaki H, Kagimoto T, et al. A fifty-year eddy-resolving simulation of the world ocean-preliminary outcomes of OFES (OGCM for the Earth Simulator)[J]. Journal of the Earth Simulator, 2004, 1: 35−56.
[58]	Yang Peiran, Jing Zhao, Sun Bingrong, et al. On the upper-ocean vertical eddy heat transport in the Kuroshio Extension. Part I: variability and dynamics[J]. Journal of Physical Oceanography, 2021, 51(1): 229−246. doi: 10.1175/JPO-D-20-0068.1