Eddy diffusivity and coherent mesoscale eddy analysis in the Southern Ocean

Wenjin Sun; Jingsong Yang; Wei Tan; Yu Liu; Baojun Zhao; Yijun He; Changming Dong

doi:10.1007/s13131-021-1881-4

Volume 40 Issue 10

Oct. 2021

Turn off MathJax

Article Contents

Article Navigation > Acta Oceanologica Sinica > 2021 > 40(10): 1-16

Wenjin Sun, Jingsong Yang, Wei Tan, Yu Liu, Baojun Zhao, Yijun He, Changming Dong. Eddy diffusivity and coherent mesoscale eddy analysis in the Southern Ocean[J]. Acta Oceanologica Sinica, 2021, 40(10): 1-16. doi: 10.1007/s13131-021-1881-4

Citation:

Wenjin Sun, Jingsong Yang, Wei Tan, Yu Liu, Baojun Zhao, Yijun He, Changming Dong. Eddy diffusivity and coherent mesoscale eddy analysis in the Southern Ocean[J]. Acta Oceanologica Sinica, 2021, 40(10): 1-16. doi: 10.1007/s13131-021-1881-4

Citation:

PDF( 1745 KB)

Eddy diffusivity and coherent mesoscale eddy analysis in the Southern Ocean

doi: 10.1007/s13131-021-1881-4

Wenjin Sun^{1, 2, 3},
Jingsong Yang^{2, 3},
Wei Tan⁴,
Yu Liu^{3, 5},
Baojun Zhao⁶,
Yijun He¹,
Changming Dong^{1, 3
,
,}

1.
School of Marine Sciences, Nanjing University of Information Science and Technology, Nanjing 210044, China
2.
State Key Laboratory of Satellite Ocean Environment Dynamics, Second Institute of Oceanography, Ministry of Natural Resources, Hangzhou 310012, China
3.
Southern Marine Science and Engineering Guangdong Laboratory (Zhuhai), Zhuhai 519080, China
4.
College of Ocean Science and Engineering, Shandong University of Science and Technology, Qingdao 266590, China
5.
Marine Science and Technology College, Zhejiang Ocean University, Zhoushan 316022, China
6.
College of Hydraulic Science and Engineering, Yangzhou University, Yangzhou 225009, China

Funds: The National Key Research Programs of China under contract No. 2017YFA0604100; the National Natural Science Foundation of China under contract Nos 41906008, 41806039 and 41706205; the Open Fund of State Key Laboratory of Satellite Ocean Environment Dynamics, Second Institute of Oceanography, MNR under contract No. QNHX2022; the Startup Foundation for Introducing Talent of Nanjing University of Information Science & Technology under contract No. 2019r049; the Startup Foundation for Introducing Talent of Zhejiang Ocean University; the Innovation Group Project of Southern Marine Science and Engineering Guangdong Laboratory (Zhuhai) under contract No. 311020004.

More Information

Corresponding author: E-mail: cmdong@nuist.edu.cn
Received Date: 2021-02-10
Accepted Date: 2021-06-13

Available Online: 2021-08-30

Publish Date: 2021-10-30

Abstract

Abstract

The spatial distribution of eddy diffusivity, basic characteristics of coherent mesoscale eddies and their relationship are analyzed from numerical model outputs in the Southern Ocean. Mesoscale fluctuation information is obtained by a temporal-spatial filtering method, and the eddy diffusivity is calculated using a linear regression analysis between isoneutral thickness flux and large-scale isoneutral thickness gradient. The eddy diffusivity is on the order of O (10³ m²/s) with a significant spatial variation, and it is larger in the area with strong coherent mesoscale eddy activity. The mesoscale eddies are mainly located in the upper ocean layer, with the average intensity no larger than 0.2. The mean radius of the coherent mesoscale cyclonic (anticyclonic) eddy gradually decays from (121.2±10.4) km ((117.8±9.6) km) at 30°S to (43.9±5.3) km ((44.7±4.9) km) at 65°S. Their vertical penetration depths (lifespans) are deeper (longer) between the northern side of the Subpolar Antarctic Front and 48°S. The normalized eddy diffusivity and coherent mesoscale eddy activity show a significant positive correlation, indicating that coherent mesoscale eddy plays an important role in eddy diffusivity.
- eddy diffusivity,
- transient mesoscale eddy,
- coherent mesoscale eddy,
- eddy penetration depth,
- Southern Ocean

FullText(HTML)

References(93)

References

[1]	Abernathey R, Ferreira D, Klocker A. 2013. Diagnostics of isopycnal mixing in a circumpolar channel. Ocean Modelling, 72: 1–16. doi: 10.1016/j.ocemod.2013.07.004
[2]	Abernathey R, Marshall J, Mazloff M, et al. 2010. Enhancement of mesoscale eddy stirring at steering levels in the Southern Ocean. Journal of Physical Oceanography, 40(1): 170–184. doi: 10.1175/2009JPO4201.1
[3]	Adams K A, Hosegood P, Taylor J R, et al. 2017. Frontal circulation and submesoscale variability during the formation of a Southern Ocean mesoscale eddy. Journal of Physical Oceanography, 47(7): 1737–1753. doi: 10.1175/JPO-D-16-0266.1
[4]	Aguiar A C B, Peliz Á, Carton X. 2013. A census of Meddies in a long-term high-resolution simulation. Progress in Oceanography, 116: 80–94. doi: 10.1016/j.pocean.2013.06.016
[5]	Bachman S, Fox-Kemper B. 2013. Eddy parameterization challenge suite I: Eady spindown. Ocean Modelling, 64: 12–28. doi: 10.1016/j.ocemod.2012.12.003
[6]	Bachman S D, Fox-Kemper B, Bryan F O. 2015. A tracer-based inversion method for diagnosing eddy-induced diffusivity and advection. Ocean Modelling, 86: 1–14. doi: 10.1016/j.ocemod.2014.11.006
[7]	Bachman D, Fox-Kemper B, Bryan F O. 2020. A diagnosis of anisotropic eddy diffusion from a high-resolution global ocean model. Journal of Advances in Modeling Earth Systems, 12(2): e2019MS001904
[8]	Bachman S D, Marshall D P, Maddison J R, et al. 2017. Evaluation of a scalar eddy transport coefficient based on geometric constraints. Ocean Modelling, 109: 44–54. doi: 10.1016/j.ocemod.2016.12.004
[9]	Bryan K, Dukowicz J K, Smith R D. 1999. On the mixing coefficient in the parameterization of bolus velocity. Journal of Physical Oceanography, 29(9): 2442–2456. doi: 10.1175/1520-0485(1999)029<2442:OTMCIT>2.0.CO;2
[10]	Byrne D, Münnich M, Frenger I, Gruber N. 2016. Mesoscale atmosphere ocean coupling enhances the transfer of wind energy into the ocean. Nature Communications, 7: s11867. doi: 10.1038/ncomms11867
[11]	Canuto V M, Cheng Y, Howard A M, et al. 2019. Three-dimensional, space-dependent mesoscale diffusivity: derivation and implications. Journal of Physical Oceanography, 49(4): 1055–1074. doi: 10.1175/JPO-D-18-0123.1
[12]	Chapman C, Sallée J B. 2017. Isopycnal mixing suppression by the Antarctic Circumpolar Current and the Southern Ocean meridional overturning circulation. Journal of Physical Oceanography, 47(8): 2023–2045. doi: 10.1175/JPO-D-16-0263.1
[13]	Chelton D B, de Szoeke R A, Schlax M G, et al. 1998. Geographical variability of the first baroclinic Rossby radius of deformation. Journal of Physical Oceanography, 28(3): 433–460. doi: 10.1175/1520-0485(1998)028<0433:GVOTFB>2.0.CO;2
[14]	Chelton D B, Schlax M G, Samelson R M. 2011. Global observations of nonlinear mesoscale eddies. Progress in Oceanography, 91(2): 167–216. doi: 10.1016/j.pocean.2011.01.002
[15]	Chen Ru, Flierl G R, Wunsch C. 2014. A description of local and nonlocal eddy-mean flow interaction in a global eddy-permitting state estimate. Journal of Physical Oceanography, 44(9): 2336–2352. doi: 10.1175/JPO-D-14-0009.1
[16]	Chen Gengxin, Gan Jianping, Xie Qiang, et al. 2012. Eddy heat and salt transports in the South China Sea and their seasonal modulations. Journal of Geophysical Research: Oceans, 117: C05021
[17]	Chen Gengxin, Hou Yijun, Chu Xiaoqing. 2011. Mesoscale eddies in the South China Sea: Mean properties, spatiotemporal variability, and impact on thermohaline structure. Journal of Geophysical Research: Oceans, 116: C06018
[18]	Chiswell S M. 2013. Lagrangian time scales and eddy diffusivity at 1000 m compared to the surface in the South Pacific and Indian oceans. Journal of Physical Oceanography, 43(12): 2718–2732. doi: 10.1175/JPO-D-13-044.1
[19]	Couvelard X, Caldeira R M A, Araújo I B, et al. 2012. Wind mediated vorticity-generation and eddy-confinement, leeward of the Madeira Island: 2008 numerical case study. Dynamics of Atmospheres and Oceans, 58: 128–149. doi: 10.1016/j.dynatmoce.2012.09.005
[20]	Dawson H R S, Strutton P G, Gaube P. 2018. The unusual surface chlorophyll signatures of Southern Ocean eddies. Journal of Geophysical Research: Oceans, 123(9): 6053–6069. doi: 10.1029/2017JC013628
[21]	Dong Changming, Lin Xiayan, Liu Yu, et al. 2012. Three-dimensional oceanic eddy analysis in the Southern California Bight from a numerical product. Journal of Geophysical Research: Oceans, 117(C7): C00H14
[22]	Dong Changming, McWilliams J C, Liu Yu, et al. 2014. Global heat and salt transports by eddy movement. Nature Communications, 5: 3294. doi: 10.1038/ncomms4294
[23]	Eden C. 2006. Thickness diffusivity in the Southern Ocean. Geophysical Research Letters, 33(11): L11606
[24]	Eden C, Greatbatch R J. 2008. Towards a mesoscale eddy closure. Ocean Modelling, 20(3): 223–239. doi: 10.1016/j.ocemod.2007.09.002
[25]	Eden C, Greatbatch R J, Willebrand J. 2007. A diagnosis of thickness fluxes in an eddy-resolving model. Journal of Physical Oceanography, 37(3): 727–742. doi: 10.1175/JPO2987.1
[26]	Ellwood M J, Strzepek R F, Strutton P G, et al. 2020. Distinct iron cycling in a Southern Ocean eddy. Nature Communications, 11: 825. doi: 10.1038/s41467-020-14464-0
[27]	Ferrari R, Wunsch C. 2009. Ocean circulation kinetic energy: reservoirs, sources, and sinks. Annual Review of Fluid Mechanics, 41: 253–282. doi: 10.1146/annurev.fluid.40.111406.102139
[28]	Fox-Kemper B, Adcroft A, Böning CW, et al. 2019. Challenges and prospects in ocean circulation models. Frontiers in Marine Science, 6: 65. doi: 10.3389/fmars.2019.00065
[29]	Frenger I, Gruber N, Knutti R, et al. 2013. Imprint of Southern Ocean eddies on winds, clouds and rainfall. Nature Geoscience, 6: 608–612. doi: 10.1038/ngeo1863
[30]	Frenger I, Münnich M, Gruber N. 2018. Imprint of Southern Ocean mesoscale eddies on chlorophyll. Biogeosciences, 15: 4781–4798. doi: 10.5194/bg-15-4781-2018
[31]	Frenger I, Münnich M, Gruber N, et al. 2015. Southern Ocean eddy phenomenology. Journal of Geophysical Research: Oceans, 120(11): 7413–7449. doi: 10.1002/2015JC011047
[32]	Gent P R. 2011. The Gent–McWilliams parameterization: 20/20 hindsight. Ocean Modelling, 39(1–2): 2–9
[33]	Gent P R, McWilliams J C. 1990. Isopycnal mixing in ocean circulation models. Journal of Physical Oceanography, 20(1): 150–155. doi: 10.1175/1520-0485(1990)020<0150:IMIOCM>2.0.CO;2
[34]	Gordon A L, Molinelli E, Baker T. 1978. Large-scale relative dynamic topography of the Southern Ocean. Journal of Geophysical Research: Oceans, 83(C6): 3023–3032. doi: 10.1029/JC083iC06p03023
[35]	Griesel A, Eden C, Koopmann N, et al. 2015. Comparing isopycnal eddy diffusivities in the Southern Ocean with predictions from linear theory. Ocean Modelling, 94: 33–45. doi: 10.1016/j.ocemod.2015.08.001
[36]	Griesel A, McClean J L, Gille S T, et al. 2014. Eulerian and Lagrangian isopycnal eddy diffusivities in the Southern Ocean of an eddying model. Journal of Physical Oceanography, 44(2): 644–661. doi: 10.1175/JPO-D-13-039.1
[37]	Grooms I, Kleiber W. 2019. Diagnosing, modeling, and testing a multiplicative stochastic gent-mcwilliams parameterization. Ocean Modelling, 133: 1–10. doi: 10.1016/j.ocemod.2018.10.009
[38]	Haigh M, Sun Luolin, Shevchenko I, et al. 2020. Tracer-based estimates of eddy-induced diffusivities. Deep-Sea Research Part I: Oceanographic Research Papers, 160: 103264. doi: 10.1016/j.dsr.2020.103264
[39]	Haller G, Hadjighasem A, Farazmand M, et al. 2016. Defining coherent vortices objectively from the vorticity. Journal of Fluid Mechanics, 795: 136–173. doi: 10.1017/jfm.2016.151
[40]	Hausmann U, McGillicuddy D J Jr, Marshall J. 2017. Observed mesoscale eddy signatures in Southern Ocean surface mixed-layer depth. Journal of Geophysical Research: Oceans, 122(1): 617–635. doi: 10.1002/2016JC012225
[41]	He Qingyou, Zhan Haigang, Cai Shuqun, et al. 2018. A new assessment of mesoscale eddies in the South China Sea: surface features, three-dimensional structures, and thermohaline transports. Journal of Geophysical Research: Oceans, 123(7): 4906–4929. doi: 10.1029/2018JC014054
[42]	Hu Jianyu, Gan Jianping, Sun Zhenyu, et al. 2011. Observed three-dimensional structure of a cold eddy in the southwestern South China Sea. Journal of Geophysical Research: Oceans, 116: C05016
[43]	Jackett D R, McDougall T J. 1997. A neutral density variable for the world’s oceans. Journal of Physical Oceanography, 27(2): 237–263. doi: 10.1175/1520-0485(1997)027<0237:ANDVFT>2.0.CO;2
[44]	Ji Jinlin, Dong Changming, Zhang Biao, et al. 2017. An oceanic eddy statistical comparison using multiple observational data in the Kuroshio Extension Region. Acta Oceanologica Sinica, 36(3): 1–7. doi: 10.1007/s13131-016-0882-1
[45]	Klocker A, Abernathey R. 2014. Global patterns of mesoscale eddy properties and diffusivities. Journal of Physical Oceanography, 44(3): 1030–1046. doi: 10.1175/JPO-D-13-0159.1
[46]	Klocker A, Marshall D P. 2014. Advection of baroclinic eddies by depth mean flow. Geophysical Research Letters, 41(10): 3517–3521. doi: 10.1002/2014GL060001
[47]	LaCasce J H, Ferrari R, Marshall J, et al. 2014. Float-derived isopycnal diffusivities in the DIMES experiment. Journal of Physical Oceanography, 44(2): 764–780. doi: 10.1175/JPO-D-13-0175.1
[48]	Li Qiuyang, Sun Liang, Xu Chi. 2018. The lateral eddy viscosity derived from the decay of oceanic mesoscale eddies. Open Journal of Marine Science, 8: 152–172. doi: 10.4236/ojms.2018.81008
[49]	Lin Xiayan, Dong Changming, Chen Dake, et al. 2015. Three-dimensional properties of mesoscale eddies in the South China Sea based on eddy-resolving model output. Deep-Sea Research Part I: Oceanographic Research Papers, 99: 46–64. doi: 10.1016/j.dsr.2015.01.007
[50]	Liu Yu, Dong Changming, Liu Xiaohui, et al. 2017. Antisymmetry of oceanic eddies across the Kuroshio over a shelfbreak. Scientific Reports, 7(1): 6761. doi: 10.1038/s41598-017-07059-1
[51]	Lu Jianhua, Speer K. 2010. Topography, jets, and eddy mixing in the Southern Ocean. Journal of Marine Research, 68(3–4): 479–502
[52]	Lu Jianhua, Wang Fuchang, Liu Hailong, et al. 2016. Stationary mesoscale eddies, upgradient eddy fluxes, and the anisotropy of eddy diffusivity. Geophysical Research Letters, 43(2): 743–751. doi: 10.1002/2015GL067384
[53]	Mak J, Maddison J R, Marshall D P. 2016. A new gauge-invariant method for diagnosing eddy diffusivities. Ocean Modelling, 104: 252–268. doi: 10.1016/j.ocemod.2016.06.006
[54]	Marshall D P, Maddison J R, Berlo P S. 2012. A framework for parameterizing eddy potential vorticity fluxes. Journal of Physical Oceanography, 42(4): 539–557. doi: 10.1175/JPO-D-11-048.1
[55]	Marshall J, Shuckburgh E, Jones H, et al. 2006. Estimates and implications of surface eddy diffusivity in the Southern Ocean derived from tracer transport. Journal of Physical Oceanography, 36(9): 1806–1821. doi: 10.1175/JPO2949.1
[56]	Marshall J, Shutts G. 1981. A note on rotational and divergent eddy fluxes. Journal of Physical Oceanography, 11(12): 1677–1680. doi: 10.1175/1520-0485(1981)011<1677:ANORAD>2.0.CO;2
[57]	Mazloff M R, Heimbach P, Wunsch C. 2010. An eddy-permitting Southern Ocean State Estimate. Journal of Physical Oceanography, 40(5): 880–899. doi: 10.1175/2009JPO4236.1
[58]	McDougall T J. 1987. Neutral surface. Journal of Physical Oceanography, 17(11): 1950–1964. doi: 10.1175/1520-0485(1987)017<1950:NS>2.0.CO;2
[59]	McDougall T J, McIntosh P C. 1996. The temporal-residual-mean velocity. Part I: Derivation and the scalar conservation equations. Journal of Physical Oceanography, 26(12): 2653–2665. doi: 10.1175/1520-0485(1996)026<2653:TTRMVP>2.0.CO;2
[60]	McDougall T J, McIntosh P C. 2001. The temporal-residual-mean velocity. Part II: Isopycnal interpretation and the tracer and momentum equations. Journal of Physical Oceanography, 31(5): 1222–1246. doi: 10.1175/1520-0485(2001)031<1222:TTRMVP>2.0.CO;2
[61]	Medvedev A S, Greatbatch R J. 2004. On advection and diffusion in the mesosphere and lower thermosphere: The role of rotational fluxes. Journal of Geophysical Research: Atmospheres, 109: D07104
[62]	Moreau S, Penna A D, Llort J, et al. 2017. Eddy-induced carbon transport across the Antarctic Circumpolar Current. Global Biogeochemical Cycles, 31(9): 1368–1386. doi: 10.1002/2017GB005669
[63]	Nencioli F, Dong Changming, Dickey T, et al. 2010. A vector geometry-based eddy detection algorithm and its application to a high-resolution numerical model product and high-frequency radar surface velocities in the Southern California Bight. Journal of Atmospheric and Oceanic Technology, 27(3): 564–579. doi: 10.1175/2009JTECHO725.1
[64]	Ni Qinbiao, Zhai Xiaoming, Wang Guihua, et al. 2020. Random movement of mesoscale eddies in the global ocean. Journal of Physical Oceanography, 50(8): 2341–2357. doi: 10.1175/JPO-D-19-0192.1
[65]	Nummelin A, Busecke J J M, Haine T W N, et al. 2021. Diagnosing the scale- and space-dependent horizontal eddy diffusivity at the global surface ocean. Journal of Physical Oceanography, 51(2): 279–297. doi: 10.1175/JPO-D-19-0256.1
[66]	Okubo A. 1970. Horizontal dispersion of floatable particles in the vicinity of velocity singularities such as convergences. Deep-Sea Research and Oceanographic Abstracts, 17(3): 445–454. doi: 10.1016/0011-7471(70)90059-8
[67]	Orsi A H, Nowlin W D Jr, Whitworth T III. 1993. On the circulation and stratification of the weddell gyre. Deep-Sea Research Part I: Oceanographic Research Papers, 40(1): 169–203. doi: 10.1016/0967-0637(93)90060-G
[68]	Patel R S, Llort J, Strutton P G, et al. 2020. The biogeochemical structure of Southern Ocean mesoscale eddies. Journal of Geophysical Research: Oceans, 125(8): e2020JC016115
[69]	Poulsen M B, Jochum M, Nuterman R. 2018. Parameterized and resolved Southern Ocean eddy compensation. Ocean Modelling, 124: 1–15. doi: 10.1016/j.ocemod.2018.01.008
[70]	Pujol M I, Faugère Y, Taburet G, et al. 2016. DUACS DT2014: The new multi-mission altimeter data set reprocessed over 20 years. Ocean Science, 12: 1067–1090. doi: 10.5194/os-12-1067-2016
[71]	Rhines P B. 2001. Mesoscale eddies. In: Steele M, Turekian K K, Thorpe S A, eds. Encyclopedia of Ocean Science. San Diego, CA, USA: Academic Press, 1982–1992
[72]	Rohr T, Harrison C, Long M C, et al. 2020. The simulated biological response to Southern Ocean eddies via biological rate modification and physical transport. Global Biogeochemical Cycles, 34(6): e2019GB006385
[73]	Rypina I I, Kirincich A, Lentz S, et al. 2016. Investigating the eddy diffusivity concept in the coastal ocean. Journal of Physical Oceanography, 46(7): 2201–2218. doi: 10.1175/JPO-D-16-0020.1
[74]	Sadarjoen I A, Post F H. 2000. Detection, quantification, and tracking of vortices using streamline geometry. Computers & Graphics, 24(3): 333–341
[75]	Solovev M, Stone P H, Malanotte-Rizzoli P. 2002. Assessment of mesoscale eddy parameterizations for a single-basin coarse-resolution ocean model. Journal of Geophysical Research: Oceans, 107(C9): 9-1–9-19
[76]	Song H, Long M C, Gaube P, et al. 2018. Seasonal variation in the correlation between anomalies of sea level and chlorophyll in the Antarctic Circumpolar Current. Geophysical Research Letters, 45(10): 5011–5019. doi: 10.1029/2017GL076246
[77]	Stammer D. 1997. Global characteristics of ocean variability estimated from regional TOPEX/POSEIDON altimeter measurements. Journal of Physical Oceanography, 27(8): 1743–1769. doi: 10.1175/1520-0485(1997)027<1743:GCOOVE>2.0.CO;2
[78]	Stanley Z, Bachman S D, Grooms I. 2020. Vertical structure of ocean mesoscale eddies with implications for parameterizations of tracer transport. Journal of Advances in Modeling Earth Systems, 12(10): e2020MS002151
[79]	Sun Wenjin, Dong Changming, Tan Wei, et al. 2018. Vertical structure anomalies of oceanic eddies and eddy-induced transports in the South China Sea. Remote Sensing, 10(5): 795. doi: 10.3390/rs10050795
[80]	Sun Wenjin, Dong Changming, Tan Wei, et al. 2019. Statistical characteristics of cyclonic warm-core eddies and anticyclonic cold-core eddies in the North Pacific based on remote sensing data. Remote Sensing, 11(2): 208. doi: 10.3390/rs11020208
[81]	Sun Wenjin, Dong Changming, Wang Ruyun, et al. 2017. Vertical structure anomalies of oceanic eddies in the Kuroshio Extension region. Journal of Geophysical Research: Oceans, 122(2): 1476–1496. doi: 10.1002/2016JC012226
[82]	Treguier A M, Held I M, Larichev V D. 1997. Parameterization of quasigeostrophic eddies in primitive equation ocean models. Journal of Physical Oceanography, 27(4): 567–580. doi: 10.1175/1520-0485(1997)027<0567:POQEIP>2.0.CO;2
[83]	Visbeck M, Marshall J, Haine T, et al. 1997. Specification of eddy transfer coefficients in coarse-resolution ocean circulation models. Journal of Physical Oceanography, 27(3): 381–402. doi: 10.1175/1520-0485(1997)027<0381:SOETCI>2.0.CO;2
[84]	Vollmer L, Eden C. 2013. A global map of meso-scale eddy diffusivities based on linear stability analysis. Ocean Modelling, 72: 198–209. doi: 10.1016/j.ocemod.2013.09.006
[85]	Waite A M, Stemmann L, Guidi L, et al. 2016. The wineglass effect shapes particle export to the deep ocean in mesoscale eddies. Geophysical Research Letters, 43(18): 9791–9800. doi: 10.1002/2015GL066463
[86]	Wang Zifeng, Li Qiuyang, Sun Liang, et al. 2015. The most typical shape of oceanic mesoscale eddies from global satellite sea level observations. Frontiers of Earth Science, 9: 202–208. doi: 10.1007/s11707-014-0478-z
[87]	Weiss J. 1991. The dynamics of enstrophy transfer in two-dimensional hydrodynamics. Physica D: Nonlinear Phenomena, 48(2–3): 273–294
[88]	Wolfram P J, Ringler T D, Maltrud M E, et al. 2015. Diagnosing isopycnal diffusivity in an eddying, idealized midlatitude ocean basin via lagrangian, in situ, global, high-performance particle tracking (LIGHT). Journal of Physical Oceanography, 45(8): 2114–2133. doi: 10.1175/JPO-D-14-0260.1
[89]	Yang Xiao, Xu Guangjun, Liu Yu, et al. 2020. Multi-source data analysis of mesoscale eddies and their effects on surface chlorophyll in the Bay of Bengal. Remote Sensing, 12(21): 3485. doi: 10.3390/rs12213485
[90]	Ying Y K, Maddison J R, Vanneste J. 2019. Bayesian inference of ocean diffusivity from lagrangian trajectory data. Ocean Modelling, 140: 101401. doi: 10.1016/j.ocemod.2019.101401
[91]	Zhang Zhiwei, Tian Jiwei, Qiu Bo, et al. 2016. Observed 3D structure, generation, and dissipation of oceanic mesoscale eddies in the South China Sea. Scientific Reports, 6: 24349. doi: 10.1038/srep24349
[92]	Zhang Zhengguang, Wang Wei, Qiu Bo. 2014. Oceanic mass transport by mesoscale eddies. Science, 345(6194): 322–324. doi: 10.1126/science.1252418
[93]	Zhang Zhengguang, Zhang Yu, Wang Wei, et al. 2013. Universal structure of mesoscale eddies in the ocean. Geophysical Research Letters, 40(14): 3677–3681. doi: 10.1002/grl.50736