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 210044, China
3.
Southern Marine Science and Engineering Guangdong Laboratory (Zhuhai), Zhuhai 519000, 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 316000, China
6.
College of Hydraulic Science and Engineering, Yangzhou University, Yangzhou 225009, China
Funds:
The National Key Research Programs of China under contract Nos 2017YFA0604100 and 2016YFC1401407; 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.
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 (10^{3} m^{2}/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.
Figure 1. Calculation of eddy diffusivity at the 30th isoneutral layer (27.65–27.70 kg/m) by the linear regression analysis. a. Distribution of mesoscale thickness flux (black arrows, units: m^{5}/(kg·s)) and magnitude of large-scale isoneutral thickness gradient (color, units: 10^{3} m^{4}/kg) at the 30th isoneutral layer. The magenta asterisk and rectangular area (3° by 3°) indicate the calculation target point and calculation region, respectively. b. Linear regression of eddy diffusivity at the center of the magenta box in Fig. 1a. The abscissa is the square of the large-scale thickness gradient (units: 10^{−6} m^{−6}/kg^{2}), and the ordinate represents the inverse of the product of mesoscale thickness flux and large scale thickness gradient (units: 10^{−4} m^{8}/(kg^{2}·s)). The blue dashed lines are the boundaries of the 95% confidence interval. The symbols “S” and “R” are the linear regression coefficient and Pearson correlation coefficient, respectively.
Figure 2. A snapshot of coherent mesoscale eddies on February 25, 2005 in an arbitrary area of the Southern Ocean at sea surface. Black asterisks indicate the coherent mesoscale eddy centers. Blue and red curves represent the boundaries of coherent mesoscale cyclonic eddies and anticyclonic eddies, respectively. Black vectors correspond to velocity anomalies. The two eddies with bold dotted boundaries are analyzed in Subsection 5.1 and shown in Fig. 6.
Figure 3. Distribution of multi-year (2005–2010) average sea surface height anomaly (a, b, units: m) and sea surface eddy kinetic energy (c, d, units: cm^{2}/s^{2}), calculated from SOSE data (a, c) and AVISO data (b, d). The blue and red curves in a and c denote the multi-year average position of the Subpolar Antarctic Front and Antarctic Front, respectively.
Figure 4. Spatial distribution of the eddy diffusivity in the Southern Ocean. (a) and (b) correspond to 27.15–27.20 kg/m^{3} and 27.95–28.00 kg/m^{3} layers in the isoneutral coordinate system. (c) and (d) correspond to 60–72 m and 826–1 092 m layers in the Cartesian coordinate system. Colors represent the eddy diffusivity (units: 10^{3} m^{2}/s). The blue and red curves are the multi-year average position of the Subpolar Antarctic Front (SAF) and Antarctic Front (AF), respectively.
Figure 5. Zonal mean of the multi-year (2005–2010) average eddy diffusivity in (a) isoneutral coordinate system (units: 10^{3} m^{2}/s) and (b) Cartesian coordinate system. The mean isobaths (50 m, 200 m, 500 m, 1 500 m and 3 500 m) and mean isoneutral contours (26.2 kg/m^{3}, 27.2 kg/m^{3}, 27.7 kg/m^{3}, 28.0 kg/m^{3}, 28.2 kg/m^{3}, 28.3 kg/m^{3} and 28.4 kg/m^{3}) are labeled in a and b, respectively. The blue and red triangles in b are the multi-year average position of the Subpolar Antarctic Front and Antarctic Front, respectively.
Figure 6. Three-dimensional structures of two coherent mesoscale eddy cases (a, c) and their vertical eddy intensity distributions (b, d). The meridional (zonal) temperature anomalies across the eddy center are shown in $ xoz $ ($ yoz $) coordinate plane. (a) and (b) are for the cyclonic eddy, (c) and (d) are for the anticyclonic eddy. Colors represent potential temperature anomaly (units: °C), which is the deviation from the large-scale average using a temporal-spatial filtering method. The blue and red curves indicate the boundaries of the coherent mesoscale cyclonic and anticyclonic eddy on the two-dimensional layers, which is defined as the outermost enclosed local stream function. White vectors indicate velocity anomaly (units: m/s), and grey outlines are the three-dimensional boundary of the eddy. Black asterisks indicate the eddy centers. Black dashed lines in Figs 6b and d indicate one standard deviation.
Figure 7. Number of multi-year (2005–2010) average coherent mesoscale cyclonic eddy (a) and anticyclonic eddy (b) based on the eddy snapshot counting method. Colors represent the number of coherent mesoscale eddies (units: 10^{2} a^{−1}). The blue and red triangles are the position of the multi-year average Subpolar Antarctic Front and Antarctic Front, respectively. The magenta curves indicate the contours with eddy numbers of 100 a^{−1} and 200 a^{−1}.
Figure 8. Distribution of the multi-year (2005–2010) average first baroclinic Rossby deformation radius (a) and eddy radius of coherent mesoscale cyclonic eddies (b) and anticyclonic eddies (c). The blue shaded area in a represents one standard deviation. Colors in b and c represent the radius of the coherent mesoscale eddy (units: 10^{3} m).
Figure 9. Distribution of multi-year (2005–2010) average intensity for (a) coherent mesoscale cyclonic eddies and (b) anticyclonic eddies. Colors represent the normalized intensity. The magenta curves indicate the isolines with the eddy intensity of 0.05 and 0.1, respectively.
Figure 10. Distribution of multi-year (2005–2010) average of coherent mesoscale eddy penetration depth (a, units: 10^{3} m), lifespan (b, units: d) and wind stress (c, units: N/m^{2}). The blue and red curves are for coherent mesoscale cyclonic and anticyclonic eddies, respectively. The error bar is also shown in the figure. The green dotted lines are the meridional average eddy penetration depth (a), eddy lifespan (b) for all coherent mesoscale eddies and wind stress (c). The magenta dotted line is the multi-year average latitude of the Subpolar Antarctic Front.
Figure 11. Scatter plots of normalized eddy activity against normalized eddy diffusivity for (a) coherent mesoscale cyclonic eddies, (b) anticyclonic eddies, and (c) all the eddies regardless of polarity. The symbols “S” and “R” are the slope of the regressed line (black line) and Pearson correlation coefficient, respectively. The colors represent latitudes, and the dashed black lines are the boundaries of the 95% confidence interval.