Eddy Shape Research Articles

A high-resolution marine mercury model MITgcm-ECCO2-Hg with online biogeochemistry

Abstract. Mercury (Hg) is a global persistent contaminant. Modeling studies are useful means of synthesizing a current understanding of the Hg cycle. Previous studies mainly use coarse-resolution models, which makes it impossible to analyze the role of turbulence in the Hg cycle and inaccurately describes the transport of kinetic energy. Furthermore, all of them are coupled with offline biogeochemistry, and therefore they cannot respond to short-term variability in oceanic Hg concentration. In our approach, we utilize a high-resolution ocean model (MITgcm-ECCO2, referred to as “high-resolution-MITgcm”) coupled with the concurrent simulation of biogeochemistry processes from the Darwin Project (referred to as “online”). This integration enables us to comprehensively simulate the global biogeochemical cycle of Hg with a horizontal resolution of 1/5∘. The finer portrayal of surface Hg concentrations in estuarine and coastal areas, strong western boundary flow and upwelling areas, and concentration diffusion as vortex shapes demonstrate the effects of turbulence that are neglected in previous models. Ecological events such as algal blooms can cause a sudden enhancement of phytoplankton biomass and chlorophyll concentrations, which can also result in a dramatic change in particle-bound Hg (HgaqP) sinking flux simultaneously in our simulation. In the global estuary region, including riverine Hg input in the high-resolution model allows us to reveal the outward spread of Hg in an eddy shape driven by fine-scale ocean currents. With faster current velocities and diffusion rates, our model captures the transport and mixing of Hg from river discharge in a more accurate and detailed way and improves our understanding of Hg cycle in the ocean.

An ensemble Synthetic Eddy Method for accurate treatment of inhomogeneous turbulence

An ensemble approach to generating turbulent inflow boundary conditions using the Synthetic Eddy Method is proposed that improves signal accuracy in recovering target statistics for inhomogeneous turbulence while reducing the cost of generating an inflow signal. This is accomplished by eliminating typical restrictions related to the Synthetic Eddy Method such as homogeneous turbulence, limited shape functions, random eddy placement, and uniform synthetic eddy convection velocity. The approach gives flexibility and freedom to prescribe arbitrary synthetic eddy length scales, shape functions, eddy placement, and convective velocities while accurately reproducing input Reynolds stresses and maintaining the simplicity of the original method. Three examples of leveraging this flexibility to provide accurate turbulent length scale inhomogeneity and reduce the required number of generated synthetic eddies are provided. Turbulent inflow signals for a channel flow configuration are generated using six variations and the resulting signal accuracy and costs are compared. These inflow signals are applied to a set of Large Eddy Simulations of turbulent channel flow and show favorable results over the original method in terms of the skin friction coefficient convergence, Q-criterion plots, and computed Reynolds stresses. The ensemble approach is shown to be more accurate in reproducing desired turbulent characteristics compared to the original Synthetic Eddy Method, in a simpler manner compared to recent variants of the method.

META3.1exp: a new global mesoscale eddy trajectory atlas derived from altimetry

Abstract. This paper presents the new global Mesoscale Eddy Trajectory Atlases (META3.1exp DT all-satellites, https://doi.org/10.24400/527896/a01-2021.001, Pegliasco et al., 2021a; and META3.1exp DT two-satellites, https://doi.org/10.24400/527896/a01-2021.002, Pegliasco et al., 2021b), composed of eddy identifications and trajectories produced with altimetric maps. The detection method used is inherited from the py-eddy-tracker (PET) algorithm developed by Mason et al. (2014), and is optimized to efficiently manage large datasets, and thus long time series. These products are an improvement on the earlier META2.0 product, which was produced by SSALTO/DUACS and distributed by AVISO+ (https://aviso.altimetry.fr, last access: 8 March 2022) with support from CNES, in collaboration with Oregon State University and support from NASA, and based on the Chelton et al. (2011) code. META3.1exp provides supplementary eddy information, such as eddy shapes, eddy edges, maximum speed contours, and mean eddy speed profiles from the center to the periphery. The tracking algorithm is based on overlapping contours, includes virtual observations, and acts as a filter with respect to the shortest trajectories. The absolute dynamic topography (ADT) field is now used for eddy detection, instead of the previous sea level anomaly (SLA) maps, in order to better represent the dynamics in the more energetic oceanic regions and in the vicinity of coasts and islands. To evaluate the impact of the changes from META2.0 to META3.1exp, a comparison methodology has been applied. The similarity coefficient (SC) is based on the ratio of the eddy overlaps to their cumulative area, and allows for extensive comparison of the different datasets in terms of geographic distribution, statistics on the main physical characteristics, changes in the lifetimes of the trajectories, etc. After evaluating the impact of each change separately, we conclude that the major differences between META3.1exp and META2.0 are due to the change in the detection algorithm. META3.1exp contains smaller eddies and trajectories lasting at least 10 d; these were not available in the META2.0 product. Nevertheless, 55 % of the structures in META2.0 are similar to META3.1exp, thereby ensuring continuity between the two products and their physical characteristics. Geographically, the eddy distributions differ mainly in the strong current regions, where the mean dynamic topography (MDT) gradients are sharp. The additional information on the eddy contours allows for more accurate collocation of mesoscale structures with data from other sources, and so META3.1exp is recommended for multi-disciplinary application.

Turbulent transient boundary layer over a flat plate

A numerical study of unsteady turbulent fluid flow over ERCOFTAC flat-plate T3A is represented. Four uniform flow rates are applied to an initially fully turbulent steady flow. The γ-SST turbulence model is adopted to determine the boundary layer development, analysis of turbulence structures, and the wall functions response in the presence of external acceleration. It is observed that imposing higher momentum rates affect the boundary layer thickness. Furthermore, enforced flow rate can change the shape of eddies and make them more stretched. Phase delay in turbulence propagation under this condition is the same as in previous studies. However, the quality and quantity of turbulence phase delay in two streamwise and wall-normal directions are investigated and compared with available experimental and numerical solutions. It is perceived that the amount of delay for each distinct acceleration, alongside the plate and at a specific distance from the wall, is almost the same. Whereas, in the normal direction, the delay is variable and emanates from the physical eddies shape. Moreover, in boundary layer, the outer region affeccted more severely than the near-wall region.

Interpreting Reynolds stress from perspective of eddy geometry

Geometric features in oceanic mesoscale eddies such as tilt and anisotropy can influence the properties of the Reynolds stress that provides feedback between the eddies and the background flow. By regarding an eddy as a wave, previous studies have parameterized the Reynolds stress based on the equivalence in the tilt angle between the phase of the eddy stream functions and the variance ellipse for the Reynolds stress (RS-ellipse). However, the wave assumption cannot predict the anisotropy of the RS-ellipse, and also largely simplifies the eddy geometry, which would naturally be an ellipsoid rather than a wave. The present study explores the shape relation between elliptical eddies and the RS-ellipse, by mathematically reformulating the Reynolds stress based on the eddy shape. The new formula reveals that the shape relation is regulated by the horizontal extent of the occurrence probability distribution (PDF) of the eddy, and that the shape of the eddy and RS-ellipse are identical at the place of maximum PDF when the horizontal scale of the PDF is sufficiently larger than the size of the eddy. A similar tendency is found in eddies detected by satellite altimetry in the Kuroshio Extension jet region. A detailed analysis of the PDF in this region shows that the tilts of the eddies are likely to be consistent with the destabilization effect on the jet, suggesting a strong relation between the eddy geometry and the jet's stability in this region. These findings may open a path toward a new method to parameterize the Reynolds stress with the background state, exploiting the shape equivalence between the eddies and the RS-ellipse.

Eddy morphology: Egg-like shape, overall spinning, and oceanographic implications

Systematic tracking of individual eddies during their entire lifetimes marks a significant milestone in satellite oceanography over the first two decades of this century. Assuming that the geometry and properties of an oceanic eddy are orientation-sensitive, an angularly aligned composite analysis of over 40 million eddy-focused surface topographic “snapshots” obtained by merging tandem altimeter data from January 1993 through January 2019 reveals that oceanic vortices appear to have a characteristic surface shape of “egg” rather than circle or ellipse as previously understood. Consequently, a second-order moment in eddy morphology is revealed which leads to a ~ 10 km departure from a standard ellipse in terms of major axis. Furthermore, the sharp poles of oceanic eddies exhibit two quasi-orthogonal modes of orientation: primarily meridional and secondarily zonal. The additional submesoscale asymmetry in eddy shape is confirmed by a consistent anisotropy in a normalized eddy-centric velocity field derived from over 25 thousand drifters. The high-order moments in terms of geometric asymmetry and dynamic anisotropy associated with mesoscale eddies (which are found to be statistically significant at 99% level) may have profound geophysical and biological impacts on energy transport, substance entrainment, as well as ecosystem dynamics in the ocean. In particular, it is demonstrated that some of the previously identified patterns in eddy properties obtained by non-rotated normalization may be notably biased due to the ignorance of existing eddy orientation.

The geometry of mesoscale eddies in the South China Sea: characteristics and implications

ABSTRACT The symmetrical circular shape of mesoscale eddies has been widely used in their scientific researches. Recently, an elliptical average eddy shape has been confirmed for eddies in the global ocean using multi-satellite altimeter data. As a regional extension of a previous study on the geometry of global eddies, a mean eddy shape in the South China Sea (SCS) has been derived by averaging a large number of orientational eddy boundaries. The mean shape is approximately a mathematic ellipse with a semimajor axis of 101.3 km and a semiminor axis of 61.3 km. Its size is larger than the global one. The principal eddy orientation in the SCS is 74°/254° (nearly northeast-southwest), different from that of eddies in the global ocean (171°/351°, nearly east–west). Composite analyses of chlorophyll (CHL) concentrations and sea surface temperature anomalies (SSTA) indicate a dipole structure for circular eddies in the non-rotated coordinate system. While a monopole structure for elliptical eddies in the eddy-centric coordinate system is obtained. The results demonstrate that the elliptical shape of eddies affects oceanographical variables. The findings provide a new approach for exploring the role of air–sea interactions on oceanic eddies.

Deformation of a Warm Eddy in the Northern South China Sea

AbstractMesoscale eddies are important for regulating oceanic energy. Variation in eddy shapes leads to uncertainty in calculations of heat or energy content. In this study, we investigated the deformation of a warm eddy in the northern South China Sea from April to June 2018 and elucidated the mechanism governing the deformation. Satellite altimetry images showed that the warm eddy originated from Luzon Strait (LS eddy), migrated westward, and then moved along 500‐m isobaths until it approached the east of Hainan Island. Thereafter, the LS eddy deformed, moved southward, merged with other eddies, and finally dissipated. Using ship and virtual‐mooring Chinese underwater glider observations, we examined the three‐dimensional structure of the LS eddy. The warm eddy had a low‐density core that reached a depth of 250 m. The LS eddy gave rise to a front along its eastern edge, and two associate submesoscale eddies with horizontal radii of approximately 10 km were found at the front. The warm eddy was circular before deformation but morphed into an egg shape after deformation. This shape change allowed the eddy to entrain additional water mass (approximately 1014 kg). The deformation event was able to be forecasted by the vorticity and deformation index, as the eddy deformed by leaking into the zone with a high vorticity and deformation index. We used modeling and energy transformation calculations to analyze the mechanism of the warm eddy deformation. Our results revealed that baroclinic instability played a primary role in the deformation event.

Comparison of Eight Detection Algorithms for the Quantification and Characterization of Mesoscale Eddies in the South China Sea

AbstractNumerous oceanic mesoscale eddies occur in the South China Sea (SCS). The present study employs eight automatic eddy detection algorithms to identify these mesoscale eddies and compares the results. Eddy probabilities and areas detected by various algorithms differ substantially. Most regions of the SCS with a high discrepancy of eddy probabilities are those with few mesoscale eddies, except for the area west of the Luzon Strait, the area west of Luzon Island between 12° and 17°N, and the southernmost end of the SCS basin. They are primarily caused by strong interference, noncircular eddy shapes, and gentle sea level anomaly (SLA) gradients, respectively. The SLA, winding angle, and hybrid methods can easily detect the mesoscale eddies with wavelike features. The Okubo–Weiss (OW) and the spatially smoothed OW methods better identify grouping phenomena of mesoscale eddies in the SCS. Suggestions are presented on choosing suitable algorithms for studying mesoscale eddies in the SCS. No single algorithm is perfect for all research purposes. For different studies, the most suitable algorithm is different.

On the intrinsic shape of oceanic eddies derived from satellite altimetry

The fundamental issue of mean eddy shape at the sea surface has been simplified as axially symmetric for a long time. This assumption is worth of a reexamination following significant advances in precise tracking of individual eddies, thanks to the recent availability of merged altimeter data with a grid resolution of 1/4° × 1/4° and a time interval of one day. Based on an orientationally aligned average of the effective boundaries of nearly 2.6 million individual eddies available to date, a characteristic shape of a “standard” eddy has been derived, which is found to be a very good approximation to a mathematical ellipsoid with a semimajor axis of a = 87.0 km, and a semiminor axis of b = 54.0 km. The oval nature of oceanic eddies appears to be universal in a climatological sense, but the best-fit ellipse varies with space and time. Statistically, the eddy ellipse has two preferred angles for its major axis: a primary angle of 104°/284° (nearly north-south) and a secondary angle of 171°/351° (nearly east-west). The intrinsic geometric asymmetry in eddy shape and orientation is believed to be one of the fundamental reasons behind the previously observed geophysical anisotropy in eddy properties. Future integrated analysis in an eddy-centric coordinate system with an ellipse geometry may open a new window into nonlinear mesoscale oceanography in terms of eddy kinetics and eddy dynamics.

Retention and Leakage of Water by Mesoscale Eddies in the East Australian Current System

AbstractMesoscale eddies are ubiquitous in the ocean, transporting semi‐isolated water masses as well as advecting tracers and biota. The extent to which eddies impact the environment depends on the time they retain water parcels. Here we quantify retention times of mesoscale eddies in a (1/10)° model of the East Australian Current and its extension along the southeast coast of Australia. We find that retention times vary widely, between 3 and 357 days, but peak around 24 and 27 days for anticyclones and cyclones, respectively. Changes in eddy shape, though not in eddy size, relate to water exchange between the eddy and the background flow. An increase in eccentricity (eddy elongation) often leads to water leakage, while a decrease is associated with water retention. Thus, the change in eddy eccentricity can be used as a diagnostic of the eddy's likelihood to exchange water with its surrounding. We find that water within a region of the eddy that is close to uniform rotation and rotating faster than uniform vorticity is more likely to be retained. Typical retention times are long enough for eddies to transport water across regions of contrasting hydrographic properties, develop a biogeochemical response, and influence connectivity patterns.

Comparing a Multivariate Global Ocean State Estimate With High-Resolution in Situ Data: An Anticyclonic Intrathermocline Eddy Near the Canary Islands

The provision of high-resolution \textit{in situ} oceanographic data is key for the ongoing verification, validation and assessment of operational products, such as those provided by the Copernicus Marine Core Service (CMEMS). Here we analyze the ability of ARMOR3D - a multivariate global ocean state estimate that is available from CMEMS - to reconstruct a mesoscale anticyclonic intrathermocline eddy that was previously sampled with high-resolution independent \textit{in situ} observations. ARMOR3D is constructed by merging remote sensing observations with \textit{in situ} vertical profiles of temperature and salinity obtained primarily from the Argo network. \textit{In situ} data from CTDs and an Acoustic Doppler Current Profiler were obtained during an oceanographic cruise near the Canary Islands (Atlantic ocean). The analysis of the ARMOR3D product using the \textit{in situ} data is done over (i) a high-resolution meridional transect crossing the eddy center and (ii) a three-dimensional grid centered on the eddy center. An evaluation of the hydrographic eddy signature and derived dynamical variables, namely geostrophic velocity, vertical vorticity and quasi-geostrophic (QG) vertical velocity, demonstrates that the ARMOR3D product is able to reproduce the vertical hydrographic structure of the independently sampled eddy below the seasonal pycnocline, with the caveat that the flow is surface intensified and the seasonal pycnocline remains flat. Maps of ARMOR3D density show the signature of the eddy, and agreement with the elliptical eddy shape seen in the \textit{in situ} data. The major eddy axes are oriented NW-SE in both data sets. The estimated radius for the \textit{in situ} eddy is $\sim$ 46 km; the ARMOR3D radius is significantly larger at $\sim$ 92 km and is considered an overestimation that is inherited from an across-track altimetry sampling issue. The ARMOR3D geostrophic flow is underestimated by a factor of 2, with maxima of 0.11 (-0.19) m s$^{-1}$ at the surface, which implies an underestimation of the local Rossby number by a factor of 3. Both the \textit{in situ} and ARMOR3D eddies have decelerating flows at their northern edges. The ARMOR3D QG vertical velocity distribution has upwelling/downwelling cells located along the eddy periphery and similar magnitudes to the \textit{in situ}-derived QG vertical velocity.

Patterns of Vertical Velocity Induced by Eddy Distortion in an Ocean Model

AbstractVertical motions within eddies play an important role in the exchange of properties and energy between the upper ocean and the ocean interior. Here we analyze alternating upward and downward cells in anticyclonic eddies in the East Australian Current region using a global eddy‐resolving model. The cells explain over 50% of the variance of vertical velocity within these eddies. We show that the upward and downward cells relate to eddy distortion, defined as the change in eddy shape over time. In anticyclonic eddies in the Southern Hemisphere, an inward distortion is associated with upward motion and an outward distortion is associated with downward motion. We discuss two mechanisms that link eddy distortion to vertical velocity. One mechanism relates to changes in stratification and relative vorticity in the eddy interior. The other mechanism relates to divergence of the horizontal flow in different quadrants of the eddy. We show that mesoscale changes in sea level anomaly can be used to infer the vertical motion within eddies.

Numerical investigation on aerodynamic noises of the lateral window in vehicles

The paper firstly conducted a numerical simulation for flow fields and aerodynamic noises of the lateral window region in vehicles, and verified its correctness using the experimental test. Numerical simulation shows that: A pillar has a complicated shape and large corner, so that airflows will be separated here. An eddy structure is caused in the lateral window region and develops along the A pillar to generate serious pressure pulsations. A low pressure region is formed behind the A pillar. Obvious airflow separation regions are in the A pillar, rear view mirrors, wheels and wheel chambers. These airflow separation regions are typical positions causing aerodynamic noises. Additionally, large separated regions are located at the tail part of the vehicle, which is a main reason for causing the aerodynamic resistance. Intensity and velocity of eddies near the lateral window surface are relatively large, while its intensity near edges of the rear view mirror is weak. The shape of eddies extends along the flow direction to be an oval shape. The separated and broken eddies are sources for causing pressure pulsations. According to sound pressures of observation points, it can be also found that the separated eddy is a main reason for causing aerodynamic noises. Sound pressures are low at the right upper corner of lateral windows. In addition, noise distributions on the lateral window become gradually uniform with the increased frequency. In order to reduce flow noises, a bionic saw-tooth structure is applied to A pillars and rear view mirrors. After the bionic structure is introduced, some fluids are adhered to A pillars and rear view mirrors, so that the energy of fluids reaching the lateral window is reduced. In addition, fluids in rear regions of the rear view mirror presented a spiral shape, so that the possibility of fluid diffusion will be also reduced. In the original model, the maximum energy is 57.77, while that in this region with the bionic saw-tooth structures is 55.00. Obviously, the eddy energy is weakened. Compared with the original model, flow noises of all the observation points are reduced to different degrees, and the noise reduction effect is obvious. The results fully prove that this region with bionic saw-teeth in this paper has obvious advantages in noise reduction.

Pore-scale simulation of vortex characteristics in randomly packed beds using LES/RANS models

Turbulent flow characteristics and vortex behaviors in the pore space of real packed beds under different flow conditions is numerically investigated. Real geometric structure of randomly packed beds is modeled using the discrete element software LIGGGHTS. Both LES and RANS methods are employed to predict vortex shape and evolution features at pore scale in actual packed beds. The numerical model is validated corresponding to experimental data, a good agreement is achieved between predicted results and measurements. Based on the computational results, the distribution characteristics of vorticity and velocity in multiple representative special structures are analysed, such as the channel formed by two pellets, similar triangle area formed by compact spherical walls and channel. Besides the effects of special structures on vortex shape and turbulence intensity is studied, such as the guiding and friction effect by the side spherical wall on gas motion, and strong shear force on both sides of the main channel. The Q criterion is used to identify vortex structures and capture distribution and evolution of vortexes in the computational domain. Moreover, the effect of inlet velocity on the position and shape of eddies is investigated, and eddy morphological changes under unsteady inlet conditions are also discussed., At last, a comparison between LES and RANS methods shows that the LES method can capture more details of the distribution and shape of the vortexes in the pore space, and therefore it is more suitable to the complicated flow field in porous media.

Erosion of a California Undercurrent eddy by bottom topography

AbstractSubsurface eddies are ubiquitous features in eastern boundary current systems. These phenomena tend to modulate the across‐shore distribution of heat and biogeochemical tracers. A California Undercurrent eddy was detected by shipboard observations in October 2009 off the northern Baja California continental slope. The spatiotemporal variation in the California Undercurrent eddy is investigated by using a mesoscale‐resolving hindcast ocean simulation. A poleward coastal current that is driven by an upwelling‐wind relaxation event and the coastline geometry instigated the separation of the California Undercurrent from the slope, forming a meander‐like structure, which evolved as a mesoscale eddy‐like structure. The latter structure evolved as a subsurface eddy with a warm anomaly core, a distinctive feature of eddies that form from the California Undercurrent. During the initial stage, the subsurface eddy presented a cone‐shape form, with the maximum amplitude of the relative vorticity in the upper section. The inviscid effect of the irregular bottom topography altered both the initial direction of propagation and the initial eddy shape: the propagation direction of the eddy changed from north‐south to southwest, and the shape changed from a cone shape to a subsurface lens shape. The strong eddy‐topography interactions triggered a sign change in the heat flux direction from the environment toward the eddy and vice versa through the horizontally divergent component of the velocity field, which accelerated the eddy's decay. This study shows the relevance of the synoptic wind stress events and the irregularity of the bottom topography on the mesoscale eddy activity in the southern portion of the California Current.

Detecting and tracking eddies in oceanic flow fields: a Lagrangian descriptor based on the modulus of vorticity

Abstract. Since eddies play a major role in the dynamics of oceanic flows, it is of great interest to detect them and gain information about their tracks, their lifetimes and their shapes. We present a Lagrangian descriptor based on the modulus of vorticity to construct an eddy tracking tool. In our approach we denote an eddy as a rotating region in the flow possessing an eddy core corresponding to a local maximum of the Lagrangian descriptor and enclosed by pieces of manifolds of distinguished hyperbolic trajectories (eddy boundary). We test the performance of the eddy tracking tool based on this Lagrangian descriptor using an convection flow of four eddies, a synthetic vortex street and a velocity field of the western Baltic Sea. The results for eddy lifetime and eddy shape are compared to the results obtained with the Okubo–Weiss parameter, the modulus of vorticity and an eddy tracking tool used in oceanography. We show that the vorticity-based Lagrangian descriptor estimates lifetimes closer to the analytical results than any other method. Furthermore we demonstrate that eddy tracking based on this descriptor is robust with respect to certain types of noise, which makes it a suitable method for eddy detection in velocity fields obtained from observation.

A Geometric Interpretation of Eddy Reynolds Stresses in Barotropic Ocean Jets

AbstractBarotropic eddy fluxes are analyzed through a geometric decomposition of the eddy stress tensor. Specifically, the geometry of the eddy variance ellipse, a two-dimensional visualization of the stress tensor describing the mean eddy shape and tilt, is used to elucidate eddy propagation and eddy feedback on the mean flow. Linear shear and jet profiles are analyzed and theoretical results are compared against fully nonlinear simulations. For flows with zero planetary vorticity gradient, analytic solutions for the eddy ellipse tilt and anisotropy are obtained that provide a direct relationship between the eddy tilt and the phase difference of a normal-mode solution. This allows a straightforward interpretation of the eddy–mean flow interaction in terms of classical stability theory: the initially unstable jet gives rise to eddies that are tilted “against the shear” and extract energy from the mean flow; once the jet stabilizes, eddies become tilted “with the shear” and return their energy to the mean flow. For a nonzero planetary vorticity gradient, ray-tracing theory is used to predict ellipse geometry and its impact on eddy propagation within a jet. An analytic solution for the eddy tilt is found for a Rossby wave on a constant background shear. The ray-tracing results broadly agree with the eddy tilt diagnosed from a fully nonlinear simulation.

Self-similarity of the large-scale motions in turbulent pipe flow

Townsend’s attached eddy hypothesis assumes the existence of a set of energetic and geometrically self-similar eddies in the logarithmic layer in wall-bounded turbulent flows, which can be scaled with their distance to the wall. To examine the possible self-similarity of the energetic eddies in fully developed turbulent pipe flow, we performed stereo particle image velocimetry measurements together with a proper orthogonal decomposition analysis. For two Reynolds numbers, $Re_{{\it\tau}}=1330$ and 2460, the resulting modes/eddies were shown to exhibit self-similar behaviour for eddies with wall-normal length scales spanning a decade. This single length scale provides a complete description of the cross-sectional shape of the self-similar eddies.

The most typical shape of oceanic mesoscale eddies from global satellite sea level observations

In this research, we normalized the characteristics of ocean eddies by using satellite observation of the Sea Level Anomaly (SLA) data to determine the most typical shape of ocean eddies. This normalization is based on modified analytic functions with nonlinear optimal fitting. The most typical eddy is the Taylor vortex (∼50%), which exhibits a Gaussian-shaped exp(−r 2) SLA and a vorticity distribution of (1 − r 2)exp(−r 2) as a function of the normalized radii r. The larger the amplitude of the eddy, the more likely the eddy is to be Gaussian-shaped. Furthermore, approximately 40% of ocean eddies are combinations of two Gaussian eddies with different parameters, but the composition of these types of eddies is more like a quadratic eddy than a Gaussian one. Only a small portion of oceanic eddies are pure quadratic eddies (<10%) with the same vorticity distribution as a Rankine vortex. We concluded that the Taylor vortex is a good approximation of the typical shape of ocean eddies.