The impact of freshwater discharges on the ocean circulation in the Skagerrak/northern North Sea area. Part II: energy analysis

We perform eddy-permitting to eddy-resolving simulations of the Skagerrak/northern North Sea with a terrain-following numerical ocean model. We demonstrate that realistic representations of freshwater input are not required when the focus is on modelling mesoscale structures such as meanders and eddies. To arrive at this conclusion, we analyze the results using a recently developed energy diagnostic scheme to study the sensitivity to realistic representations of the lateral freshwater flux provided to the area from the Baltic Sea and by the major rivers. The scheme is suitable for analysis of growth of instabilities, and it has four basic instability processes prominent. We recognize both horizontal and vertical shear instabilities. There are two processes where average potential energy is converted to eddy kinetic energy, and they are related to the mean gradient in surface elevation and the mean lateral density gradient, respectively. The latter process is known as frontal instability. We demonstrate that the change in the eddy kinetic energy field is small, despite the large variations in the hydrographic properties from experiment to experiment. Moreover, generation of eddy activity appears at the same locations and with approximately the same strength regardless of actual representations of freshwater input. Furthermore, we find that vertical shear instability dominates the energy conversion processes in the Norwegian Coastal Current. Finally, we find that the areas off the northwest coast of Denmark recognized with enhanced eddy kinetic energy level is not caused by instability processes but eddy–eddy interaction rooted in variations in the sea level.     

Numerical analysis of the Black Sea currents and mesoscale eddies in 2006 and 2011

Two prognostic experiments taking into account real atmospheric forcing for 2006 and 2011 were carried out based on the eddy-resolving numerical model with a horizontal resolution of 1.6 km for the Black Sea. The main dynamic features such as the Rim Current, the Sevastopol, and Batumi anticyclones are reproduced in both experiments. The model results are confirmed via observation data. We accomplished the analysis of simulated circulation and energetics. The results demonstrate that both the vertical viscosity and vertical diffusion along with the energy inflow from the wind have been the main contributors to the annual and seasonal budgets of kinetic and potential energies of the Black Sea circulation. It is shown that two regimes of the Black Sea general circulation are implemented depending on a magnitude of wind contribution to the kinetic energy in winter. Intensive mesoscale eddy formation was observed along the Anatolian, Caucasian, and Crimean coasts. The analysis of the Black Sea circulation and eddy energetics allowed us to conclude that the generation and development of the mesoscale coastal eddies is associated with the barotropic instability in case of intensive coastal currents and is associated with both the barotropic and baroclinic instability in case of weak coastal currents.     

Mesoscale eddies and baroclinic instability over the eastern Sakhalin shelf of the Sea of Okhotsk: a model-based analysis

Based on an eddy-permitting numerical model, the mesoscale variability in the East-Sakhalin Current is investigated during the winter-spring period. Analysis of necessary conditions for the development of baroclinic instability showed that the nearshore component of the East-Sakhalin Current is potentially baroclinic unstable in the first half-year. The simulated circulation uncovered a generation of anticyclonic eddies on the eastern Sakhalin shelf. It was established that a spatial scale of these eddies and the first baroclinic Rossby radius of deformation are values of the same order; a lifetime of these eddies varies from 4 to 6 weeks, given the Rossby number varies from 0.05 to 0.2. Analysis of the rate of eddy energy conversion on the eastern Sakhalin shelf showed that the generation of the revealed mesoscale eddies results from, mainly, baroclinic instability, whereas barotropic instability can be both favoring and preventing to the generation of these eddies.     

Eddy energy sources and mesoscale eddies in the Sea of Okhotsk

Based on eddy-permitting ocean circulation model outputs, the mesoscale variability is studied in the Sea of Okhotsk. We confirmed that the simulated circulation reproduces the main features of the general circulation in the Sea of Okhotsk. In particular, it reproduced a complex structure of the East-Sakhalin current and the pronounced seasonal variability of this current. We established that the maximum of mean kinetic energy was associated with the East-Sakhalin Current. In order to uncover causes and mechanisms of the mesoscale variability, we studied the budget of eddy kinetic energy (EKE) in the Sea of Okhotsk. Spatial distribution of the EKE showed that intensive mesoscale variability occurs along the western boundary of the Sea of Okhotsk, where the East-Sakhalin Current extends. We revealed a pronounced seasonal variability of EKE with its maximum intensity in winter and its minimum intensity in summer. Analysis of EKE sources and rates of energy conversion revealed a leading role of time-varying (turbulent) wind stress in the generation of mesoscale variability along the western boundary of the Sea of Okhotsk in winter and spring. We established that a contribution of baroclinic instability predominates over that of barotropic instability in the generation of mesoscale variability along the western boundary of the Sea of Okhotsk. To demonstrate the mechanism of baroclinic instability, the simulated circulation was considered along the western boundary of the Sea of Okhotsk from January to April 2005. In April, the mesoscale anticyclonic eddies are observed along the western boundary of the Sea of Okhotsk. The role of the sea ice cover in the intensification of the mesoscale variability in the Sea of Okhotsk was discussed.     

Delayed baroclinic response of the Antarctic circumpolar current to surface wind stress

The Antarctic Circumpolar Current (ACC) responds to the surface windstress via two processes, i.e., the instant barotropic process and the delayed baroclinic process. This study focuses on the baroclinic instability mechanism in ACC, which was less reported in the literatures. Results show that the strengthening of surface zonal windstress causes the enhanced tilting of the isopycnal surface, leading to more intense baroclinic instability. Simultaneously, the mesoscale eddies resulting from the baro- clinic instability facilitate the transformation of mean potential energy to eddy energy, which causes the remarkable decrease of the ACC volume transport with the 2-year lag time. This delayed negative cor- relation between the ACC transport and the zonal windstress may account for the steadiness of the ACC transport during last two decades.     

The intrinsic nonlinear multiscale interactions among the mean flow,low frequency variability and mesoscale eddies in the Kuroshio region

Using a new functional analysis tool, multiscale window transform(MWT), and the MWT-based localized multiscale energetics analysis and canonical transfer theory, this study reconstructs the Kuroshio system on three scale windows, namely,the mean flow window, the interannual-scale(low-frequency) window, and the transient eddy window, and investigates the climatological characteristics of the intricate nonlinear interactions among these windows. Significant upscale energy transfer is observed east of Taiwan, where the mean Kuroshio current extracts kinetic energy from both the interannual and eddy windows.It is found that the canonical transfer from the interannual variability is an intrinsic source that drives the eddy activities in this region. The multiscale variabilities of the Kuroshio in the East China Sea(ECS) are mainly controlled by the interaction between the mean flow and the eddies.The mean flow undergoes mixed instabilities(i.e., both barotropic and baroclinic instabilities) in the southern ECS, while it is barotropically stable but baroclinically unstable to the north. The multiscale interactions are found to be most intense south of Japan, where strong mixed instabilities occur; both the canonical transfers from the mean flow and the interannual scale are important mechanisms to fuel the eddies. It is also found that the interannual-scale energy mainly comes from the barotropically unstable jet, rather than the upscale energy transfer from the high frequency eddies.     

Generation mechanisms for mesoscale eddies in the Gulf of Lions: radar observation and modeling

Coastal mesoscale eddies were evidenced during a high-frequency radar campaign in the Gulf of Lions (GoL), northwestern Mediterranean Sea, from June 2005 to January 2007. These anticyclonic eddies are characterized by repeated and intermittent occurrences as well as variable lifetime. This paper aims at studying the link between these new surface observations with similar structures suggested at depth by traditional acoustic Doppler current profiler measurements and investigates the eddy generation and driving mechanisms by means of an academic numerical study. The influence of the wind forcing on the GoL circulation and the eddy generation is analyzed, using a number of idealized configurations in order to investigate the interaction with river discharge, buoyancy, and bathymetric effects. The wind forcing is shown to be crucial for two different generation mechanisms: A strong northerly offshore wind (Mistral) generates a vortex column due to the bathymetric constraint of a geostrophic barotropic current, which can surface after the wind relaxes; a southerly onshore wind generates a freshwater bulge from the Rhône river discharge, which detaches from the coast and forms a well-defined surface anticyclonic eddy based on buoyancy gradients. These structures are expected to have important consequences in terms of dispersion or retention of biogeochemical material at local scales.     

Open-ocean response and normal mode excitation in an eddy-resolving general circulation model

Abstract

Analysis of a two-layer, flat-bottom, steady-wind driven, eddy-resolving general circulation model reveals a distinct separation in frequency of baroclinic and barotropic motion in the region distant from the model Gulf Stream. The far-field motions at periods less (greater) than about 100 days are predominantly barotropic (baroclinic), unlike the near-field, eddy-generating, free-jet region which contains barotropic and baroclinic energy throughout the modei frequency range. The far-field barotropic energy produces a peak in the model sea-level spectra between 25 and 50 days with a magnitude comparable to energy levels observed in spectra of sea level from oceanic island tide gauges. The far-field barotropic motion is clearly composed of large-scale, resonant, barotropic normal modes drive by mesoscale activity of the turbulent, free-jet region. Oceanic mesoscale turbulence may therefore provide for planetary normal modes an excitation mechanism distinct from atmospheric forcing. The open-ocean, barotropic, model response is very similar to that of a fluctuating-wind driven model, which suggests that atmospheric and intrinsic forcing of mid-ocean eddies may be of comparable importance.     

A mesoscale eddy detection method of specific intensity and scale from SSH image in the South China Sea and the Northwest Pacific

Mesoscale eddies exist almost everywhere in the ocean and play important roles in the ocean circulation of the world. These eddies may cause sound spread singular regions and bring great influences to the upwater ship and underwater aircraft. Due to the lack of hydrographic survey datasets, study of mesoscale eddies has been greatly restricted. Fortunately, satellite altimeter provided an effective way to study mesoscale eddies. An automatic detection algorithm is introduced to detect mesoscale eddies of specific intensity and spatial/temporal scale based on satellite sea surface height (SSH) data and the algorithm is applied in a strong eddy activity region: the South China Sea and the Northwest Pacific. The algorithm includes four steps. The first step is preprocessing of the SSH image, which includes elimination of error SSH data and interpolation. The second step is to detect suspected mesoscale eddies from preprocessed SSH images by dynamic threshold adjustment and morphological method, and the suspected mesoscale eddy detection includes two procedures: suspected mesoscale eddy core region detection and suspected mesoscale eddy brim extraction. The third step is to pick out mesoscale eddies satisfied with specified criteria from suspected mesoscale eddies. The criteria include three items, that is, intensity criterion, spatial scale, criterion and temporal scale criterion. The last step is algorithm performance analysis and verification. The algorithm has the capability of adaptive parameter adjustment, and can extract mesoscale eddies of interested intensity and spatial/temporal scale. The paper can provide a basis for analyzing space-time characteristics of mesoscale eddy in the South China Sea and the Northwest Pacific.     

Three-dimensional structure of mesoscale eddies in the western tropical Pacific as revealed by a high-resolution ocean simulation

The three-dimensional structure of mesoscale eddies in the western tropical Pacific(6°S–20°N, 120°E–150°E)is investigated using a high-resolution ocean model simulation. Eddy detection and eddy tracking algorithms are applied to simulated horizontal velocity vectors, and the anticyclonic and cyclonic eddies identified are composited to obtain their three-dimensional structures. The mean lifetime of all long-lived eddies is about 52 days, and their mean diameter is 147 km. Two typical characteristics of mesoscale eddies are revealed and possible dynamic explanations are analyzed. One typical characteristic is that surface eddies are generally separated from subthermocline eddies along the bifurcation latitude(~13°N) of the North Equatorial Current in the western tropical Pacific, which may be associated with different eddy energy sources and vertical eddy energy fluxes in subtropical and tropical gyres. Surface eddies have maximum swirl velocities of 8–9 cm s~(-1) and can extend to about 1500 m depth. Subthermocline eddies occur below 200 m, with their cores at about 400–600 m depth, and their maximum swirl velocities can reach 10 cm s~(-1). The other typical characteristic is that the meridional velocity component of the eddy is much larger than the zonal component. This characteristic might be due to more zonal eddy pairs(two eddies at the same latitude),which is also supported by the zonal wavelength(about 200 km) in the high-frequency meridional velocity component of the horizontal velocity.     

Estimate of eddy energy generation/dissipation rate in the world ocean from altimetry data

Assuming eddy kinetic energy is equally partitioned between the barotropic mode and the first baroclinic mode and using the weekly TOPEX/ERS merged data for the period of 1993~2007, the mean eddy kinetic energy and eddy available gravitational potential energy in the world oceans are estimated at 0.157 and 0.224 EJ; the annual mean generation/dissipation rate of eddy kinetic energy and available gravitational potential energy in the world oceans is estimated at 0.203 TW. Scaling and data analysis indicate that eddy available gravitational potential energy and its generation/dissipation rate are larger than those of eddy kinetic energy.     

Low-frequency current variability observed at the shelfbreak in the northeastern Gulf of Mexico: May–October, 2004

High-resolution current measurements were made in the Northeastern Gulf of Mexico by the Naval Research Laboratory (NRL) as part of its Slope to Shelf Energetics and Exchange Dynamics (SEED) project. The major goal of SEED is to understand the mechanisms that transfer properties across the shelf slope. Fourteen acoustic Doppler current profilers (ADCPs) were deployed just west of the DeSoto Canyon on the shelf and down the slope from May to November, 2004 to measure nearly full water column current profiles. Currents were found more variable on the shelf than on the slope but in the mean strongly tended to follow bathymetry, particularly on the slope. During the SEED time period currents were driven by both local and remote winds, by cyclonic eddies associated with the Loop Current extension and Loop Current rings, by smaller eddies associated with the cyclonic eddies, by frontal meanders or streamers associated with the eddies, and by tropical storms. Currents were highly barotropic, accounting for more than 80% of the eddy kinetic energy (EKE). Current magnitudes generally increased from west to east, towards the DeSoto Canyon. Tropical storms had a relatively minor short-term effect upon mass transports. Cross-shelf transports were much smaller than the along-shelf transports. Onshore transports were stronger on the western side of the array while offshore transports were stronger on the eastern side of the array near the DeSoto Canyon. Offshore transports generally occurred during eastward flow periods, onshore transports during westward flow periods, and both during eddy periods. Mesoscale eddies also provided contributions to cross-shelf exchange. Large scale circulation features could be determined from the first two empirical-orthogonal function (EOF) modes which accounted for 83% of the variance and were strongly related to the integrated wind stress.     

Using an eddy-tracking algorithm to understand the impact of assimilating altimetry data on the eddy characteristics of the Agulhas system

A complex and highly dynamical ocean region, the Agulhas Current System plays an important role in the transfer of energy, nutrients and organic material from the Indian to the Atlantic Ocean. Its dynamics are not only important locally, but affect the global ocean-atmosphere system. In working towards improved ocean reanalysis and forecasting capabilities, it is important that numerical models simulate mesoscale variability accurately—especially given the scarcity of coherent observational platforms in the region. Data assimilation makes use of scarce observations, a dynamical model and their respective error statistics to estimate a new, improved model state that minimises the distance to the observations whilst preserving dynamical consistency. Qualitatively, it is unclear whether this minimisation directly translates to an improved representation of mesoscale dynamics. In this study, the impact of assimilating along-track sea-level anomaly (SLA) data into a regional Hybrid Coordinate Ocean Model (HYCOM) is investigated with regard to the simulation of mesoscale eddy characteristics. We use an eddy-tracking algorithm and compare the derived eddy characteristics of an assimilated (ASSIM) and an unassimilated (FREE) simulation experiment in HYCOM with gridded satellite altimetry-derived SLA data. Using an eddy tracking algorithm, we are able to quantitatively evaluate whether assimilation updates the model state estimate such that simulated mesoscale eddy characteristics are improved. Additionally, the analysis revealed limitations in the dynamical model and the data assimilation scheme, as well as artefacts introduced from the eddy tracking scheme. With some exceptions, ASSIM yields improvements over FREE in eddy density distribution and dynamics. Notably, it was found that FREE significantly underestimates the number of eddies south of Madagascar compared to gridded altimetry, with only slight improvements introduced through assimilation, highlighting the models’ limitation in sustaining mesoscale activity in this region. Interestingly, it was found that the threshold for the maximum eddy propagation velocity in the eddy detection scheme is often exceeded when data assimilation relocates an eddy, causing the algorithm to interpret the discontinuity as eddy genesis, which directly influences the eddy count, lifetime and propagation velocity, and indirectly influences other metrics such as non-linearity. Finally, the analysis allowed us to separate eddy kinetic energy into contributions from detected mesoscale eddies and meandering currents, revealing that the assimilation of SLA has a greater impact on mesoscale eddies than on meandering currents.     

A three-dimensional numerical shelf-sea front model with variable eddy viscosity and diffusivity

A three-dimensional numerical model of circulation and eddy development in shelf-sea fronts is applied to three frontal structures, with two parameterization schemes for vertical eddy viscosity and diffusivity. The three fronts resemble those in the German Bight (a front between relatively fresh coastal water and saltier water offshore, with an interface extending from surface to bottom), the Norwegian Coastal Current (also formed by fresh coastal water but with a thermocline on one side), and the Celtic Sea (a front between water which is stratified in summer and water which is well mixed throughout the year). The two mixing assumptions, modelling the reduction of turbulence in stratified zones, are based on the Munk-Anderson scheme and the turbulent energy equation. Many features of frontal dynamics are common to all the results: strong surface currents along the front, cross-frontal circulation cells, a considerable enhancement of vertical velocities when eddies are formed, and development of eddies into cyclonic-anticyclonic vortex pairs. Cross-frontal circulation and frontal sharpening are the variables most sensitive to the different mixing assumptions. The German Bight front is the one most affected by changing these assumptions. The comparisons suggest that realistic results may be obtained from models despite the present uncertainty about vertical mixing in stratified shelf seas.     

Interactions between mean flow and finite-amplitude mesoscale eddies in a barotropic ocean

Abstract

For the purpose of deriving an analytical parametrization, oceanic mesoscale eddies are represented as a horizontally propagating wave field in a non-uniform environment. The mathematical analysis rests upon the assumption of scale disparity between a short eddy scale and a long mean-flow scale. The novelty resides in the treatment of finite-amplitude eddies, which, moreover, form either a band-like or a cell-like pattern. A barotropic ocean is chosen as a first step to illustrate the mathematical analysis, but dissipation is included. The main result is an analytical derivation of a mesoscale-eddy parametrization: the mean-flow equation contains Reynolds-stress terms which are computed from parameters of the eddy field, which, in turn, are predicted by separate evolution equations. Due to restrictive assumptions (barotropy, orthogonal waves,…), the parametrization established here should be viewed only as a first step toward the design of a more practical parameterization for large-scale modelling.     

Dynamic model of mesoscale eddies. Eddy parameterization for coarse resolution ocean circulation models

In the framework of the eddy dynamic model developed in two previous papers (Dubovikov, M.S., Dynamical model of mesoscale eddies, Geophys. Astophys. Fluid Dyn., 2003, 97, 311–358; Canuto, V.M. and Dubovikov, M.S., Modeling mesoscale eddies, Ocean Modelling, 2004, 8, 1–30 referred as I–II), we compute the contribution of unresolved mesoscale eddies to the large-scale dynamic equations of the ocean. In isopycnal coordinates, in addition to the bolus velocity discussed in I–II, the mesoscale contribution to the large scale momentum equation is derived. Its form is quite different from the traditional down-gradient parameterization. The model solutions in isopycnal coordinates are transformed to level coordinates to parameterize the eddy contributions to the corresponding large scale density and momentum equations. In the former, the contributions due to the eddy induced velocity and to the residual density flux across mean isopycnals (so called Σ-term) are derived, both contributions being shown to be of the same order. As for the large scale momentum equation, as well as in isopycnal coordinates, the eddy contribution has a form which is quite different from the down-gradient expression.     

Evolution of an anticyclonic eddy southwest of Taiwan

Satellite images of sea-surface temperature, surface chlorophyll a concentration, and sea-level anomaly, together with ocean reanalysis data of Asia and Indian–Pacific Ocean (AIPOcean1.0), are utilized to study the three-dimensional characteristics and evolution of an anticyclonic warm eddy adjacent to the southwest coast of Taiwan during October and November 2006. Originated from the Kuroshio intrusion in the Luzon Strait, but unlike previously found westward moving anticyclonic eddies (AE) in the northeastern South China Sea, this AE was so close to the Taiwan coast and stayed where it was formed for over 1 month until it dissipated. Energy analysis is utilized to study the evolution process of the AE, and it shows that the barotropic instability (BTI) and baroclinic instability introduced by the Kuroshio intrusion flow appear to be the main energy sources for the AE. Periodical enhancement/relaxation of local northeasterly monsoon and its associated negative wind stress curl modify the current patterns in this region, reinforce the intraseasonal variability of the Kuroshio intrusion flow, and act together with Kuroshio to form the AE. Eddies detected from AIPOcean1.0 data also show that AEs are most likely to be generated southwest of Taiwan during the transition period of summer monsoon to winter monsoon, and generally, the BTI of Kuroshio intrusion contributes more than the direct wind stress work to the increase of the eddy kinetic energy for the generation and growth of the AEs.     

Numerical simulations of mesoscale variability in the Straits of Florida

The circulation in the Straits of Florida is dominated by the throughflow of the Florida Current, as modified by tidal flows, responses to atmospheric cold front and extratropical cyclone (easterly wave and tropical cyclone) passages in winter (summer), and intrinsic mesoscale variability due to instabilities of the Florida Current front and jet system. Monthly meanders of the Florida Current, persistent oceanic fronts associated with the Florida Current’s baroclinic jet, and frontal eddies shed weekly by the Florida Current are the primary mesoscale features. A limited area model (Princeton Ocean Model: POM) is implemented to cover the Straits of Florida with a curvilinear grid that resolves the mesoscale structure, especially where the baroclinic flow is locked to steep topography in a 90 degree bend of the Straits. Florida Current cyclonic frontal eddies are spawned spontaneously, grow as they translate downstream, interact with shelf waters, and exhibit the same space-time attributes that characterize their observed counterparts, as evidenced by satellite imagery, shipboard synoptic mapping, coastal HF radar, and moored time series. Here, a deeper understanding is attempted for the frontal eddy kinematics and dynamics by examining, for example, their sensitivity to model parameter values, synoptic versus monthly atmospheric forcing, and other determinants of the flow. The mean flow shears are concentrated along the shelfbreak, where these frontal eddies are trapped, favoring the formation of the eddies by mean flow instabilities. In particular, it is found that the Florida Current frontal eddies exist independent of the wind-forcing considered (i.e., no winds, monthly winds, and synoptic (but not mesoscale) winds); however, they are modulated by the synoptic wind-forcing. Nevertheless, intriguingly, the frontal eddies have the same weekly time scale as the weather cycle.     

Application of altimetry data assimilation on mesoscale eddies simulation

Mesoscale eddy plays an important role in the ocean circulation. In order to improve the simulation accuracy of the mesoscale eddies, a three-dimensional variation (3DVAR) data assimilation system called Ocean Variational Analysis System (OVALS) is coupled with a POM model to simulate the mesoscale eddies in the Northwest Pacific Ocean. In this system, the sea surface height anomaly (SSHA) data by satellite altimeters are assimilated and translated into pseudo temperature and salinity (T-S) profile data. Then, these profile data are taken as observation data to be assimilated again and produce the three-dimensional analysis T-S field. According to the characteristics of mesoscale eddy, the most appropriate assimilation parameters are set up and testified in this system. A ten years mesoscale eddies simulation and comparison experiment is made, which includes two schemes: assimilation and non-assimilation. The results of comparison between two schemes and the observation show that the simulation accuracy of the assimilation scheme is much better than that of non-assimilation, which verified that the altimetry data assimilation method can improve the simulation accuracy of the mesoscale dramatically and indicates that it is possible to use this system on the forecast of mesoscale eddies in the future.