Baroclinic Mode Research Articles

The Effect of Different Implementations of the Weak Temperature Gradient Approximation in Cloud Resolving Models

AbstractThe Weak Temperature Gradient (WTG) approximation is a popular method used to couple convection in limited‐area domain simulations with large‐scale dynamics. However, several different schemes have been created to implement this approximation, and these different WTG schemes show a wide range of different results in an idealized framework. Our investigation shows that different model behavior is caused by the treatment of the different baroclinic modes by the different WTG schemes. More specifically, we hypothesize that the relative strengths of the baroclinic modes plays a large role in these differences, and show that modifying these schemes such that they treat the baroclinic modes in a similar manner accounts for many of the significant differences observed.

Equatorial wave diagnosis for the Atlantic Niño in 2019 with an ocean reanalysis

Abstract. The propagation of equatorial waves is essential for the onset of Atlantic Niño, but diagnosing waves with ocean reanalysis or in situ data remains a challenge. This study uses an ocean reanalysis to diagnose the wave energy transfer route during the 2019 event. The climatological values and the anomaly in 2019 at each grid point are decomposed into the first four baroclinic modes based on their local density profiles. The decomposed geopotential can well reproduce the displacement of the thermocline during the event. Wave energy flux is calculated by means of a group-velocity-based scheme. In addition to detecting wind-forced Kelvin waves and reflected Rossby waves, the wave energy flux reveals another possible energy transfer route along the western boundary, where some off-equatorial wave energy can excite coastally trapped Kelvin waves and transfer back to the equatorial Atlantic. Five transects are selected, across which the passing wave energy fluxes in 2019 are integrated. The results suggest that the Kelvin waves in the third and fourth mode are locally forced, while the wave energy in the second mode is more likely from the off-equatorial region. Therefore, in the autumn of 2019, the second-mode Kelvin waves can deepen the thermocline ahead of other modes from September, serving to precondition the Niño event.

Steric heights of submesoscale processes and internal gravity waves in the subtropical northwestern Pacific and northern South China Sea as revealed by moored observations

The Surface Water and Ocean Topography (SWOT) altimeter mission provides a good opportunity to globally detect submesoscale processes (submesoscales) from high-resolution sea surface height (SSH) measurements. However, in addition to the balanced mesoscale eddies and submesoscales, the measured SSH also contains signals of unbalanced internal gravity waves (IGWs) including internal tides (ITs) and supertidal IGWs (IGWs with frequencies of 3–8 cycles per day). Therefore, a quantitative understanding of the contributions of the above multiscale dynamic processes to the SSH is a prerequisite for exploring submesoscales from the SWOT-derived SSH data. Here, this issue was investigated through analyzing one-year moored observation-derived near-surface steric heights (SHs) in the subtropical northwestern Pacific (NWP) and northern South China Sea (SCS) which have different dynamic backgrounds. In the sense of annual mean, the root-mean-squared (RMS) SHs of submesoscales (defined as processes with periods of 2–15 days here) and IGWs in the SCS are 1.30 and 5.54 cm, respectively, while they are only 0.70 and 3.19 cm in the NWP. Seasonally, the RMS SH of submesoscales is larger in winter than summer in both regions; with respect to the IGWs, their RMS SH is larger in summer than winter in the SCS but it is opposite in the NWP. Generally, the SHs of diurnal and semidiurnal ITs are dominated by the stationary component in both regions but the proportion of the nonstationary component is much larger in the NWP than the SCS. The sum of the SHs by nonstationary diurnal and semidiurnal ITs exceeds that of submesoscales except in winter in the SCS. Furthermore, we also found that the SHs of supertidal IGWs are always larger than those of submesoscales in both regions and both seasons. By decomposing the IGWs with frequencies of 1–8 cpd (i.e., cycles per day) into different baroclinic modes, we found that for all of the IGWs bands, the SHs are overwhelmingly attributed to the first mode. The results in this study will provide useful information for the application of SWOT data in regions with active IGWs.

On the role of vertical resolution for resolving mesoscale eddy dynamics and the prediction of ocean sound speed variability

This work investigates how vertical resolution affects the prediction of ocean sound speed through a suite of regional simulations covering the DeSoto Canyon in the Gulf of Mexico. Simulations have identical horizontal resolution of 0.5 km, partially resolving submesoscale dynamics, and vertical resolution from 30 to 200 terrain-following layers. The focus is on mesoscale eddies and how modeled sound speeds vary whenever more vertical baroclinic modes are resolved. While domain-averaged sound speed profiles do not differ substantively, the standard deviation increases for increasing resolution due to the sharper representation of mesoscale circulations underneath the mixed layer and their associated density anomalies.

Estimating Three‐Dimensional Structures of Eddy in the South Indian Ocean From the Satellite Observations Based on the isQG Method

AbstractBy incorporating the high‐resolution satellite remote sensing sea surface temperature (SST) with low‐resolution sea level anomaly and sea surface salinity (SSS), this study explores the reconstructability of the three‐dimensional (3D) eddy structures via the “interior + surface quasigeostrophic” (isQG) method in the South Indian Ocean. We apply the incorporation of high‐resolution SST to improve the spatial resolution of the reconstruction. We also propose a correction scheme for density reconstruction within the mixed layer to offset the absence of mixed layer dynamics in the SQG framework. Comparison against the in situ observations demonstrates a satisfactory reconstructability for subsurface velocity and density anomalies. Statistically, the zonal velocity reconstructability outperforms its meridional counterpart and the corresponding velocity phase. The reconstructed shallow‐layer velocity exhibits a superior skill in eddy‐active regions, when compared with drogued drifter observations. Reconstructed subsurface velocities reproduce the spatial structures of eddy‐induced velocity anomaly along the GO‐SHIP observation transect, although present smaller magnitudes. Results demonstrate the potential applicability of the isQG method for reconstructing mesoscale eddies, particularly in the ocean at mid‐to‐high latitudes, where subsurface dynamics are strongly influenced by barotropic and the first baroclinic modes. With the upcoming high‐advanced satellite observations, the isQG framework is expected to achieve better subsurface estimations.

Mooring Measurements of Full-Depth Zonal Currents along the 143°E Meridian in the Northwestern Pacific Ocean

Abstract Full-depth ocean zonal currents in the tropical and extratropical northwestern Pacific (TNWP) are studied using current measurements from 17 deep-ocean moorings deployed along the 143°E meridian from the equator to 22°N during January 2016–February 2017. Mean transports of the North Equatorial Current and North Equatorial Countercurrent are estimated to be 42.7 ± 7.1 Sv (1 Sv ≡ 106 m3 s−1) and 10.5 ± 5.3 Sv, respectively, both of which exhibit prominent annual cycles with opposite phases in this year. The observations suggest much larger vertical extents of several of the major subsurface currents than previously reported, including the Lower Equatorial Intermediate Current, Northern Intermediate Countercurrent, North Equatorial Subsurface Current, and North Equatorial Undercurrent (NEUC) from south to north. The Northern Subsurface Countercurrent and NEUC are found to be less steady than the other currents. Seasonal variations of these currents are also revealed in the study. In the deep ocean, the currents below 2000 m are reported for the first time. The observations confirm the striation patterns of meridionally alternating zonal currents in the intermediate and deep layers. Further analyses suggest a superposition of at least the first four and two baroclinic modes to represent the mean equatorial and off-equatorial currents, respectively. Meanwhile, seasonal variations of the currents are generally dominated by the first baroclinic mode associated with the low-mode Rossby waves. Overall, the above observational results not only enhance the knowledge of full-depth current system in the TNWP but also provide a basis for future model validation and skill improvement.

Free surface and internal periodical waves generated by an oscillating floater in two-layer fluids using fully nonlinear numerical wave tank

This study simulated free-surface and internal periodical waves generated by an oscillating floater in two-layer fluids using a numerical wave tank (NWT) with dual-fluid domains. Each domain was based on the potential flow and boundary element method (BEM). To validate the present NWT, the simulated results were compared with Kashiwagi's theoretical and experimental data, which results in good agreement. The fully nonlinear NWT results were compared systematically with the linear results to quantify their differences through higher-order components in barotropic (or surface wave) and baroclinic (or internal wave) modes both in the surface and internal waves. Free-surface and internal waves were analyzed systematically in terms of the two wave modes, respective-order components, several density ratios, and body-oscillation amplitudes and frequencies. For the present NWT(FN-NWT) with dual fluid domains, three different approaches for updating the instantaneous free surface and interface in the mixed Eulerian-Lagrangian (MEL) method were compared to cross-check the robustness of the developed schemes. When the forced oscillation amplitude and density difference are large, both surface and internal waves have strong nonlinearity, especially in the low-frequency region mainly due to the increased effects of the baroclinic mode. On the other hand, for the surface wave, the increased effects of primary and higher-order components from the barotropic mode are observed, particularly in high frequencies.

On the Observed Wind-Driven Circulation Response in Small Semienclosed Bays

Abstract This study analyzes horizontal and vertical wind-driven circulation responses in small semienclosed bays, the associated offshore dynamic conditions, and the relative importance of each term in the momentum balance equations using a multiplatform observational system. The observational platform consists of three ADCPs and a land-based radar monitoring the velocity field within the bay and in the contiguous offshore area. The wind-driven patterns in the bay can switch from a barotropic cyclonic or anticyclonic circulation to a two-layer baroclinic mode response as a function of the wind regime (its direction and magnitude). For the baroclinic mode, the vertical location of the inflection point in the velocity profile can vary according to the proximity of the boundary current to the entrance of the bay. The influence of offshore combined meteorological and marine conditions on the inner-bay dynamics is evidenced under moderate to strong wind conditions and is almost nonexistent under negligible wind. The momentum balance analysis as well as the nondimensional numbers evidence the impact of wind stress, coastline shape, stratification, and the nonlinear advective terms. Advection can be at the same order of magnitude as pressure gradient, Coriolis, or wind stress terms and can be greater than the bottom stress terms. The nonlinear terms in the momentum equations are frequently neglected when analyzing wind-driven circulation by means of in situ data or analytical models.

Wind and Heat Forcings of the Seasonal and Interannual Sea Level Variabilities in the Southwest Pacific

Abstract Sea level variabilities in the southwest Pacific contribute to the variations of equatorial current bifurcation and the Indonesian Throughflow transport. These processes are closely related to the recharge/discharge of equatorial heat content and dynamic distribution of anthropogenic ocean heating over the Indo-Pacific basin, thus being of profound significance for climate variability and change. Here we identify the major features of seasonal and interannual sea level variabilities in this region, confirming the dominance of the first baroclinic mode in the tropics (contributing 60%–80% of the variances) and higher baroclinic modes in the extratropics (40%–60% of the seasonal variance). Seasonally, except in the western Coral Sea where the Ekman pumping is significant, the wind-driven first-mode baroclinic Rossby waves originating to the east of the date line control the sea level variations over most tropical Pacific regions. In the domain where the 1.5-layer reduced gravity model becomes deficient, the surface heat fluxes dominate, explaining ∼40%–80% of sea level variance. For interannual variability, ∼40%–60% of the variance are El Niño–Southern Oscillation (ENSO) related. The wind-driven Rossby and Kelvin waves east of the date line explain ∼40%–78% of the interannual variance in the tropical Pacific. Outside the tropics, small-scale diffusive processes are presumed critical for interannual variability according to a thermodynamic analysis using an eddy-permitting ocean model simulation. Further process and predictive understandings can be achieved with the coupled climate models properly parameterizing the subgrid-scale processes.

Estimating the Volume Transport of Kuroshio Extension Based on Satellite Altimetry and Hydrographic Data

Abstract In this study, an effective method of estimating the volume transport of the Kuroshio Extension (KE) is proposed using surface geostrophic flow inferred from satellite altimetry and vertical stratification derived from climatological temperature/salinity (T/S) profiles. Based on velocity measurements by a subsurface mooring array across the KE, we found that the vertical structure of horizontal flow in this region is dominated by the barotropic and first baroclinic normal modes, which is commendably described by the leading mode of empirical orthogonal functions (EOFs) of the observed velocity profiles as well. Further analysis demonstrates that the projection coefficient of moored velocity onto the superimposed vertical normal mode can be represented by the surface geostrophic velocity as derived from satellite altimetry. Given this relationship, we proposed a dynamical method to estimate the volume transport across the KE jet, which is well verified with both ocean reanalysis and repeated hydrographic data. This finding implicates that, in the regions where the currents render quasi-barotropic structure, it takes only satellite altimetry observation and climatological T/S to estimate the volume transport across any section. Significance Statement The Kuroshio Extension (KE) plays an important role in the midlatitude North Pacific climate system. To better understand the KE dynamic and its influences, it is very important to estimate the KE transport. However, direct observation is very difficult in this area. Combining a subsurface mooring array and climatological temperature/salinity data, the vertical structure of the KE is explored in this study using mode decomposition methods. The relationship between the vertical structure of the zonal velocity and surface geostrophic flow observed by satellite altimetry in the KE region is further investigated. Based on this relationship, the KE transport can be well estimated by using satellite altimetry observation and historical hydrographic observation.

Impact of vertical resolution on representing baroclinic modes and water mass distribution in the North Atlantic

In contrast to the large volume of studies on the impact of horizontal resolution in oceanic general circulation models (OGCMs), the impact of vertical resolution has been largely overlooked and there is no consensus on how one should construct the vertical grid to represent the vertical structure of the baroclinic modes as well as the distribution of distinct water masses throughout the global ocean. In this paper, we document the importance of vertical resolution in the representations of vertical modes and water masses in the North Atlantic and show i) that vertical resolution is unlikely to undermine the resolution capability of the horizontal grid in representing the vertical modes and a 32-layer isopycnal configuration is adequate to represent the first five baroclinic modes in mid-latitudes and ii) that vertical resolution should focus on representing water masses. A coarse vertical resolution (16-layer) simulation exhibits virtually no transport in the dense overflow water which leads to a weaker and significantly shallower Atlantic meridional overturning circulation (AMOC) despite resolving the first baroclinic mode throughout the domain, whereas there are overall very small differences in the subtropical and subpolar North Atlantic circulation in the simulations with finer vertical resolution (24 to 96 layers). We argue that accurately representing the water masses is more important than representing the baroclinic modes for an OGCM in modeling the low-frequency large-scale circulation.

The weakening of the tropical circulation is caused by the lifting of the tropopause height

In this study we analyse the physical processes causing the weakening of the tropical circulation in the Coupled Model Intercomparison Project 6 (CMIP6). We apply a diagnostic model for the large-scale tropical circulation (vertical motion) based on the moist static energy for the first baroclinic mode (MSEB) and evaluate the sensitivity of the tropical circulation changes to the changes in advection of moisture and heat, the net radiation, the moist static stability, the baroclinic mode, and to the height of the tropopause. Based on the CMIP6 model simulations we find that the tropical circulation weakens by about 10-15% over the twenty-first century. The analysis of the MSEB model suggests that the primary cause for this weakening of the tropical circulation is the lifting of the tropopause height. This effect is fairly uniform throughout the tropics and present in all model simulations. The tropopause height increase shifts the first baroclinic mode away from lower levels with unstable air masses into high levels of the troposphere where stable air masses lead to a stabilisation of the large-scale circulation. Other factors such as changes in the advection of moisture and heat, increased net heating or increased instability of the lower tropospheric gross moist stability do have strong regional differences, and mostly increase tropical circulations, counteracting the weakening caused by the lifting of the tropopause.

Observed Oceanic Surface Modes in the Northern South China Sea

Abstract Using observations and theoretical models, a substantial topographic modulation on the quasigeostrophic (QG) dynamics, which results in a primary surface mode distinct from the classic first baroclinic (BC1) mode with a flat bottom, is revealed in the northern South China Sea (NSCS). In contrast to open oceans, the surface-intensified modes decay downward more rapidly over the continental slope of the NSCS, with a mean e-folding scale of approximately 1/5 of water depth. The subinertial flow variability appears to be vertically incoherent, with planetary and topographic Rossby waves dominating in the upper and deep layers, respectively. With a larger deformation radius (Rd), the surface-mode Rossby waves propagate at a phase speed ∼1.5 times of that of the BC1 mode. Moreover, the modal structures can be substantially modified by seasonal NSCS circulation, which is significantly enhanced over continental slopes. Analysis of the triad interactions further implies that the short waves tend to transfer energy to larger scales via the inverse cascade and only those with wavelengths larger than Rd ≈ 70 km in the NSCS can persist because of a slower unstable growth rate but a higher fraction of upscale energy transfer. The present theory excludes the bottom-trapped mode, which is closely associated with topographic Rossby waves and is observed to be significant in the abyssal NSCS. Hence, a complete normal-mode basis for any QG state is required for a study that focuses on flow variability throughout the water column. Our findings provide an insight into the vertical partition of horizontal kinetic energy for QG motions, as well as the relevant oceanic variation in marginal seas.

Modulations of Storm-Track Activity Associated with the Baroclinic Annular Mode

Abstract The baroclinic annular mode (BAM) is the leading mode of variability in extratropical eddy activity characterized by its hemispheric-scale pulsing. Based on atmospheric reanalysis data for the Southern Hemisphere, this study reveals BAM-associated systematic modulations not only in fluxes associated with subweekly transient disturbances, as found by earlier studies, but also in their spatial structure involved in the dynamics of the BAM. Specifically, in the positive phase of the BAM characterized by enhanced activity of transient disturbances, their lower-tropospheric baroclinic structure becomes more distinct, and they tend to be more elongated meridionally in both the upper and lower troposphere. These BAM-associated structural modulations of the disturbances favor the more efficient baroclinic development via enhanced poleward heat transport and their downstream development, which can contribute to hemispheric-scale enhancement of kinetic energy associated with the disturbances. In addition, a tendency of the disturbances to exhibit horizontally tilting structure becomes more evident in the positive phase of the BAM, which is favorable for enhanced transport of westerly momentum from the subtropics to the midlatitude polar-front jet, or equivalently enhanced wave-activity propagation from the midlatitude storm track into the subtropics. This modulation lags the peak of anomalous kinetic energy of the disturbances, thus acting to contribute to the decay of the BAM signature. A set of numerical simulations suggests that the BAM-associated pulsing in storm-track activity and structural modulations are manifestations of atmospheric internal dynamics, which can be significantly amplified in the presence of a midlatitude oceanic frontal zone through the formation of more organized and coherent baroclinic wave packets.

Experimental and numerical study on wave characteristics by a moving submerged body in a two-layer fluid

Waves induced by an immersed moving body in a two-layer fluid were studied experimentally and numerically. Unmixed fluids (water and cooking oil) were used as the two-layer fluid. A submerged body was manufactured to move with a wire loop system connected to the motor. The measured data were compared with numerical results and theoretical solutions. Numerical calculations were performed using the computational fluid dynamics (CFD) program. The characteristics of the generated waves, such as wave patterns and wavelengths, were qualitatively similar to the numerical results and theoretical values. Of the two wave propagation modes in a two-layer fluid, the baroclinic mode was dominant when the immersed body moved at a low speed. In contrast, the barotropic mode became more prominent as the body velocity increased. Based on these characteristics, transverse waves dominated when the velocity of the body was low, and divergent waves became more distinct as the velocity increased. In addition, the fluid depth and the location of a submerged body can affect the characteristics of the wave patterns.

Internal ring waves in a three-layer fluid on a current with a constant vertical shear

Oceanic internal waves often have curvilinear fronts and propagate over vertically sheared currents. We present the first study of long weakly-nonlinear internal ring waves in a three-layer fluid in the presence of a horizontally uniform background current with a constant vertical shear. The leading order of this theory leads to the angular adjustment equation—a nonlinear first-order ordinary differential equation describing the dependence of the linear long-wave speed on its angle to the direction of the current. The compact ring waves, well studied in the absence of a current, correspond to the singular solution (envelope of the general solution) of this equation, and they can exist only under certain conditions. The constructed solutions reveal qualitative differences in the shapes of the wavefronts of the two baroclinic modes: the wavefront of the faster mode is elongated in the direction of the current, while the wavefront of the slower mode is squeezed. Moreover, depending on the vorticity strength, several different regimes have been identified. When the vertical shear is weak, part of the wavefront is able to propagate upstream, while when the shear is strong enough, the whole wavefront propagates downstream. A richer pattern of behaviour is observed for the slower mode. As the shear increases, singularities of the swallowtail-type may arise and, eventually, solutions with compact wavefronts crossing the downstream axis cease to exist. We show that the latter is related to the long-wave instability of the base flow. We obtain the cKdV-type amplitude equation and examine analytical expressions for its coefficients. Using this cKdV-type equation we numerically model the evolution of the waves for both modes. The initial stage of the evolution is in agreement with the leading-order predictions for the deformations of the wavefronts. Then, as the wavefronts expand, strong dispersive effects occur in the upstream direction. Moreover, when nonlinearity is enhanced, fission of waves is observed in the upstream part of the ring waves.

Variance in baroclinic modes across frequency bands in a global ocean simulation

Variance in baroclinic modes across frequency bands in a global ocean simulation

A shallow layer laboratory model of large-scale atmospheric circulation

A new shallow layer laboratory model of global atmospheric circulation is realised and studied by experiments and numerical simulations. A shallow rotating cylindrical fluid layer of 30 mm thickness and 690 mm diameter, with a localised heater at the bottom periphery and localised cooler in the central part of the upper boundary is considered. The rim heater imitates the equator heating and disc cooler – the North pole cooling. The flow transforms from the Hadley-like regime to the baroclinic wave regime through transitional states. The decrease in the thermal Rossby number for the fixed value of Taylor number results in the regularisation of the baroclinic waves. All wave regimes, even with regular wave structures, are characterised by strong non-periodic fluctuations. The observed baroclinic wave structures are a combination of temporarily evolving different baroclinic modes. The important outcome of the shallow layer model is a realisation of the Earth-like meridional three-cell structure. It is shown that the three-cell structure with analogs of polar, Ferrel and Hadley cells exist only in a limited range of parameters. A comparison of the results for the water and silicon oil demonstrated that the physical properties of the fluid can have a strong impact on the baroclinic wave structure.

Energy Conversion Rate from Subinertial Surface Tides to Internal Tides

Abstract Subinertial, topographically trapped diurnal internal tides are an important energy source for turbulent mixing in the subarctic oceans. However, their generation may not be estimated by the conventional barotropic-to-baroclinic conversion because their vertical structure is sometimes barotropic, unlike superinertial internal tides that are always baroclinic. Here, a new energy diagram is presented, in which the barotropic mode is decomposed into the surface and topographic modes, with the latter being classified as part of the internal modes together with the baroclinic mode. The energy equation for the newly defined topographic mode is then derived, providing an appropriate formulation of the energy conversion rate from the subinertial surface tides to the topographically trapped internal tides. A series of numerical experiments confirm that the formulation successfully predicts the energy conversion rate for various cases, with the relative contribution of the baroclinic and topographic modes varying significantly depending on the bottom topography and stratification. Furthermore, this surface-to-internal conversion is demonstrated to give a significantly larger estimate than the barotropic-to-baroclinic conversion for subinertial tides. Applying the formulation to the results of a realistic numerical simulation in the Kuril Straits, an area with the strongest mixing due to subinertial diurnal tides, shows that the surface mode is converted into the baroclinic and topographic modes with comparable magnitudes, responsible for most of the energy dissipation in this area. These results indicate the need to reestimate the global distribution of the generation rate of the subinertial internal tides using our new formulation and to clarify their dissipation mechanisms. Significance Statement Diurnal internal tides in mid- to high-latitude oceans are very different from semidiurnal internal tides, in that they are trapped by topographic features and characterized by uniform rotation throughout the water column rather than by vertical oscillations within the water column. Focusing on this character, we formulate for the first time the generation rate of diurnal internal tides trapped over variable bottom topography. A series of idealized numerical experiments and application to the Kuril Straits show the validity and usefulness of this formulation, which provides a significantly larger generation estimate than previous studies. The results of this study are important for accurate global mapping of turbulent mixing induced by the breaking of internal tides.

The vertical structure and intraseasonal variability of the deep currents in the Southern Philippine Basin

Based on the four-mooring array measurements along 130°E over 2015–2020, the vertical structure and variability of deep currents in the central Southern Philippine Basin (SPB) are revealed. The deep currents below 1500 m in the central SPB are characterized by alternating westward and eastward zonal jets with strong intraseasonal variability (ISV). These zonal jets have a weak mean velocity of less than 1.5 cm s−1 but vary with a relatively large amplitude of 10 cm s−1 at the intraseasonal period of 20–120 days. The full-depth zonal velocity in the central SPB has three typical vertical structures that are mainly controlled by the first baroclinic mode, the second and higher baroclinic modes, and the barotropic mode in descending order of occurrence frequency. These structures are vertically coherent below ∼2000–2500 m, below ∼1200 m, and over the whole water column, respectively. Further analysis of numerical ocean modeling results demonstrates that the ISV of deep currents is induced by the deep mesoscale eddy. The deep ISV intensifies when a deep eddy passes by and keeps at a low value when there is no deep eddy activity around. The deep eddy extends to the bottom with the upper boundaries at ∼1500 m below the subsurface layer or at ∼300 m including the subsurface layer. These deep eddies arise primarily from barotropic instability and secondarily from baroclinic instability.