Higher Baroclinic Modes Research Articles

Baroclinic Tide Generation at the Dolphin and Union Strait in the Southern Canadian Arctic Archipelago

We studied baroclinic tide generation at the Dolphin and Union Strait, a channel in the southern Canadian Arctic Archipelago that consists of a shallow sill. Utilizing both observational data and numerical simulations, we found that, due to the presence of strong stratification in the summertime, baroclinic tides are generated at both M2 and K1 frequencies as a result of the interaction between the amplified tidal currents and bottom topography. The M2 baroclinic current, which is comparable to the M2 barotropic current in terms of amplitude, is dominated by linear dynamics in the first baroclinic mode. The amplitude of the M2 baroclinic current increases as the strength of stratification increases. In contrast, the K1 baroclinic current has a smaller amplitude in general. Dynamics of the K1 baroclinic current are more complicated, possibly due to nonlinear effects as well as contributions from the higher baroclinic modes. On the other hand, increasing the strength of stratification leads to a noticeable reduction of K1 elevation in the nearby basin, but has a very minor effect on M2 elevation.

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.

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.

Turbulent Transition of a Flow from Small to O(1) Rossby Numbers

Abstract Oceanic flows are energetically dominated by low vertical modes. However, disturbances in the form of atmospheric storms, eddy interactions with various forms of boundaries, or spontaneous emission by coherent structures can generate weak high-baroclinic modes. The feedback of the low-energy high-baroclinic modes on large-scale energetically dominant low modes may be weak or strong depending on the flow Rossby number. In this paper we study this interaction using an idealized setup by constraining the flow dynamics to a high-energy barotropic mode and a single low-energy high-baroclinic mode. Our investigation points out that at low Rossby numbers the barotropic flow organizes into large-scale coherent vortices via an inverse energy flux while the baroclinic flow accumulates predominantly in anticyclonic barotropic vortices. In contrast, with increasing Rossby number, the baroclinic flow catalyzes a forward flux of barotropic energy. The barotropic coherent vortices decrease in size and number, with a strong preference for cyclonic coherent vortices at higher Rossby numbers. On partitioning the flow domain into strain-dominant and vorticity-dominant regions based on the barotropic flow, we find that at higher Rossby numbers baroclinic flow accumulates in strain-dominant regions, away from vortex cores. Additionally, a major fraction of the forward energy flux of the flow takes place in strain-dominant regions. Overall, one of the key outcomes of this study is the finding that even a low-energy high-baroclinic flow can deplete and dissipate large-scale coherent structures at O(1) Rossby numbers.

Vertical Structure and Seasonal Variability of Shear on the Southwestern Continental Slope of the East China Sea

The vertical structure and seasonal variability of shear were examined using nearly three years of mooring ADCP (acoustic Doppler current profiler) data on the southwestern continental slope of the East China Sea (ECS). Shear spectra suggest that the sub-inertial currents (SICs); near-inertial waves (NIWs); and diurnal (D1), semidiurnal (D2), and tridiurnal (D3) internal tides (ITs) dominate the local shear field. The shear exhibits a remarkable surface-intensified pattern with high values occurring mostly in the upper 200 m. Significant seasonal variations can be found in the shear, but with differences between the upper (50–200 m averaged) and lower layers (210–570 m averaged). Satellite altimeter data indicate that the meander of the Kuroshio mainstream and the Kuroshio intrusion affect the seasonal variation of total shear by mainly influencing the shear caused by SICs. In addition, the shear efficiency (SE) of D2 ITs is obviously less than that of NIWs and that of D1 and D3 ITs via analyzing the kinetic energy (KE) densities and shear caused by these motions, since the predominant mode of the former is the first baroclinic mode, while the latter is dominated by higher baroclinic modes with large vertical wavenumbers. Moreover, the SE of incoherent ITs is relatively stronger than that of coherent ITs as a result of a larger proportion of high baroclinic modes in the incoherent component compared to the coherent component, based on modal decomposition.

Determination of Spatiotemporal Variability of the Indian Equatorial Intermediate Current

AbstractUsing 4-yr mooring observations and ocean circulation model experiments, this study characterizes the spatial and temporal variability of the Equatorial Intermediate Current (EIC; 200–1200 m) in the Indian Ocean and investigates the causes. The EIC is dominated by seasonal and intraseasonal variability, with interannual variability being weak. The seasonal component dominates the midbasin with a predominant semiannual period of ~166 days but weakens toward east and west where the EIC generally exhibits large intraseasonal variations. The resonant second and fourth baroclinic modes at the semiannual period make the largest contribution to the EIC, determining the overall EIC structures. The higher baroclinic modes, however, modify the EIC’s vertical structures, forming multiple cores during some time periods. The EIC intensity has an abrupt change near 73°E, which is strong to the east and weak to the west. Model simulation suggests that the abrupt change is caused primarily by the Maldives, which block the propagation of equatorial waves. The Maldives impede the equatorial Rossby waves, reducing the EIC’s standard deviation associated with reflected Rossby waves by ~48% and directly forced waves by 20%. Mode decomposition further demonstrates that the semiannual resonance amplitude of the second baroclinic mode reduces by 39% because of the Maldives. However, resonance amplitude of the four baroclinic mode is less affected, because the Maldives fall in the node region of mode 4’s resonance. The research reveals the spatiotemporal variability of the poorly understood EIC, contributing to our understanding of equatorial wave–current dynamics.

On the roles of baroclinic modes in eddy-resolving midlatitude ocean dynamics

This work concerns how different baroclinic modes interact and influence solutions of the midlatitude ocean dynamics described by the eddy-resolving quasi-geostrophic model of wind-driven gyres. We developed multi-modal energetics analysis to illuminate dynamical roles of the vertical modes, carried out a systematic analysis of modal energetics and found that the eddy-resolving dynamics of the eastward jet extension of the western boundary currents, such as the Gulf Stream or Kuroshio, is dominated by the barotropic, and the first and second baroclinic modes, which become more energized with smaller eddy viscosity. In the absence of high baroclinic modes, the energy input from the wind is more efficiently focused onto the lower modes, therefore, the eddy backscatter maintaining the eastward jet and its adjacent recirculation zones is the strongest and overestimated with respect to cases including higher baroclinic modes. In the presence of high baroclinic modes, the eddy backscatter effect on the eastward jet is much weaker. Thus, the higher baroclinic modes play effectively the inhibiting role in the backscatter, which is opposite to what has been previously thought. The higher baroclinic modes are less energetic and have progressively decreasing effect on the flow dynamics; nevertheless, they still play important roles in inter-mode energy transfers (by injecting energy into the region of the most intensive eddy forcing, in the neighborhood of the eastward jet) that have to be taken into account for correct representation of the backscatter and, thus, for determining the eastward jet extension.

Revisiting the cause of the eastern equatorial Atlantic cold event in 2009

AbstractAn extreme cold sea surface temperature event occurred in the Atlantic cold tongue region in boreal summer 2009. It was preceded by a strong negative Atlantic meridional mode event associated with north‐westerly wind anomalies along the equator from March to May. Although classical equatorial wave dynamics suggest that westerly wind anomalies should be followed by a warming in the eastern equatorial Atlantic, an abrupt cooling took place. In the literature two mechanisms—meridional advection of subsurface temperature anomalies and planetary wave reflection—are discussed as potential causes of such an event. Here, for the first time we use in situ measurements in addition to satellite and reanalysis products to investigate the contribution of both mechanisms to the 2009 cold event. Our results suggest that meridional advection is less important in cold events than in corresponding warm events, and, in particular, did not cause the 2009 cold event. Argo float data confirm previous findings that planetary wave reflection contributed to the onset of the 2009 cold event. Additionally, our analysis suggests that higher baroclinic modes were involved.

Multi-layer quasi-geostrophic ocean dynamics in Eddy-resolving regimes

The multi-layer quasi-geostrophic model of the wind-driven ocean gyres is numerically investigated using a combination of long-time runs (200 years) needed for accurate statistics, spatial resolutions (grid interval of less than one kilometer) needed for accurate representation of mesoscale eddies, and large Reynolds number (Re > 104) needed for more realistic flow regimes. We gradually increased the Reynolds number by lowering the eddy viscosity and analysed the corresponding changes of the large-scale circulation, energetics and eddy fluxes, with the goal to understand how the nonlinear eddy dynamics affects the large-scale ocean circulation, as more and more degrees of freedom become dynamically available. Three- and six-layer configurations of the model are considered in order to understand effects of higher baroclinic modes. A parameter sensitivity study is also carried out to show that the explored flow regime is robust.As Re increases, most properties of the flow show no signs of approaching an asymptote, and the following tendencies are found. The time-mean flow properties tend to an asymptote in the three-layer model but not in the six-layer one, suggesting that higher baroclinic modes are dynamically more active at larger Re. The eddy kinetic and potential energies grow faster in the six-layer case. The intensity of the eddy forcing (eddy flux divergence) increases with Re. The inter-gyre eddy potential vorticity flux is predominantly northward and up-gradient for all Re studied. A comparison of the three- and six-layer model solutions revealed an inhibitory influence of high baroclinic modes on the penetration length of the eastward jet extension of the western boundary currents and on the strength of the adjacent recirculation zones. In large-Re regimes, the population of eddies is mostly sustained by the eddy generation at the eastern end of the eastward jet rather than in its central section. Finally, by studying the numerical convergence of the solutions, we found the empirical dependency between the eddy viscosity and the required grid resolution: halving the viscosity requires halving the grid spacing.

Vertical structure of eddies and Rossby waves, and their effect on the Atlantic meridional overturning circulation at 26.5°N

AbstractThe meridional overturning circulation (MOC) at in the Atlantic has a standard deviation of 4.9 Sv and contains large fluctuations at subannual periods. The geostrophic component of the MOC is believed to be influenced on subannual time scales by eddies and Rossby waves. To quantify this effect, the vertical structure and surface characteristics of westward propagating signals are studied using altimetric data and full‐depth mooring measurements from the RAPID array at . Westward propagating features are observed in the western North Atlantic in both data sets and have periods of 80–250 days in the first baroclinic mode. These features are still observed by the RAPID moorings 20 km offshore of the western boundary. The western boundary also exhibits deep variability characterized by enhanced energy in higher baroclinic modes. The effect of eddies and Rossby waves on the geostrophic transport is quantified by representing their vertical structure with the first baroclinic mode. In total, 42% of the variance of the transbasin thermocline transport inferred from geostrophic calculations at can be attributed to first mode variability, which is associated with eddies and Rossby waves at periods of 80–250 days. The standard deviation of the transbasin thermocline transport due to eddies and Rossby waves is estimated to be 2.6 Sv.

The effect of non-uniform depth on the baroclinic response to wind in elongated basins

We examined the effect of along-thalweg depth variability on the baroclinic response to wind in elongated narrow basins with a sharp thermocline. The effect of depth variability was examined by deriving a modal-based forced model with two density layers and applying the model to a symmetric curved-bottom basin (CB), an asymmetric wedge-shaped basin (with a sloping bottom towards a vertical wall, WB), and a flat-bottom basin (FB). The baroclinic responses of CB, WB, and FB to uniform wind were found to differ in time-scale, number and energy of excited modes, and temporal pattern and along-thalweg structure of baroclinic flow and thermocline deflection. For all bottom profiles that were examined, the fundamental mode was found to dominate the response to spatially-uniform wind. Compared to FB, the asymmetric depth variability in WB increased the number and energy of excited higher modes and localized the interface shear, while the symmetric deviation from flat bottom in CB caused the opposite effects. Linear deviation from uniform wind was found to feed energy into higher baroclinic modes for the symmetric CB, but was found to reduce the energy of higher baroclinic modes for WB when the deviation from uniform wind is comparable to the spatial-average magnitude. Our results can explain the observation of the second baroclinic mode and irregular wave patterns in some lakes and reservoirs. Further, our results suggest that one-dimensional vertical mixed-layer models provide better results for shear entrainment in curved-bottom basins than in wedge-shaped basins.

Cascade Inequalities for Forced–Dissipated Geostrophic Turbulence

AbstractAnalysis of spectral kinetic energy fluxes in satellite altimetry data has demonstrated that an inverse cascade of kinetic energy is ubiquitous in the ocean. In geostrophic turbulence models, a fully developed inverse cascade results in barotropic eddies with large horizontal scales. However, midocean eddies contain substantial energy in the baroclinic mode and in compact horizontal scales (scales comparable to the deformation radius Ld). This paper examines the possibility that relatively strong bottom friction prevents the oceanic cascade from becoming fully developed. The importance of the vertical structure of friction is demonstrated by contrasting numerical simulations of two-layer quasigeostrophic turbulence forced by a baroclinically unstable mean flow and damped by bottom Ekman friction with turbulence damped by vertically symmetric Ekman friction (equal decay rates in the two layers). “Cascade inequalities” derived from the energy and enstrophy equations are used to interpret the numerical results. In the symmetric system, the inequality formally requires a cascade to large-scale barotropic flow, independent of the stratification. The inequality is less strict when friction is in the bottom layer only, especially when stratification is surface intensified. Accordingly, model runs with surface-intensified stratification and relatively strong bottom friction retain substantial small-scale baroclinic energy. Altimetric data show that the symmetric inequality is violated in the low- and midlatitude ocean, again suggesting the potential impact of the “bottomness” of friction on eddies. Inequalities developed for multilayer turbulence suggest that high baroclinic modes in the mean shear also enhance small-scale baroclinic eddy energy. The inequalities motivate a new interpretation of barotropization in weakly damped turbulence. In that limit the barotropic mode dominates the spatial average of kinetic energy density because large values of barotropic density are found throughout the model domain, consistent with the barotropic cascade to large horizontal scales, while baroclinic density is spatially localized.

Effects of tidal mixing at the Kuril Straits on North Pacific ventilation: Adjustment of the intermediate layer revealed from numerical experiments

The effects of tidal mixing at the Kuril Straits on the North Pacific intermediate layer are investigated using an ocean general circulation model. A comparison of numerical experiments with and without a tidal mixing effect suggests that tidal mixing at the Kuril Straits enhances the ventilation of the North Pacific intermediate layer. The enhanced ventilation results in both freshening and cooling down to ∼27.6 σθ. In particular, the simulated North Pacific Intermediate Water (NPIW) becomes fresher and denser (by 0.3 psu and 0.1 σθ at the maximum) and hence more realistic. The enhanced ventilation is caused both through the supply of the ventilated water from the Kuril Straits, which subsequently spreads along the subarctic and subtropical gyres, and through a modification of the circulation there. The ventilation of the supplied water in turn originates from a combination of tidally enhanced convection in the Okhotsk Sea and downward diffusion at the Kuril Straits as discussed in a previous paper. The former affects the upper part of the NPIW, while the latter is dominant in the denser layers. The circulation is modified through a dynamical adjustment to the mass input into an intermediate layer that is produced by the convergence of diapycnal transport due to the tidally enhanced convection and diffusion. The dynamical adjustment is conducted mainly through Kelvin waves which have the ability to induce intergyre flow along the western boundary and also by eastward moving long Rossby waves. The latter can be present under the influence of the wind‐driven gyres for the second and higher baroclinic modes and act to spread information into the interior directly from the western boundary. As a direct consequence of this adjustment, transport of the ventilated water from the Kuril Straits to the subtropical gyre is enhanced by the intergyre flow along the western boundary, which appears as the southward intrusion of the Oyashio Current. The transported water leaves the coast to encircle the interior, and returns to the western boundary, eventually flowing into the equatorial region. Such equatorward transport associated with mass convergence in the intermediate layer is compensated by transport toward the Kuril Straits in the shallower and deeper layers, thereby enhancing both shallow and deep meridional overturning cells by 2–3 Sv. The above dynamical adjustment is thus central to our understanding of the ventilation of the intermediate layer and provides a basis for the analytical model developed in an accompanying paper.

Vertical structure variability in the equatorial Pacific before and after the Pacific climate shift of the 1970s

Oceanic baroclinic modes in the equatorial Pacific are estimated using results from the SODA system. Our result suggests that the vertical stratification increases at the upper levels after the late 1970s due to changes in the vertical temperature structure. After the late 1970s, the variability of the higher‐order baroclinic mode contributions to current anomalies and surface pressure significantly increases in the central equatorial Pacific. This is associated with an increase of the dominant period of the ENSO variability. Simple coupled model experiments indicate that when atmospheric forcing projects more onto the higher baroclinic modes according to the results of the SODA decomposition, the amplitude and dominant period of ENSO increase similarly to what is observed at the Pacific decadal shift. Our results support that the changes in the behavior of ENSO after the late 1970s are associated with oceanic vertical structural changes in temperature that tend to increase the contribution of higher‐order baroclinic modes.

Search for the origins of Pacific decadal climate variability

The origin of Pacific decadal climate variability is investigated in a coupled ocean‐atmosphere general circulation model. The impact of regional ocean‐atmosphere coupling and oceanic teleconnection on decadal variability is evaluated by performing a set of specifically designed experiments. It is found that decadal variability in the tropical and North Pacific originates predominantly from local coupled ocean‐atmosphere processes within the tropical and North Pacific region, respectively. Furthermore, tropical Pacific decadal variability appears to be associated with higher baroclinic modes and can be enhanced substantially by extratropical‐tropical oceanic teleconnection.

The Scales and Equilibration of Midocean Eddies: Freely Evolving Flow

Quasigeostrophic turbulence theory and numerical simulation are used to study the mechanisms determining the scale, structure, and equilibration of mesoscale ocean eddies. The present work concentrates on using freely decaying geostrophic turbulence to understand and explain the vertical and horizontal flow of energy through a stratified, horizontally homogeneous geostrophic fluid. It is found that the stratification profile, in particular the presence of a pycnocline, has significant, qualitative effects on the efficiency and spectral pathways of energy flow. Specifically, with uniform stratification, energy in high baroclinic modes transfers directly, quickly (within a few eddy turnaround times), and almost completely to the barotropic mode. By contrast, in the presence of oceanlike stratification, kinetic energy in high baroclinic modes transfers intermediately to the first baroclinic mode, whence it transfers inefficiently (and incompletely) to the barotropic mode. The efficiency of transfer to the barotropic mode is reduced as the pycnocline is made increasingly thin. The b effect, on the other hand, improves the efficiency of barotropization, but for oceanically realistic parameters this effect is relatively unimportant compared to the effects of nonuniform stratification. Finally, the nature of turbulent cascade dynamics is such as to lead to a concentration of first baroclinic mode kinetic energy near the first radius of deformation, which, in the case of a nonuniform and oceanically realistic stratification, has a significant projection at the surface. This may in part explain recent observations of surface eddy scales by TOPEX/Poseidon satellite altimetry, which indicate a correlation of surface-height variance with the scale of the first deformation radius.

Climate Variability Inferred from a Continuously Stratified Model of the Ideal-Fluid Thermocline*

Climate variability in the subtropical gyre interior induced by anomalous surface thermal forcing, Ekman pumping, mixed layer depth variability, and anomalous subpolar water formation is examined, using a continuously stratified model of the ideal-fluid thermocline. Cooling (heating) induces a negative (positive) potential vorticity perturbation in the ventilated thermocline, and the associated density perturbations propagate downstream in the form of second and higher baroclinic modes. The second baroclinic mode resembles the traditional second baroclinic mode because it has a thermal structure with cooling (warming) in the upper thermocline and warming (cooling) in the lower thermocline. Anomalous Ekman pumping can also induce density perturbations that propagate westward in the form of the first baroclinic mode. In addition, if the outcrop lines are nonzonal, there are density perturbations that propagate downstream in the form of the second or third baroclinic modes. Perturbations in the sea surface elevation are mostly confined to the region of anomalous forcing. On the other hand, when the low potential vorticity anomaly in the subpolar mode water spreads into the subtropical basin, both the unventilated and ventilated thermocline move downward. Consequently, temperature at a given depth seems to increase.

On the Catalytic Role of High Baroclinic Modes in Eddy-driven Large-Scale Circulations

Abstract This paper investigates the tridimensional consistency of the resolution of eddy scales in simulating large-scale flows. The generation of classical wind-forced, eddy-driven double-gyre circulation is investigated with a multilayered quasi-geostrophic model. Six-layers on the vertical have been chosen to assure the convergence of the baroclinic instability. Emphasis is on the resolution of the high baroclinic modes and its effects on the dynamics of the midlatitude jet. Several eddy-resolving experiments, identical except for the horizontal resolution, which can be low (20 km) or high (10 km), are compared. In every experiment, the scales associated with the first and second baroclinic modes are well resolved, but those associated with the third and higher baroclinic modes are so only in 10-km experiments For a better illustration of the importance of the high vertical modes, three-layer experiments having configurations equivalent to that of the six-layer experiments have been conducted. Note th...

The Interaction of Equatorial Kelvin Waves with Realistically Sheared Zonal Currents

Abstract We investigate the interaction of baroclinic equatorial Kelvin waves with realistically sheared background zonal currents in a linearized, continuously stratified model. The background flows are in thermal wind balance and allowed to vary continuously in the meridional and vertical directions. The governing equations for long-wave perturbations that are harmonic in time and longitude are reduced to a second-order partial differential equation for pressure on the meridional plane, then solved numerically in finite difference form. Our results indicate that the presence of a background jet can significantly modify the structures and dispersion characteristics of baroclinic Kelvin waves, depending on the speed and the spatial scales of the jet relative to those of the waves. The lowest baroclinic mode, which has a zonal phase speed much larger than typical mean flows, is the least structurally modified and Doppler-shifted. Higher baroclinic modes am more noticeably Doppler-shifted and experience str...