Baroclinic Deformation Radius Research Articles

A numerical investigation on the energetics of a current along an ice-covered continental slope

Abstract. The Chukchi Slope Current is a westward-flowing current along the Chukchi slope, which carries Pacific-origin water from the Chukchi shelf into the Canada Basin and helps set the regional hydrographic structure and ecosystem. Using a set of experiments with an idealized primitive equation numerical model, we investigate the energetics of the slope current during the ice-covered period. Numerical calculations show that the growth of surface eddies is suppressed by the ice friction, while perturbations at mid-depths can grow into eddies, consistent with linear instability analysis. However, because the ice stress is spatially variable, it is able to drive Ekman pumping to decrease the available potential energy (APE) and kinetic energy of both the mean flow and mesoscale eddies over a vertical scale of 100 m, well outside the frictional Ekman layer. The rate at which the APE changes is determined by the vertical density flux, which is negative as the ice-induced Ekman pumping advects lighter (denser) water upward (downward). A scaling analysis shows that Ekman pumping will dominate the release of APE for large-scale flows, but the effect of baroclinic instability is also important when the horizontal scale of the mean flow is the baroclinic deformation radius and the eddy velocity is comparable to the mean flow velocity. Our numerical results highlight the importance of ice friction in the energetics of the slope current and eddies, and this may be relevant to other ice-covered regions.

On Dynamical Decomposition of Multiscale Oceanic Motions

AbstractThe ocean hosts a variety of fluid motions characterized by contrasting dynamical regimes and spatiotemporal scales. A practical decomposition of multiscale motions in realistic oceanic settings is crucial to advancing dynamical interpretation and prediction of oceanic processes, but remains a major challenge. To this end, methodology is developed in this study for decomposing multiscale oceanic motions based on their respective dynamical characteristics. Specifically, large‐scale currents and barotropic tides have the largest horizontal scales but contrasting frequencies; low‐mode internal gravity waves (IGWs) are well constrained by linear dispersion relations, whereas mesoscale flows are of relatively low frequency and with horizontal scales above the first baroclinic deformation radius; the intrinsic frequency of high‐mode IGWs (submesoscale flows) is above (well below) the inertial frequency. The validity and usefulness of the proposed methodology are demonstrated with a proof‐of‐concept application to simulated flows in the central basin of the South China Sea.

A Three-Dimensional Inertial Model for Coastal Upwelling along Western Boundaries

Abstract A three-dimensional inertial model that conserves quasigeostrophic potential vorticity is proposed for wind-driven coastal upwelling along western boundaries. The dominant response to upwelling favorable winds is a surface-intensified baroclinic meridional boundary current with a subsurface countercurrent. The width of the current is not the baroclinic deformation radius but instead scales with the inertial boundary layer thickness while the depth scales as the ratio of the inertial boundary layer thickness to the baroclinic deformation radius. Thus, the boundary current scales depend on the stratification, wind stress, Coriolis parameter, and its meridional variation. In contrast to two-dimensional wind-driven coastal upwelling, the source waters that feed the Ekman upwelling are provided over the depth scale of this baroclinic current through a combination of onshore barotropic flow and from alongshore in the narrow boundary current. Topography forces an additional current whose characteristics depend on the topographic slope and width. For topography wider than the inertial boundary layer thickness the current is bottom intensified, while for narrow topography the current is wave-like in the vertical and trapped over the topography within the inertial boundary layer. An idealized primitive equation numerical model produces a similar baroclinic boundary current whose vertical length scale agrees with the theoretical scaling for both upwelling and downwelling favorable winds.

Bi‐Directional Energy Cascades in the Pacific Ocean From Equator to Subarctic Gyre

AbstractOcean circulation receives its energy input at basin scales while dissipates at microscopic mixing scale. How this energy is transferred across different lengthscales is of paramount importance for understanding the ocean circulation equilibration and variability. Advancement in high‐resolution numerical simulations in recent years has significantly improved our understanding of kinetic energy (KE) cascades from basin to kilometer scales, although observational evidence to verify the simulated processes remains limited. Using repeat ship‐board velocity measurements along 165°E across the equatorial, subtropical and subarctic Pacific Ocean, we show that the length scale separating the inverse and forward cascades, LS, falls in the 8 ∼ 300 km range and it does not scale straightforwardly with the baroclinic deformation radius. Balanced and unbalanced oceanic motions co‐exist in this range but contribute oppositely to the directional energy cascades. LS is observed to depend on the relative strengths of these motions, as well as by their interaction.

Topographic Influences on the Wind-Driven Exchange between Marginal Seas and the Open Ocean

AbstractThe wind-driven exchange through complex ridges and islands between marginal seas and the open ocean is studied using both numerical and analytical models. The models are forced by a steady, spatially uniform northward wind stress intended to represent the large-scale, low-frequency wind patterns typical of the seasonal monsoons in the western Pacific Ocean. There is an eastward surface Ekman transport out of the marginal sea and westward geostrophic inflows into the marginal sea. The interaction between the Ekman transport and an island chain produces strong baroclinic flows along the island boundaries with a vertical depth that scales with the ratio of the inertial boundary layer thickness to the baroclinic deformation radius. The throughflows in the gaps are characterized by maximum transport in the center gap and decreasing transports toward the southern and northern tips of the island chain. An extended island rule theory demonstrates that throughflows are determined by the collective balance between viscosity on the meridional boundaries and the eastern side boundary of the islands. The outflowing transport is balanced primarily by a shallow current that enters the marginal sea along its equatorward boundary. The islands can block some direct exchange and result in a wind-driven overturning cell within the marginal sea, but this is compensated for by eastward zonal jets around the southern and northern tips of the island chain. Topography in the form of a deep slope, a ridge, or shallow shelves around the islands alters the current pathways but ultimately is unable to limit the total wind-driven exchange between the marginal sea and the open ocean.

Discrete SQG models with two boundaries and baroclinic instability of jet flows

In this paper, new vertically discrete versions of the surface quasigeostrophic (SQG) model with two boundaries are formulated. For any number of partition levels, the equations of the discrete model are written in the form of conservation laws for two Lagrangian invariants, which have the meaning of buoyancy distributions at the horizontal boundaries of the fluid layer. The values of the invariants are expressed in terms of the values of the stream function at two internal levels and contain higher order elliptic operators. The use of discrete models greatly simplifies the solution of problems of the linear theory of hydrodynamic stability and provides high accuracy even with a small number of vertical discrete levels. Using the two-level version of the SQG model, which is similar to the classical two–layer Phillips model, we investigated the linear stability of jet flows induced by piecewise constant boundary distributions of buoyancy. For these flows, analytical expressions for the growth rate of perturbations have been obtained and it is shown that the most unstable perturbation has a wavelength of the order of the Rossby baroclinic radius of deformation. Flows with vertical shear induced by smooth and slowly varying boundary buoyancy distributions are also considered. The instability of these flows is found to be absolute, that is, independent of the velocity profile horizontal structure.

Can the Intermediate Western Boundary Current recirculation trigger the Vitória Eddy formation?

South of the Vitória-Trindade Ridge, a seamount chain off East Brazil, the Brazil Current (BC) meanders cyclonically within Tubarão Bight, occasionally forming the Vitória Eddy. It was recently found that the Intermediate Western Boundary Current (IWBC), which flows equatorward below the BC, cyclonically recirculate within Tubarão Bight. We present an analysis of AVISO observations that suggest that the Vitória Eddy formation is conditioned by the strength of the BC upstream of Tubarão Bight. A weak BC is prone to local meandering and eddy formation in the bight, while a strong BC suppresses eddy formation in the bight but triggers downstream meander growth. To study the effects of the IWBC recirculation on the BC meandering and the Vitória Eddy formation, we formulate a simple two-layer quasi-geostrophic model. In the model, the BC is represented by a meridional jet in the upper layer and the IWBC recirculation is a steady eddy in the lower layer. The lower-layer eddy effectively acts as a topographic bump, affecting the upper-layer jet via the stretching term \(\psi _{2}/{R_{d}^{2}}\), where ψ2 is the lower-layer streamfunction and Rd is the baroclinic deformation radius. Based on the AVISO sea-surface height data and previous observational studies, we define a stationary eddy and reference jet. We conduct a number of initial-value problem experiments varying the upper-layer jet speed. A weak upper-layer jet slowly meanders and develops a cyclone above the lower-layer eddy. As we increase the jet velocity, the meandering is faster and the cyclone is larger. But a too-strong jet has an opposite effect: the potential vorticity anomalies induced by the lower-layer eddy are quickly swept away, leading to explosive downstream meander growth; no cyclone is formed above the lower-layer eddy. In all cases, the initial meandering trigger is a linear process (the steering of the upper-layer jet by the lower-layer eddy). But even when the upper-layer jet is weak, nonlinearity quickly becomes important, dominating the dynamics after 10 days of simulation. The downstream meander growth is fully nonlinear. Our idealized QG model confirms that the IWBC recirculation can trigger the Vitória Eddy formation and elucidates the mechanisms involved in this process.

Marine Observational Systems as an Integral Part of Operational Oceanology: A Review

The paper presents an overview of the current marine observational systems which provide primary information for operational monitoring and predicting the variability of the main hydrophysical fields on the scales from several tens to several thousand kilometers (of the order of the Rossby baroclinic deformation radius and higher). Such systems provide the regular implementation of oceanographic and marine meteorological observations, their rapid interpretation and delivery to users; this is a subject of a relatively new discipline, operational oceanology. The active development of this discipline during the recent two decades suggests that the forecasting of the marine environment state will eventually reach the same level of accuracy and reliability as in operational meteorology, a more successful and older discipline.

Oceanic Eddy Characteristics and Generation Mechanisms in the Kuroshio Extension Region

AbstractThe Kuroshio Extension region is well known for its strong eddy activity. In this paper, using satellite altimetry‐measured sea surface height anomaly data from 1993 to 2012 in an extended Kuroshio Extension region (140–180°E, 25–45°N), we analyze eddy characteristics: eddy size, polarity, lifetime, intensity, trajectory, and spatial and temporal distributions. Using temperature and salinity vertical profiles measured by Argo floats, we examine the eddy impact on vertical stratification. During the 20‐year period, 7,574 eddies are identified (based on following complete eddy trajectories) with a lifetime equal to or longer than 4 weeks. The numbers of cyclonic and anticyclonic eddies are found to be approximately the same. The distribution of eddy sizes peaks at a radius of about 40 km. The radius at the peak is at the same order as the first baroclinic deformation radius or the horizontal shear scale of the Kuroshio flow. The normalized eddy statistical characteristics show that eddies have different characteristics at different stages of their lifetimes. Among eddies with lifetimes longer than 50 weeks, more anticyclonic (cyclonic) eddies are found north (south) of 35°N. In contrast, among eddies with lifetimes shorter than 20 weeks, more cyclonic (anticyclonic) eddies are found north (south) of 35°N. The asymmetric distribution of eddies suggests two different eddy generation mechanisms: (1) the development of meanders in the Kuroshio path leading to the pinch off of eddies with longer lifetime (larger size) and (2) horizontal shear instability (barotropic instability) leading to eddies of shorter life (smaller size). We further apply an eddy‐resolved numerical product to quantitatively investigate the eddy generation mechanisms.

Antisymmetry of oceanic eddies across the Kuroshio over a shelfbreak

From the analysis of oceanic eddies detected in the drifter trajectories of the Global Drifter Program (GDP) data set, it was found that oceanic eddies are asymmetrically distributed across the Kuroshio in the East China Sea: predominant cyclonic (anticyclonic) eddies are on the western (eastern) sides of Kuroshio. This distribution is confirmed by high-resolution numerical modeling output as well. Most of these eddies are 5~20 km in radius, less than the local first baroclinic deformation radius, thus categorized as submesoscale. The generation mechanism of these submesoscale eddies is speculated to be related to the horizontal velocity shear of the Kuroshio when it flows northeastward along the shelf break in the East China Sea. The budget analysis of eddy kinetic energy shows that both the horizontal shear and vertical buoyancy flux are important energy sources for eddy generation on the two sides of Kuroshio axis. The finding highlights the unique feature of oceanic eddies along the western boundary currents.

Intrusive layering of the Antarctic slope front

Cascading of cold Antarctic shelf water (ASW) initiates compensatory isopycnic upwelling of the warm Circumpolar Deep Water (CDW). The baroclinic/thermoclinic Antarctic slope front (ASF) is formed, and a mesoscale intrusive structure develops on the shelf edge and slope. Mesoscale processes when the ASF peaks are periodically accompanied by local baroclinic instability, which forms a smaller-scale intrusive structure. Therefore, the ASF is naturally subdivided into two layers according to the intrusion scales (vertical δН and horizontal L) and the horizontal parameters of the front (thermoclinity (T L)ρ and baroclinity γρ). Analysis of ASF intrusive layering due to the baroclinic factor supports the following conclusion: the higher the (T L)ρ of the ASF, the greater the intrusion intensity |δθ| (temperature anomaly amplitude), while an increase in γρ of the ASF leads to a decrease in intrusion scales δН and L. Frontal intrusions can be distinguished by a development degree. Regardless of the degree of development, all warm intrusions are characterized by vertical density stratification, while cold intrusions are characterized by density quasihomogeneity. According to field data, the ASF instability process is subdivided into four stages. When theASF is baroclinically unstable, the local baroclinic deformation radius Rd L of the front is close in magnitude to the horizontal scale L of the intrusions that form, and their characteristic vertical scale δH is close to the typical vertical scale of front instability.

Vortex dynamics in the southeastern Baltic Sea from satellite radar data

The analysis of radar satellite images shows that vortex dipoles are a typical element of the water circulation in the southeastern part of the Baltic Sea. The wide range of spatial dimensions of observed vortices (from approximately 2 to 25 km) corresponds to mesoscale and submesoscale vortex formations (signifying whether the diameter is respectively larger or smaller than the baroclinic Rossby radius of deformation, equal to 5–6 km). Vortex dipoles typical for different areas and their spatial characteristics are considered. These areas were the Hel Spit, the Taran Cape, the central part of the Gulf of Gdansk and the area northward of the Gulf. It is shown that the mesoscale vortex dipoles and the associated jets condition horizontal water exchange in an area comparable with the size of the considered water area. The differences in the appearance of the cyclonic and anticyclonic components of vortex dipoles revealed in satellite radar images are discussed.

Statistical study of submesoscale eddies identified from synthetic aperture radar images in the Luzon Strait and adjacent seas

Based on synthetic aperture radar (SAR) images, this study illustrates the characteristics of oceanic eddies in the Luzon Strait and its adjacent seas. An eddy detection method is applied to 426 SAR frames (including the European Remote Sensing satellite, ERS-2, and the Environmental Satellite, ENVISAT) from 2005 to 2011, and 60 eddies are identified. About 78% of these eddies have sizes smaller than 12 km, which is smaller than the local first baroclinic deformation radius, and thus can be categorized as submesoscale eddies. Their polarities are dominated by cyclonic features. Our results indicate that oceanic eddy activity may be largely underestimated by observational techniques that only resolve mesoscale features, and that SAR is an effective tool for detecting and studying submesoscale eddies.

Zonal jets in equilibrating baroclinic instability on the polar beta‐plane: Experiments with altimetry

AbstractResults from the laboratory experiments on the evolution of baroclinically unstable flows generated in a rotating tank with topographic β‐effect are presented. We study zonal jets of alternating direction which occur in these flows. The primary system we model includes lighter fluid in the South and heavier fluid in the North with resulting slow meridional circulation and fast mean zonal motion. In a two‐layer system, the velocity shear between the layers results in baroclinic instability which equilibrates with time and, due to interaction with β‐effect generates zonal jets. This system is archetypal for various geophysical systems including the general circulation and jet streams in the Earth's atmosphere, the Antarctic Circumpolar Current, or the areas in the vicinity of western boundary currents where baroclinic instability and multiple zonal jets are observed. The gradient of the surface elevation and the thickness of the upper layer are measured in the experiments using the Altimetric Imaging Velocimetry and the Optical Thickness Velocimetry techniques, respectively. Barotropic and baroclinic velocity fields are then derived from the measured quantities. The results demonstrate that the zonal jets are driven by “eddy forcing” due to continuously created baroclinic perturbations. The flow is baroclinic to a significant degree and the jets are “surface intensified.” The meridional wavelength of the jets varies linearly with the baroclinic radius of deformation and is also in a good agreement with a modified Rhines scale. This suggests a linear dependence of the perturbation velocity in the equilibrated baroclinically unstable flow on the β‐parameter.

The Rossby radius in the Arctic Ocean

Abstract. The first (and second) baroclinic deformation (or Rossby) radii are presented north of ~60° N, focusing on deep basins and shelf seas in the high Arctic Ocean, the Nordic seas, Baffin Bay, Hudson Bay and the Canadian Arctic Archipelago, derived from climatological ocean data. In the high Arctic Ocean, the first Rossby radius increases from ~5 km in the Nansen Basin to ~15 km in the central Canadian Basin. In the shelf seas and elsewhere, values are low (1–7 km), reflecting weak density stratification, shallow water, or both. Seasonality strongly impacts the Rossby radius only in shallow seas, where winter homogenization of the water column can reduce it to below 1 km. Greater detail is seen in the output from an ice–ocean general circulation model, of higher resolution than the climatology. To assess the impact of secular variability, 10 years (2003–2012) of hydrographic stations along 150° W in the Beaufort Gyre are also analysed. The first-mode Rossby radius increases over this period by ~20%. Finally, we review the observed scales of Arctic Ocean eddies.

A Drag-Induced Barotropic Instability in Air–Sea Interaction

Abstract A new mechanism that induces barotropic instability in the ocean is discussed. It is due to the air–sea interaction with a quadratic drag law and horizontal viscous dissipation in the atmosphere. The authors show that the instability spreads to the atmosphere. The preferred spatial scale of the instability is that of the oceanic baroclinic Rossby radius of deformation. It can only be represented in numerical models, when the dynamics at this scale is resolved in the atmosphere and ocean. The dynamics are studied using two superposed shallow water layers: one for the ocean and one for the atmosphere. The interaction is due to the shear between the two layers. The shear applied to the ocean is calculated using the velocity difference between the ocean and the atmosphere and the quadratic drag law. In one-way interaction, the shear applied to the atmosphere neglects the ocean dynamics; it is calculated using the atmospheric wind only. In two-way interaction, it is opposite to the shear applied to the ocean. In one-way interaction, the atmospheric shear leads to a barotropic instability in the ocean. The instability in the ocean is amplified, in amplitude and scale, in two-way interaction and also triggers an instability in the atmosphere.

Studying the stability of the Antarctic slope front in the Commonwealth Sea

In 2004–2007 and 2011–2013, oceanography sections with the high spatial resolution were carried out on the shelf and continental slope of the Commonwealth Sea and in the Prydz Bay in the Antarctic. In combination with a fine vertical resolution, this provides an advanced interpretation of the obtained data. It becomes possible to analyze the local thermohaline structure of the baroclinic Antarctic slope front (the ASF) and to investigate its stability. The reliable determination of the ASF characteristics enables to apply the parameterizations and criteria obtained during laboratory experiments for analysis of its stability. The ASF instability is preceded by the local vertical dramatic intensification of the front, where the ASF approaches the pure baroclinic state. Therefore, the local baroclinic instability in the ASF area prevails over the barotropic one at the significant mutual impact of layers (δ = HASF/Hb ≈ ≈ 0.3–0.6, Hb is the total depth) and accompanied with the hydrostatic instability. Instability conditions in the frontal zone with a width of ∼(1–2)RdL (RdL is local baroclinic deformation radius) relative to the wide ASF (LASF ≈ (3–5)RdL) coincide with those of the narrow (intensified) ASF (LASF ≈ RdL*). In the case of the runoff of dense Antarctic shelf water, on the shelf edge the realization is possible of the self-oscillatory mechanism of the ASF instability caused by the topographic beta-effect as well as the periodic generation of baroclinic vortices.

Inertial instability of intense stratified anticyclones. Part 2. Laboratory experiments

AbstractLarge-scale laboratory experiments were performed on the Coriolis rotating platform to study the stability of intense vortices in a thin stratified layer. A linear salt stratification was set in the upper layer on top of a thick barotropic layer, and a cylinder was towed in the upper layer to produce shallow cyclones and anticyclones of similar size and intensity. We focus our investigations on submesoscale eddies, where the radius is smaller than the baroclinic deformation radius. Towing speed, cylinder size and stratification were changed in order to cover a large range of the parameter space, staying in a relatively high horizontal Reynolds number ($Re= 2000{{\unicode{x2013}}}7000$). The Rayleigh criterion states that inertial instabilities should strongly destabilize intense anticyclonic eddies if the vorticity in the vortex core is negative enough ${\zeta }_{0} / f\lt - 1$, where ${\zeta }_{0} $ is the relative vorticity in the core of the vortex, and $f$ is the Coriolis parameter. However, we found that some anticyclones remain stable even for very intense negative vorticity values, up to ${\zeta }_{0} / f= - 3. 5$, when the Burger number is large enough. This is in agreement with the linear stability analysis performed in part 1 (J. Fluid Mech., vol. 732, 2013, pp. 457–484), which shows that the combined effect of a strong stratification and a moderate vertical dissipation may stabilize even very intense anticyclones, and the unstable eddies we found were located close to the marginal stability limit. Hence, these experimental results agree well with the simple stability diagram proposed in the Rossby, Burger and Ekman parameter space for inertial destabilization of viscous anticyclones within a shallow and stratified layer.

Using a resolution function to regulate parameterizations of oceanic mesoscale eddy effects

Mesoscale eddies play a substantial role in the dynamics of the ocean, but the dominant length-scale of these eddies varies greatly with latitude, stratification and ocean depth. Global numerical ocean models with spatial resolutions ranging from 1° down to just a few kilometers include both regions where the dominant eddy scales are well resolved and regions where the model’s resolution is too coarse for the eddies to form, and hence eddy effects need to be parameterized. However, common parameterizations of eddy effects via a Laplacian diffusion of the height of isopycnal surfaces (a Gent–McWilliams diffusivity) are much more effective at suppressing resolved eddies than in replicating their effects. A variant of the Phillips model of baroclinic instability illustrates how eddy effects might be represented in ocean models. The ratio of the first baroclinic deformation radius to the horizontal grid spacing indicates where an ocean model could explicitly simulate eddy effects; a function of this ratio can be used to specify where eddy effects are parameterized and where they are explicitly modeled. One viable approach is to abruptly disable all the eddy parameterizations once the deformation radius is adequately resolved; at the discontinuity where the parameterization is disabled, isopycnal heights are locally flattened on the one side while eddies grow rapidly off of the enhanced slopes on the other side, such that the total parameterized and eddy fluxes vary continuously at the discontinuity in the diffusivity. This approach should work well with various specifications for the magnitude of the eddy diffusivities.

Nonlinear Dynamics of Two Western Boundary Currents Colliding at a Gap

Abstract The nonlinear collision of two western boundary currents (WBCs) of equal transport at a gap of the western boundary is studied using a 1.5-layer reduced-gravity quasigeostrophic ocean model. It is found that, when the gap (of width 2a) is narrow, a ≤ 7.3LM (LM the Munk thickness), neither of the WBCs can penetrate into the western basin because of the restriction of the viscous force. When 7.3LM < a < 9.0LM, both WBCs penetrate into the western basin for small transport and choke for large transport. When 9.0LM ≤ a ≤ 9.6LM, the two WBCs penetrate for small transport, choke for intermediate transport, and shed eddies periodically for large transport. When a > 9.6LM, no steady choking state is found. Instead, the WBCs have only two equilibrium states: the penetrating and the periodic eddy shedding states. A Hopf bifurcation is found for a > 9.0LM. The Reynolds number (Re) of the Hopf bifurcation is sensitive to the magnitude of γ(a/LM) and the baroclinic deformation radius, being small for larger γ or deformation radius. In addition, a reverse Hopf bifurcations is identified in the decreased Re experiments, occurring at a smaller Re than that of the Hopf bifurcation. The Re of the reverse Hopf bifurcation is not sensitive to the magnitude of the baroclinic deformation radius. Hysteresis behavior of the WBCs is found for a > 9.0LM, because of the existence of the Hopf and reverse Hopf bifurcations. In between them, steady penetrating or choking states coexist with eddy-shedding states. The steady states are found to be sensitive to perturbations of relative vorticity and can transit to periodic eddy-shedding states at the forcing of a mesoscale eddy.