Baroclinic Flow Research Articles

Resolving the Ubiquitous Small-Scale Semipermanent Features of the General Ocean Circulation: A Multiplatform Observational Approach

Abstract Based on 20 years of Argo and ship/animal-borne/glider hydrographic profile data, we derive a new high-resolution hydrographic Atlas and associated circulation field for the oceans above 2000 dbar. Satellite altimetric observations are used to explicitly regress out eddy noise in the fit, greatly reducing one of the major sources of noise. Geostrophic shears are found from the fitted geopotential anomaly fields. Ekman velocities are estimated using satellite wind stresses. Both Argo trajectory observations at 1000 dbar and surface drifter observations are used to reference geostrophic shears derived from the Atlas hydrography. Surface drifter velocities are analyzed with an additional wind friction term to remove the wind-related flow. Agreement between the surface geostrophic (referenced to Argo trajectories) and drifter-based surface velocity is high at both large scales and mesoscales, lending confidence to the derived geostrophic circulation fields. The Atlas reveals standing mesoscale eddies and meanders in western boundary systems and the braided jet structure of the Antarctic Circumpolar Current. In the interior, the upper-ocean flow consists of a highly baroclinic large-scale Sverdrup flow and smaller-scale (∼200-km width) semizonal jets, which are more barotropic (low vertical shear) and have an average zonal width of around 5000 km. These semizonal jets are globally ubiquitous—found in all basins pole to pole. The many permanent mesoscale features of the mean general circulation contrast with that predicted by theories of the large-scale flow in simplified flat-bottomed domains. The Atlas presents a new opportunity to benchmark modern high-resolution ocean and climate models. Significance Statement This study exploits the radical increase in the number of observations of the ocean vertical structure in the past 20 years due to the use of robotic profilers. Combined with satellite observations, this much larger data coverage allows us to uncover the structure of the mean (or time average) ocean and its flow at much smaller horizontal length scales than in the past, like going from a blurry view to a clear one. In this new view, we find small permanent eddies and meanders of major ocean flows and jets around islands and through bathymetric constrictions. We also find ubiquitous semizonal striations throughout the global ocean interior. In the past, these were only seen at the surface, but we now show they reach down to at least 2000 m and comprise a significant part of the ocean’s mean flow field. These features are likely important to how the ocean mixes heat and other important quantities such as oxygen and carbon around Earth.

Baroclinic instability in the Eady model for two coupled flows

The linear instability of baroclinic flows in two superimposed and coupled, immiscible fluids is studied theoretically. These flows are westerlies, and they are thermally or mechanically coupled. The fluids are stably stratified, internally and mutually (the upper fluid is lighter than the lower fluid). In each fluid, two-level surface quasi-geostrophy governs the evolution of the perturbed westerly flow. The perturbations are horizontal normal modes. Firstly, the models are not coupled and the flow instability in each fluid is validated separately against the results of the classical Eady model of baroclinic instability. Secondly, the two fluids are thermally and/or mechanically coupled. With thermal coupling, and for meridionally uniform perturbations, a new mode of instability appears for long waves. This pair of unstable modes converges towards the modes of the uncoupled fluids at medium wavelengths. For perturbations with a non trivial meridional structure, the thermal coupling essentially damps the instability. For an upper flow with a larger deformation radius than in the lower flow, the growth rates of the perturbation are therefore more strongly altered in the former than in the latter. With mechanical coupling, the instability is essentially damped at large to medium scales, while the short-wave cut-off is extended towards smaller waves. When the fluids are both thermally and mechanically coupled, these effects add up. This very idealised study is a first step towards studying more realistic cases.

Instability of solid-body rotation of heton type

It is traditionally believed that in a liquid of uniform density, an axisymmetric barotropic flow with solid-body rotation is stable. Within the framework of a two-level quasi-geostrophic model, this work shows that this is not in the case of a baroclinic flow with solid-body rotation of the heton type. Such a flow has different directions of rotation at two levels. Due to the vertical velocity shift, this flow is always unstable. The paper develops a linear theory of the instability of such flows both in a model without friction and in a model with Ekman friction. It is shown that for instability in a model with friction, the horizontal wave number of the disturbance should not exceed a certain critical value. It has been established that instability with respect to long-wave disturbances in the model without friction is absolute in nature, i.e. always exists. The development of instability may be associated with the formation of observed disturbances in the axial zone of intense atmospheric vortices.

Experimental and numerical investigation of shelf flow crossing over a strait

Motivated by the phenomenon of Scotian Shelf Crossover events, the problem of a shelf flow that is interrupted by a strait is considered. Laboratory experiments in a rotating tank with barotropic and baroclinic flow over flat and sloping shelves confirm that the flow is steered by the bathymetric contours and mainly circumnavigates the gulf. In order to jump across the strait, as suggested by earlier theories, the flow must have unrealistically high Rossby numbers. However, the near bottom friction relaxes the bathymetric constraint and causes the formation of a peculiar jet crossing the strait diagonally. For the dissipation values such that a half of the transport goes around the gulf and half crosses the strait diagonally, the diagonal crossover jet becomes most evident. Numerical solutions for realistic values of the frictional parameter reproduce the results of the laboratory experiments and consideration of the actual Gulf of Maine bathymetry reproduces patterns similar to those observed by drift trajectories and in the satellite derived sea surface temperature fields.

Dark-soliton asymptotics for a repulsive nonlinear system in a baroclinic flow

In geophysical hydrodynamics, baroclinic instability denotes the process in which the perturbations draw the energy from the mean flow potential power. Researchers focus their attention on the baroclinic instability in the Earth's atmosphere and oceans for the meteorological diagnosis and prediction. Under investigation in this paper is a repulsive nonlinear system modeling the marginally unstable baroclinic wave packets in a baroclinic flow. With respect to the amplitude of the baroclinic wave packet and correction to the mean flow resulting from the self-rectification of the baroclinic wave, we present a Lax pair with the changeable parameters and then derive the N-dark-dark soliton solutions, where N is a positive integer. Asymptotic analysis on the N-dark-dark solitons is processed to obtain the algebraic expressions of the N-dark-dark soliton components. We find that the obtained phase shift of each dark-dark soliton component is relevant with the N − 1 spectral parameters. Furthermore, we take N = 3 as an example and graphically illustrate the 3-dark-dark solitons, which are consistent with our asymptotic-analysis results. Our analysis may provide the explanations of the complex and variable natural mechanisms of the baroclinic instability.

On a priori bounding the growth of thermal instability waves

We have previously shown that the nonlinear growth of a finite-amplitude perturbation to a basic state given by a baroclinic zonal flow on the β-plane in a thermal quasigeostrophic reduced-gravity model can be a priori bounded. In this note, we show that, unlike we stated earlier, Lyapunov stability can be proved even when buoyancy varies linearly with the meridional coordinate. In addition to rectifying our earlier results, we expand them by deriving an instability saturation bound by making use of the existence of such a class of Lyapunov-stable basic states. This bound can be smaller than that one we estimated before, reinforcing our previous conclusions. We also present a numerical test of the accuracy of the derived bound.

Building transport models from baroclinic wave experimental data

In this paper, we study baroclinic waves from both the experimental and the theoretical perspective. We obtain data from a rotating annulus experiment capable of producing a series of baroclinic eddies similar to those found in the mid-latitude atmosphere. We analyze the experimental outputs using two methods. First, we apply a technique that involves filtering data using the empirical orthogonal function (EOF) analysis, which is applied to both velocity and surface temperature fields. The second method relies on the construction of a simple kinematic model based on key parameters derived from the experimental data. To analyze eddy-driven fluid transport, we apply the method of Lagrangian descriptors to the underlying velocity field, revealing the attracting material curves that act as transport barriers in the system. These structures effectively capture the essential characteristics of the baroclinic flow and the associated transport phenomena. Our results show that these barriers are in good agreement with the transport patterns observed in the rotating annulus experiment. In particular, we observe that the structures obtained from the kinematic model, or the one derived in terms of filtered velocities, perform well in this regard.

Examining the dynamics of a Borneo vortex using a balance approximation tool

Abstract. Cyclonic vortices that are weaker than tropical storm category can bring heavy precipitation as they propagate across the South China Sea and surrounding countries. Here we investigate the structure and dynamics responsible for the intensification of a Borneo vortex that moved from the north of Borneo across the South China Sea and impacted Vietnam and Thailand in late October 2018. This case study is examined using Met Office Unified Model (MetUM) simulations and a semi-geotriptic (SGT) balance approximation tool. Satellite observations and a MetUM simulation with 4.4 km grid initialised at 12:00 UTC on 21 October 2018 show that the westward-moving vortex is characterised by a coherent maximum in total column water and by a comma-shaped precipitation structure with the heaviest rainfall to the northwest of the circulation centre. The Borneo vortex comprises a low-level cyclonic circulation and a mid-level wave embedded in the background easterly shear flow, which strengthens with height up to around 7 km. Despite being in the tropics at 6∘ N, the low-level vortex and mid-level wave are well represented by SGT balance dynamics. The mid-level wave propagates along a vertical gradient in moist stability, i.e. the product between the specific humidity and the static stability, at 4.5 to 5 km and is characterised by a coherent signature in the potential vorticity, meridional wind, and balanced vertical velocity fields. The vertical motion is dominated by coupling with diabatic heating and is shifted relative to the potential vorticity so that the diabatic wave propagates westwards, relative to the flow, at a rate consistent with prediction from moist semi-geostrophic theory. Initial vortex development at low levels is consistent with baroclinic growth initiated by the mid-level diabatic Rossby wave, which propagates on baroclinic shear flow on the southern flank of a large-scale cold surge.

A special phenomenon of wave interactions: An application of nonlinear evolution equation in (3+1)-dimension

The Lie group transformation approach can be used in the reduction of the generalized (3+1)-dimensional nonlinear evolution equation to ordinary differential equations (ODEs). In this work, infinitesimal generators, commutator table of Lie algebra, adjoint representation of subalgebras, symmetry group, and similarity reduction for (3+1)-dimensional shallow-water-like (gSWL) equation are obtained. Interactions of soliton solutions of a gSWL equation are evaluated that depict how near-inertial waves affect the dynamics of barotropic and baroclinic balanced flows. It is shown that the temporo-spatial localization of multi-soliton complexes (MSCs), gradually escalating incoherent interactivity amidst multi parameter group of MSCs along with spatial inhomogeneity alter the shape of quasi-periodic MSCs. The interactions among bright and dark solitons are shown. The increased number of solitons and increased self-interactions among solitary waves contribute to an unstable wave field. Breathers have a well-separating and initial localized energy domain. A limiting case of breather solutions is the peregrine soliton. Thus, interactions among these soliton structures show that multiple breathers retain their wave characteristic.

A split-explicit second order Runge–Kutta method for solving 3D hydrodynamic equations

Numerical models of marine hydrodynamics have to deal with processes exhibiting a wide range of timescales. These processes include fast external gravity waves and slower internal fully three-dimensional motions. In order to be both time-efficient and numerically stable, the time stepping scheme has to be chosen carefully to cope with the characteristic time scale of each phenomenon. An usual approach is to split the fast and slow dynamics into separate modes. The fast waves are modeled with a two-dimensional system through depth averaging while the other motions, where characteristic times are much longer, are dealt with in three dimensions. However, if the splitting is inexact, for instance in projecting the fields in a new 3D mesh, this procedure can lead to improper results regarding to the physical properties such as mass conservation and tracer consistency. In this work, a new split-explicit Runge–Kutta scheme is adapted and developed for the Discontinuous-Galerkin Finite Element method in order to obtain a new second-order time stepping, yielding to more accurate results. This method combines a three-stage low-storage Runge–Kutta for the slow processes and a two-stage low-storage for the fast ones. The 3D iterations are not affecting the surface elevation, hence an Arbitrary Lagrangian Eulerian implementation is straightforward. Water volume and tracers are conserved. A set of test cases for baroclinic flows as well as a laboratory application demonstrate the performance of the scheme. They suggest that the new scheme has little numerical diffusion.

On the dynamics of nonlinear barotropic–baroclinic interactions through a coupled Gardner hierarchies approach

The aim of this paper is on the propagations of barotropic–baroclinic coherent structures based on the two-layer quasi-geostrophic model (2LQG) through a Fourier spectrum compliant approach. First, by introducing the barotropic and baroclinic stream functions starting from the 2LQG model, a new coupled Gardner-type evolution equations, representing the interaction processes between the barotropic flow and baroclinic one, are obtained by combining the multi-scale method and the perturbation expansion method. Second, based on the obtained coupled model equations, the physical mechanisms of the nonlinear barotropic–baroclinic interaction are analyzed qualitatively. Within the range of parameters chosen in this paper, quantitative results show that the basic flow, the β effect, and the bottom topography are necessary factors to excite the nonlinear Rossby isolated waves. The results also declare that the dipole-like blockings are readily excited in the flow field and move slowly eastward in both barotropic and baroclinic flow fields.

How does buoyancy behavior impact microplastic transport in an estuarine environment?

Much is still unknown about the transport behavior of microplastic pollutants within the marine environment, particularly smaller scale coastal systems such as estuaries. Through the use of a Lagrangian particle-tracking model coupled with a validated 3D hydrodynamic model, we examined the transport, pathway and ultimate fate of microplastic particles, both in an idealized estuary and Galveston Bay, Texas, USA. Emphasis was placed on differences based on settling behavior (neutrally versus negatively buoyant), use of random walk for diffusion processes, and release location. For Galveston Bay, settling behavior had a noteworthy impact on both the transport pathway of microplastic particles, as well as overall time spent within the bay. Particles with negative buoyancy were retained approximately seven times longer than those with neutral buoyancy. Negatively buoyant particles also showed a tendency to be dispersed eastward to Trinity Bay through the bottom baroclinic flow, while neutrally buoyant particles took a more direct route along the ship channel to the mouth of the bay. Idealized model simulations suggest impact of settling depends on the vertical mixing strength. For a system with stronger tidal mixing, negatively buoyant particles with small settling velocities may still behave similarly to neutrally buoyant particles, and differences only become apparent for particles that sink rather quickly (> 10 m d−1). Future sea-level rise or channel deepening tends to flush out neutrally buoyant particles more quickly, while increasing the retention time for negatively buoyant particles. Our results suggest that plastics within estuaries could show substantially different behavior depending on their buoyancy characteristics, highlighting a need to quantify specific settling velocities of plastic pollutants entering the coastal estuarine system.

On a variable-coefficient AB system in a baroclinic flow: Generalized Darboux transformation and non-autonomous localized waves

In this paper, we focus our attention on a variable-coefficient AB system, which models the marginally unstable baroclinic wave packets in a baroclinic flow. With respect to the amplitude of the baroclinic wave packet and correction to the mean flow resulting from the self-rectification of the baroclinic wave, we construct an N-fold generalized Darboux transformation (GDT) via symbolic computation, where N is a positive integer. Via the obtained GDT, several kinds of the non-autonomous localized waves, e.g., the multi-pole solitons, multi-pole breathers, rogue waves and their interactions, are investigated. We have selected four types of the variable coefficients, i.e., constant, linear about t, quadratic about t and trigonometric about t, where t is the normalized retarded time coordinate. We explore the influence of those selected variable coefficients on the non-autonomous localized waves. Moreover, we discuss the bound states among the non-autonomous multiple-pole solitons and one soliton, which exhibit the periodic attractions and repulsions between the adjacent solitons.

Impact of dynamic factors on the exchange flow between two neighboring bays with contrasting topography during summer: A numerical study

A high-resolution, three-dimensional numerical ocean model was employed to understand the exchange flow through Noryang Channel, which connects Gwangyang Bay and Jinju Bay. These two bays exhibit contrasting topographies, with Gwangyang Bay connected to the open ocean through a broad and deep channel, whereas Jinju Bay is relatively isolated from the open ocean by a narrow and shallow channel. Numerical experiments were conducted to determine the contribution of river discharge, wind stress, surface heat flux, and tides to the exchange flow between the two bays during summer. The results suggested that river discharge was the dominant factor affecting the exchange flow along Noryang Channel. Particularly, a high river discharge during summer increased the sea level in Jinju Bay, creating a barotropic flow toward Gwangyang Bay. However, the dense water entering Gwangyang Bay through the wide and deep channel generated a baroclinic flow toward Jinju Bay along the lower layer of Noryang Channel. An analytical model supported the conclusion that river discharge is the main driver of the exchange flow in Noryang Channel.

Spin-down of a baroclinic vortex by irregular small-scale topography

This study explores the impact of small-scale variability in the bottom relief on the dynamics and evolution of broad baroclinic flows in the ocean. The analytical model presented here generalizes the previously reported barotropic ‘sandpaper’ theory of flow–topography interaction to density-stratified systems. The multiscale asymptotic analysis leads to an explicit representation of the large-scale effects of irregular bottom roughness. The utility of the multiscale model is demonstrated by applying it to the problem of topography-induced spin-down of an axisymmetric vortex. We find that bathymetry affects vortices by suppressing circulation in their deep regions. As a result, vortices located above rough topography tend to be more stable than their flat-bottom counterparts. The multiscale theory is validated by comparing corresponding topography-resolving and parametric simulations.

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.

Can oceanic flows be heard? Abyssal melodies

Fluid flows generate an acoustic noise field. In principle, oceanic flows on varying time and length scales produce a sound field and its detectability is considered here. A fragile lower bound analysis is made of the acoustic signature, using the Lighthill theory, of a simple train of boundary vortices generated by baroclinic tidal flows. Subject to numerous assumptions, the accompanying sound should be detectable within the hum band of seismo-acoustic pressure fields, and more generally, across the entire oceanic spectrum-likely through wave number analyses of spatially coherent acoustic array data.

Circulation and overturning in the eastern North Atlantic subpolar gyre

This study describes new transport estimates of the North Atlantic Current in the Iceland Basin, and uses these results along with other contemporaneous measurements to determine mass and overturning budgets for the eastern North Atlantic subpolar gyre. As part of the Overturning in the Subpolar North Atlantic Program (OSNAP), estimates of the North Atlantic Current are determined using three full-depth dynamic height moorings spanning the Iceland Basin and are supplemented by Argo and satellite altimetry data. Along with historical estimates of the exchanges over the Iceland-Scotland Ridge, additional OSNAP results from the Rockall Trough and Rockall-Hatton Bank regions are used to calculate transport budgets in different density layers over a broad portion of the eastern subpolar gyre. Results show that 13–14 Sv of the North Atlantic Current (σθ < 27.8 kg m−3) flow northward into the middle of the Iceland Basin through a primary baroclinic flow near 23.5°W and a secondary quasi-barotropic flow near 26°W. Together with the observed northward flow in the Rockall-Hatton area, we conclude that 19–20 Sv of the upper limb of the Atlantic Meridional Overturning Circulation (σθ < 27.56 kg m−3) flows into the region where nearly 40 % of it (7.3 Sv) is converted into the lower limb primarily through progressive water mass modification from atmospheric cooling. This accounts for nearly half of the strength of Atlantic Meridional Overturning Circulation defined by the full OSNAP array extending across the basin from Greenland to Scotland.

Exploring the three-dimensional flow-sediment dynamics and trapping mechanisms in a curved estuary: The role of salinity and circulation

Combined with the observed data in the wet season in June 2015, structures of longitudinal and lateral residual current and characteristics of the estuarine turbidity maximum (ETM) in the Yongjiang estuary (YE) are studied using a three-dimensional baroclinic flow and sediment numerical model. The mechanisms of residual current and sediment trapping are investigated according to the momentum balance analysis and sediment transport decomposition. The results show that at spring tide, the outflowing longitudinal residual current is dominated by longitudinal advection and barotropic pressure gradient. At neap tide, a remarkable baroclinic effect emerges at the bottom of the river mouth area, driving the landward residual current and forming the estuarine circulation. Lateral residual current at upstream bends with lower salinity is dominated by longitudinal advection and barotropic pressure gradient. The flow directs toward the concave bank at the surface and toward the convex bank near the bottom at these sections. At downstream bends with higher salinity, the lateral residual current is greatly affected by the baroclinic gradient, which will shift the lateral flow circulation structure. In transition straight reaches located at Qingshuipu and Zhenhai, the lateral residual current presents a double-cell circulation with surface convergence and bottom divergence. During spring tide, the ETM is located near Qingshuipu, driven by landward tidal pumping transport due to the strong tidal energy. During neap tide, a strong exchange flow generates landward circulation transport around the river mouth, and the ETM moves downstream to Zhenhai. At bends, sediment along the cross section is laterally trapped on the convex bank, driven by bottom lateral flow induced circulation transport. While in transition straight reaches, high turbidity is still concentrated in the deep groove, caused by bottom divergent flow and circulation transport.

Baroclinic Instability of a Time-Dependent Zonal Shear Flow

In the real atmosphere, the development of large-scale motion is often related to the baroclinic properties of the atmosphere. So, it is necessary to discuss the stability condition of baroclinic flow. It is advantageous to use a layered model to discuss baroclinic instability, not only to apply the potential vortex equation directly, but also to deal with shear of basic flow. The stability and oscillatory shear ability of Rossby waves are studied based on the two-layer Phillips model in the β plane; then, we summarize the baroclinic instability of time-dependent zonal shear flows. The multiscale method is used to eliminate some terms of natural frequency oscillations of nonlinear operators in the third-order expansion, thus generating an equation about the amplitude of the lowest-order Rossby wave in the long-time variable. The large amplitude perturbation begins to decrease, which produces the desired behavior. After the amplitude decreases for some time, the amplitude of Rossby waves can still be found to oscillate periodically with the time variable.