Geostrophic Contours Research Articles

Inertial Effect and Its Dependency on the Topographic Geometries in Barotropic Channel Models under the Weakly Nonlinear Regime

Abstract Recent studies have shown that the sensitivity of the circumpolar transport of channels to the westerlies is controlled by wind-driven gyre circulations. Although the form stress associated with the gyres has been shown to be controlled by eddies, bottom friction, and topographic width, the role of inertial effects has not been fully understood. In this study, we conduct a series of sensitivity analyses using the barotropic model with and without the advection term (hereinafter, the model without the advection term is denoted as linear model). Experiments showed that the sensitivity of the circumpolar transport decreased under the westerly winds compared to the linear model, while it increased under the easterly winds. We show that the inertial effect of western boundary currents generates anomalous anticyclonic circulations over the topography, producing the westward topographic form stress anomalies regardless of the wind directions. In addition, we discuss the sensitivity of the inertial effect mechanism to topographic height, width, and geometries. The inertial effect mechanism is robust as long as the gyre circulations dominate while its relative importance changes. We also found that the dynamics of the barotropic channel strongly depend on the geometries of geostrophic contours f/h. Therefore, we conclude that the dynamics of barotropic channel models might be interpreted with caution to understand the dynamics of the Southern Ocean. Significance Statement Previous studies have studied baroclinic and barotropic channel models as a benchmark of the Southern Ocean, but the nonlinear dynamics of channels have not been fully understood. In this paper, we show that the inertial effect by the mean flow works to decrease the sensitivity to the westerly winds in the barotropic channel models using numerical experiments. We also show that the inertial effect is robust as long as gyre circulations exist, while its relative importance differs.

Contribution of the wind, Loop Current Eddies, and topography to the circulation in the southern Gulf of Mexico

The Bay of Campeche, located in the southern Gulf of Mexico (GoM), is characterized by a semi-permanent cyclonic circulation commonly referred to as the Campeche Gyre (CG). Several studies documenting its upper layer structure have suggested a possible relationship between its seasonal variability and the wind stress, and that non-seasonal variability arises mainly from the interaction of the gyre with Loop Current Eddies (LCEs) that arrive in the region. Nevertheless, a partition of the contributions of these forcings to the circulation of the CG in a statistically consistent manner is still needed. This study examines the wind- and eddy-driven circulation with long-term numerical simulations of the GoM using the HYbrid Coordinate Ocean Model. Our results show that, in the absence of LCEs, the wind can sustain a seasonal-modulated circulation in the CG, confined within the upper 600 m. When considering LCEs, high fluctuations on the flow at intraseasonal time scales are imposed. We found that the LCEs influence the western Bay of Campeche circulation through two main mechanisms: (a) by decelerating and inhibiting the CG through a positive vorticity flux out of the bay, leading to reversals in the flow if LCE southward penetration is large, or (b) by strengthening the CG when a big cyclone, accompanying the LCE, enters the region. It is proposed that the second mechanism is responsible for inducing a net weak cyclonic circulation in the Bay in the absence of wind. Furthermore, past studies have shown that the CG behaves as an equivalent-barotropic flow, with topography acting to confine the CG to the west of the bay. In our modeling results, the role of topography manifests similarly among the different numerical experiments, resulting in closed geostrophic contours to the west of the bay that confine an upper-layer, nearly-symmetric, equivalent-barotropic CG.

Ocean Barotropic Vorticity Balances: Theory and Application to Numerical Models

AbstractThe barotropic vorticity (BV) balance is fundamental when interpreting the ocean gyre circulation. Here we propose an intercomparison of vorticity equations for the depth‐integrated flow applied to ocean models. We review four distinct variants of the BV balances, each giving access to diagnostic equations for the depth‐integrated ocean circulation, either meridional, across geostrophic contours or its divergence. We then formulate those balances in the Vorticity Balances in NEMO (VoBiN) diagnostic package aimed at the NEMO ocean platform and more generally C‐grid ocean models. We show that spatial discretization of the equations of motion have profound implications for those vorticity balances. Finally, we diagnose the main balances of a global ocean climate simulation. In all vorticity balances, topographic torques arise from interactions of the flow with slanting topography. We identify significant spurious topographic torques related to the model's C‐grid discretizations, and we suggest ways to address them. In the depth‐integrated and BV balances, bottom vortex stretching and bottom pressure torque drive the flow interaction with topography, respectively. Contrary to Sverdrup theory, the wind stress curl, although dominant in the interior Subtropics, becomes a minor player anywhere significant bottom velocities prevail. The geostrophic contour vorticity balance highlights the limits of barotropic models of the ocean circulation through the so‐called JEBAR term. Finally, the transport divergence vorticity balance stresses the limitations of Ekman plus geostrophic dynamics for the mass balance closure in ocean models. This framework should encourage ocean modellers to diagnose more routinely momentum and vorticity equations.

Effects of mesoscale turbulence on the wind-driven circulation in a closed basin with topography

This paper studies the effects of time-dependent, mesoscale turbulence on the wind-driven ocean circulation in a closed basin with variable topography. Numerical simulations of a single-layer fluid with finite topography at the sloping boundaries are performed. The flow is forced by a suitable combination of a steady, basin-scale wind that generates the classical western-intensified anticyclonic gyre, plus a shorter, time-dependent forcing that injects energy at a narrow range of scales. Two contrasting situations are considered. First, in the absence of the large-scale forcing, the turbulence generates a cyclonic flow that follows the geostrophic contours around the basin. Second, the resulting mean circulation is studied when the large and small-scale forcing terms are considered together. In particular, it is discussed that the alteration of the anticyclonic gyre may be due to the turbulent-induced cyclonic circulation.

Ichnology, sedimentology, and orbital cycles in the hemipelagic Early Jurassic Laurasian Seaway (Pliensbachian, Cardigan Bay Basin, UK)

An uncommonly continuous Lower Jurassic (uppermost Sinemurian and Pliensbachian) section (Llanbedr (Mochras Farm) Borehole, Cardigan Bay Basin, UK) comprises hemipelagic calcareous mudstone, wackestone/siltstone and subordinate packstone/sandstone. Some beds show bigradational grading, and their sedimentary structures are typical of contourite drift facies. On the basis of the long-term persistence and stability of the currents that formed these deposits, sedimentation was likely controlled by thermohaline-driven geostrophic contour currents circulating between the Boreal ocean and Peri-Tethys through the narrow and relatively deep Cardigan Bay Basin (Cardigan Bay Strait). Trace fossils are strongly dominated by Phycosiphon incertum , which was produced by opportunistic colonizers. Thalassinoides , Schaubcylindrichnus and Teichichnus are common, accompanied by less common Zoophycos , Planolites , Palaeophycus , Trichichnus and dwelling structures such as cf. Polykladichnus , Siphonichnus and Skolithos . The ichnofabrics are usually simple, which results from generally high rates of deposition, unstable, water-saturated soft-ground substrate, and the domination of well-adapted Phycosiphon, but there are also cyclic appearances of more complex ichnofabrics with dwelling structures, reflecting more stable bottom conditions. A new detailed analysis of the core has allowed cycles to be distinguished based on combination of ichnological and sedimentological features, pointing to distinct cyclicity of oceanographic mechanisms influenced by orbital forcing and driving the inferred fluctuations in benthic life conditions, controlled mainly by variation in contour current intensity and oxygenation of bottom water reflected by trace fossils. The ichnological cycles show four-order hierarchy, which can be attributed to the orbital cycles: precession and obliquity (4th order), short eccentricity (3rd order), and long eccentricity (2nd order). The longest (~ 2.5 Myr) 1st order cyclicity is attributable to the longer ‟grand orbital cycles” (period related to the Earth–Mars secular resonance), with long-term impacts on palaeoclimatic and oceanic circulation dynamics, and is recorded in large-scale changes in ichnodiversity, correlating with long-term changes of clay minerals and carbonate content. Possibly, there is also ~ 9 Myr cyclicity, expressed in observed modulation of frequency of precession cycles by eccentricity. Harmonic analysis of the cyclicity gives high confidence of orbital signals and allows refined estimation of duration of the Pliensbachian (~8.4 Myr) and the jamesoni ( ~ 2.8 Myr), ibex (~ 2.0 Myr), davoe i (~ 0.47 Myr), margaritatus (~ 2.33 Myr) and spinatum zones (~ 0.8 Myr) with an overall stable sedimentation rate of 4.5–5.1 cm/kyr. Obtained durations show improved fit between 2nd–4th and 1st order cycle and removes the problem of an anomalously long duration and resulting much lower sedimentation rate for the spinatum Zone, previously obtained by other methods. A higher diversity of trace fossils is noticed in intervals enriched in smectite; most likely, this clay mineral occluded pore spaces and limited the competition from the opportunist Phycosiphon makers, allowing development of other, more specialized forms. The continuous, expanded ichnological record of deep-water hemipelagic/contour drift sediments is sensitive to climatic and oceanographic changes controlled by orbital cycles. The Cardigan Bay Strait played an important role in the Early Jurassic (at least Pliensbachian) oceanic circulation, providing a major link between the northern and southern part of the Laurasian Seaway (and in general between the Boreal and Peri-Tethys domains), funneling currents flowing from the north to the south. • Contourite depositional system in the Laurasian Seaway/Cardigan Bay Basin • Orbital forcing expressed in deep sea sedimentary and ichnological cycles. • Corrected duration of Pliensbachian ammonite zones • Long-term ~2.5 My cycles driven by major oceanographic/climate changes.

Topographic Control of Southern Ocean Gyres and the Antarctic Circumpolar Current: A Barotropic Perspective

AbstractIn the Southern Ocean the Antarctic Circumpolar Current is significantly steered by large topographic features, and subpolar gyres form in their lee. The geometry of topographic features in the Southern Ocean is highly variable, but the influence of this variation on the large-scale flow is poorly understood. Using idealized barotropic simulations of a zonal channel with a meridional ridge, it is found that the ridge geometry is important for determining the net zonal volume transport. A relationship is observed between ridge width and volume transport that is determined by the form stress generated by the ridge. Gyre formation is also highly reliant on the ridge geometry. A steep ridge allows gyres to form within regions of unblocked geostrophic (f/H) contours, with an increase in gyre strength as the ridge width is reduced. These relationships among ridge width, gyre strength, and net zonal volume transport emerge to simultaneously satisfy the conservation of momentum and vorticity.

A Barotropic Model of Eddy Saturation

AbstractEddy saturation refers to a regime in which the total volume transport of an oceanic current is insensitive to the wind stress strength. Baroclinicity is currently believed to be the key to the development of an eddy-saturated state. In this paper, it is shown that eddy saturation can also occur in a purely barotropic flow over topography, without baroclinicity. Thus, eddy saturation is a fundamental property of barotropic dynamics above topography. It is demonstrated that the main factor controlling the appearance or not of eddy-saturated states in the barotropic setting is the structure of geostrophic contours, that is, the contours of f/H (the ratio of the Coriolis parameter to the ocean’s depth). Eddy-saturated states occur when the geostrophic contours are open, that is, when the geostrophic contours span the whole zonal extent of the domain. This minimal requirement for eddy-saturated states is demonstrated using numerical integrations of a single-layer quasigeostrophic flow over two different topographies characterized by either open or closed geostrophic contours with parameter values loosely inspired by the Southern Ocean. In this setting, transient eddies are produced through a barotropic–topographic instability that occurs because of the interaction of the large-scale zonal flow with the topography. By studying this barotropic–topographic instability insight is gained on how eddy-saturated states are established.

Dominant Circulation Patterns of the Deep Gulf of Mexico

AbstractThe large-scale circulation of the bottom layer of the Gulf of Mexico is analyzed, with special attention to the historically least studied western basin. The analysis is based on 4 years of data collected by 158 subsurface floats parked at 1500 and 2500 m and is complemented with data collected by current meter moorings in the western basin during the same period. Three main circulation patterns stand out: a cyclonic boundary current, a cyclonic gyre in the abyssal plain, and the very high eddy kinetic energy observed in the eastern Gulf. The boundary current and the cyclonic gyre appear as distinct features, which interact in the western tip of the Yucatan shelf. The persistence and continuity of the boundary current is addressed. Although high variability is observed, the boundary flow serves as a pathway for water to travel around the western basin in approximately 2 years. An interesting discovery is the separation of the boundary current over the northwestern slope of the Yucatan shelf. The separation and retroflection of the along-slope current appears to be a persistent feature and is associated with anticyclonic eddies whose genesis mechanism remains to be understood. As the boundary flow separates, it feeds into the westward flow of the deep cyclonic gyre. The location of this gyre—named the Sigsbee Abyssal Gyre—coincides with closed geostrophic contours, so eddy–topography interaction via bottom form stresses may drive this mean flow. The contribution to the cyclonic vorticity of the gyre by modons traveling under Loop Current eddies is discussed.

Beta-plane turbulence above monoscale topography

Using a one-layer quasi-geostrophic model, we study the effect of random monoscale topography on forced beta-plane turbulence. The forcing is a uniform steady wind stress that produces both a uniform large-scale zonal flow $U(t)$ and smaller-scale macroturbulence characterized by standing and transient eddies. The large-scale flow $U$ is retarded by a combination of Ekman drag and the domain-averaged topographic form stress produced by the eddies. The topographic form stress typically balances most of the applied wind stress, while the Ekman drag provides all of the energy dissipation required to balance the wind work. A collection of statistically equilibrated numerical solutions delineate the main flow regimes and the dependence of the time average of $U$ on parameters such as the planetary potential vorticity (PV) gradient $\unicode[STIX]{x1D6FD}$ and the statistical properties of the topography. We obtain asymptotic scaling laws for the strength of the large-scale flow $U$ in the limiting cases of weak and strong forcing. If $\unicode[STIX]{x1D6FD}$ is significantly smaller than the topographic PV gradient, the flow consists of stagnant pools attached to pockets of closed geostrophic contours. The stagnant dead zones are bordered by jets and the flow through the domain is concentrated into a narrow channel of open geostrophic contours. In most of the domain, the flow is weak and thus the large-scale flow $U$ is an unoccupied mean. If $\unicode[STIX]{x1D6FD}$ is comparable to, or larger than, the topographic PV gradient, then all geostrophic contours are open and the flow is uniformly distributed throughout the domain. In this open-contour case, there is an ‘eddy saturation’ regime in which $U$ is insensitive to large changes in the wind stress. We show that eddy saturation requires strong transient eddies that act effectively as PV diffusion. This PV diffusion does not alter the kinetic energy of the standing eddies, but it does increase the topographic form stress by enhancing the correlation between the topographic slope and the standing-eddy pressure field. Using bounds based on the energy and enstrophy power integrals, we show that as the strength of the wind stress increases, the flow transitions from a regime in which the form stress balances most of the wind stress to a regime in which the form stress is very small and large transport ensues.

Contourites: Physical oceanography, process sedimentology, and petroleum geology

Abstract The purpose of this critical review is to address fundamental principles associated with contourites and other bottom-current deposits. The four basic types of deep-marine bottom currents are: (1) thermohaline-induced geostrophic contour currents, (2) wind-driven bottom currents, (3) tide-driven bottom currents, mostly in submarine canyons, and (4) internal wave/tide-driven baroclinic currents. Contourites are deposits of thermohaline-driven geostrophic contour currents. Contourites can be muddy or sandy in texture, siliciclastic or calciclastic in composition. Traction structures are common in deposits of all four types of bottom currents. However, there are no diagnostic sedimentological or seismic criteria for distinguishing ancient contourites from other three types. The Gulf of Cadiz is the type locality for the contourite facie model based on muddy lithofacies. However, this site is affected not only by contour currents associated with the Mediterranean Outflow Water (MOW) but also by other factors, such as internal waves and tides, turbidity currents, tsunamis, cyclones, mud volcanism, methane seepage, sediment supply, porewater venting, and bottom topography. IODP (Integrated Ocean Drilling Program) 339 cores from the Gulf of Cadiz do not show primary sedimentary structures, which are necessary for interpreting depositional processes. Therefore, the contourite facies model is sedimentologically obsolete. Bottom-current reworked sands of all four types have the potential for developing petroleum reservoirs. Modern sandy carbonate contourites have a measured maximum porosity of 40% and a maximum permeability of 9881 mD due to the winnowing away of muds from the intergranular primary pores by vigorous contour currents. These carbonate contourites are hemiconical-shaped bodies that are up to 600 m in thickness and nearly 60 km in length. Empirical data of modern contourites also show potential for seal and source-rock development. Therefore, future petroleum exploration and development should focus attention on these often overlooked siliciclastic and calciclastic deep-marine reservoirs.

Instability and Mixing of Zonal Jets along an Idealized Continental Shelf Break

AbstractThe interaction between an Antarctic Circumpolar Current–like channel flow and a continental shelf break is considered using eddy-permitting simulations of a quasigeostrophic and a primitive equation model. The experimental setup is motivated by the continental shelf of the West Antarctic Peninsula. Numerical experiments are performed to study how the width and slope of an idealized continental shelf topography affect the characteristics of the flow. The main focus is on the regime where the shelfbreak width is slightly greater than the eddy scale. In this regime, a strong baroclinic jet develops on the shelf break because of the locally stabilizing effect of the topographic slope. The velocity of this jet is set at first order by the gradient of the background barotropic geostrophic contours, which is dominated by the slope of the topography. At statistical equilibrium, an aperiodic cycle is observed. Initially, over a long stable period, an upper-layer jet develops over the shelf break. Once the vertical shear reaches the critical condition for baroclinic instability, the jet becomes unstable and drifts away from the shelf break. The cross-shelf mixing is intrinsically linked with the jet drifting, as most of the meridional flux occurs during this instability period. Investigation of the zonal momentum budget reveals that a strong Reynolds stress divergence inversion across the jet is associated with a drifting event, accelerating one flank of the jet and decelerating the other. The hypothesis that jet drifting may be due to one flank of the jet being more baroclinically unstable than the other is tested using topographic profiles with variable curvatures.

Topographic effects on current variability in the Caspian Sea

Satellite‐derived surface height fields reveal that variability in the central and southern basins of the Caspian Sea is correlated with topography. Consistently, empirical orthogonal functions from current meter data from the southern basin are aligned with the isobaths. In addition, the gravest mode, which accounts for over 80% of the variance, has an equivalent barotropic structure in the vertical. To what extent this variability can be modeled using a linear analytical model is examined. The latter assumes equivalent barotropic flow aligned with the geostrophic contours, which in turn are dominated by the topography. With ECMWF winds and ETOPO2 topography, the model yields surface height deviations which are significantly correlated with satellite‐derived estimates on seasonal and longer time scales in the central basin. The model is somewhat less successful in the southern basin, where the stratification is stronger. Nevertheless, the results are encouraging, given the extreme simplicity of the model.

On the Effective Capacity of the Dense-Water Reservoir for the Nordic Seas Overflow: Some Effects of Topography and Wind Stress

Abstract The overflow of the dense water mass across the Greenland–Scotland Ridge (GSR) from the Nordic Seas drives the Atlantic meridional overturning circulation (AMOC). The Nordic Seas is a large basin with an enormous reservoir capacity. The volume of the dense water above the GSR sill depth in the Nordic Seas, according to previous estimates, is sufficient to supply decades of overflow transport. This large capacity buffers overflow’s responses to atmospheric variations and prevents an abrupt shutdown of the AMOC. In this study, the authors use a numerical and an analytical model to show that the effective reservoir capacity of the Nordic Seas is actually much smaller than what was estimated previously. Basin-scale oceanic circulation is nearly geostrophic and its streamlines are basically the same as the isobaths. The vast majority of the dense water is stored inside closed geostrophic contours in the deep basin and thus is not freely available to the overflow. The positive wind stress curl in the Nordic Seas forces a convergence of the dense water toward the deep basin and makes the interior water even more removed from the overflow-feeding boundary current. Eddies generated by the baroclinic instability help transport the interior water mass to the boundary current. But in absence of a robust renewal of deep water, the boundary current weakens rapidly and the eddy-generating mechanism becomes less effective. This study indicates that the Nordic Seas has a relatively small capacity as a dense water reservoir and thus the overflow transport is sensitive to climate changes.

Spin-up and spin-down in a half cone: A pathological situation or not?

The spin-up and spin-down of a fluid in a rapidly rotating, fluid-filled, and closed half cone are studied both numerically and experimentally. This unusual set up is of interest because it represents a pathological case for the classical linear theory of Greenspan and Howard [J. Fluid Mech. 17, 385–404 (1963)10.1017/S0022112063001415] since there are no closed geostrophic contours nor a denumerable set of inertial waves (even a modified theory incorporating Rossby waves by Pedlosky and Greenspan [J. Fluid Mech. 27, 291–304 (1967)10.1017/S0022112067000321]—relies on geostrophy to leading order). The linearised spin-up/spin-down dynamics in a half cone is found to be dominated by topographical effects which force an ageostrophic leading balance and cause the large-scale starting vorticity to coherently move into the “westward” corner of the half cone for both spin-up and spin-down. Once there, viscous boundary layer effects take over as the dominant process ensuring that the spin-up/spin-down time scales conventionally with E−1/2, where E is the Ekman number. The numerical coefficient in this time scale is approximately a quarter of that for a full cone when the semi-angle is 30°. Nonlinear spin up from rest is also studied as well as an impulsive 50% reduction in the rotation rate which shows boundary layer separation and small scales. We conclude that spin-up in a rapidly rotating half cone is not pathological because the fluid dynamics is fundamentally the same as that in a container with small topography: in both topography-forced vortex stretching is to the fore.

Abyssal Circulation Driven by a Periodic Impulsive Source in a Small Basin with Steep Bottom Slope with Implications to the East Sea

In the theory of source-driven abyssal circulation, the forcing is usually assumed to be steady source (deep-water formation). In many cases, however, the deep-water formation occurs instantaneously and it is not clear whether the theory can be applied well in this case. An attempt is made to resolve this problem by using a simple reduced gravity model. The model basin has large depth change compared for its size, like the East Sea, such that isobaths nearly coincide with geostrophic contours. Deep-water is formed every year impulsively and flows into the model basin through the boundary. It is found that the circulation driven by the impulsive source is generally the same as that driven by a steady source except that the former has a seasonal fluctuation associated with unsteadiness of forcing. The magnitudes of both the annual average and seasonal fluctuations increase with the rate of deep-water formation. The problem can be approximated to that of linear diffusion of momentum with boundary flux, which well demonstrates the essential feature of abyssal circulation spun-up by periodic impulsive source. Although the model greatly idealizes the real situation, it suggests that abyssal circulation can be driven by a periodic impulsive source in the East Sea.

Subtropical Western Boundary Currents over Slopes Detaching from Coasts with Inshore Pool Regions: An Indication to the Kuroshio Nearshore Path

Abstract The dynamics of subtropical western boundary currents over slopes detaching from coasts with inshore pool regions, where the water of the subtropical gyre does not enter and the velocity is small, are investigated. This study is intended to understand the dynamics of the nearshore path of the Kuroshio, which has a distinct boundary between the boundary current and the coastal water. Numerical experiments under idealized conditions are made. The results show flow patterns with pool regions similar to the Kuroshio under simple conditions. A deep countercurrent is present on the lower bottom slope, which represents observed deep currents. This is part of a deep cyclonic recirculation north of the jet, which extends to the lower bottom slope despite steep topography. This extension can be explained by the geostrophic contours. In this region, the upper boundary current feels the bottom slope and the westward intensification is blocked. In the other region, where the bottom-layer velocity is very small, the upper boundary current is free from the bottom slope and westward intensification occurs at the coast. The sensitivity to the volume transport of the boundary current is investigated by case studies. The pool regions are broken in cases with large volume transports. It is indicated that these unsteady inshore regions are produced by instability caused by an outcrop of the upper isopycnal, which is led by a large baroclinic volume transport.

Effects of mass source/sink at the western boundary on the wind-driven gyres: Implications for the ventilation of the north pacific intermediate layer through convection in the Okhotsk Sea and tidal mixing at the Kuril Straits

A steady quasi-geostrophic 2.5-layer model, forced by both Ekman pumping and a mass source/sink situated at the western boundary has been constructed to investigate the effect of diapycnal transport due to convection in the Okhotsk Sea and tidal mixing at the Kuril Straits on the intermediate layer in the North Pacific. The model illustrates a combined effect of the wind-driven and mass-driven circulations. First, net mass input induces a “barotropic” mode inter-gyre flow along the western boundary through the dynamical influence of Kelvin waves. This flow creates characteristic curves (geostrophic contours) that facilitate inter-gyre communication through the western boundary layer from the location of the mass source to the subtropical gyre. Due to the effect of wind-driven circulation, the offshore part turns eastward into the interior, encircles the outer rim of the region (which would otherwise be the pool region in the absence of mass input), and then encounters the western boundary. Eventually, the water fed into the lower layer flows mostly along this path and later flows away to the equatorial region. Conversely, in the upper layer, water is fed from the equator to the subtropics, and to the subpolar interior region through the western boundary current. The water then circulates along the outer rim and is absorbed into the mass sink. The model is controlled mainly by three nondimensional parameters: (1) the ratio of net mass input rate to the maximum Sverdrup transport (Q/T Sv max ), which affects the inter-gyre communication by altering the paths of geostrophic contours, (2) the ratio of a mass input rate into the lower layer to that in total (Q 2/Q), which controls the vertical structure of the inter-gyre flow, and (3) the measure of the wind forcing effect relative to the β effect, which determines the horizontal extent of the area influenced by the mass input. The other parameter regimes with respect to Q/T Sv max and Q 2/Q are also presented.

The construction of exact Taylor states. II: The influence of an inner core

The geodynamo mechanism, responsible for sustaining Earth’s magnetic field, is believed to be strongly influenced by the solid inner core through its influence on the structure of convection within the tangent cylinder. In the rapidly rotating low-viscosity regime of the geodynamo equations relevant to the Earth’s core, the magnetic field must satisfy a continuum of conditions known as Taylor’s constraint. Magnetic fields that satisfy this constraint, termed Taylor states, have the property that their axial magnetic torque vanishes when averaged over any geostrophic contour, cylinders of fluid coaxial with the rotational axis. In recent theoretical developments, we proved that when adopting a truncated spherical harmonic expansion, the continuous constraint in space reduced to a finite spectral set of conditions. Furthermore, an expedient choice of regular radial basis presents an under-determined problem when constructing Taylor states in a full-sphere showing the ubiquity of such solutions. A spherical-shell geometry, with a conducting inner core, complicates the formulation of Taylor’s constraint due to the partitioning of the geostrophic contours into three distinct regions, ostensibly trebling the stringency of the constraint. This raises questions as to the admissible structures of such Taylor states, and their relation to those in a full-sphere. In this paper, we address these issues in two stages. First, we present a mathematical characterisation of the structure of Taylor’s constraint in a spherical-shell. We then enumerate the effective number of conditions that must be satisfied by any magnetic field that is everywhere C ∞ inside the core, and show that, assuming an equal truncation in radial and solid angle representation, the number of conditions is approximately 5/3 times that for a full-sphere Taylor state. Second, we investigate the influence of the inner core on the structure of admissible Taylor states by constructing a low-degree family of optimally smooth observationally consistent examples in both a spherical-shell and a full-sphere. We show that the introduction of an inner core into a full-sphere increases the minimum magnetic field complexity, simply by virtue of the increased potency of Taylor’s constraint, a trait more pronounced in our quasi-axisymmetric models. We speculate that axisymmetric dynamo-generated exact Taylor states, particularly those generated in a spherical-shell, in general have small radial length scales that may be difficult to resolve.

Basin and Channel Contributions to a Model Antarctic Circumpolar Current

Abstract The idea that basinlike dynamics may play a major role in determining the Antarctic Circumpolar Current (ACC) transport is revisited. A simple analytic model is developed to describe the relationship between the wind stress and transport. At very low-wind stress, a nonzero minimum is predicted. This is followed by two distinct dynamical regimes for stronger forcing: 1) a Stommel regime in which transport increases linearly with forcing strength; and 2) a saturation regime in which the transport levels off. The baroclinic structure of the Sverdrup flux into the Drake Passage latitude band is central to the analytic model, and the geometry of characteristics, or geostrophic contours, is key to predicting the transition between the two regimes. A robustness analysis is performed using an eddy-permitting quasigeostrophic model in idealized geometries. Many simulations were carried out in large domains across a range of forcing strengths. The simulations agree qualitatively with the analytic model, with two main discrepancies being related to zonal jet structures and to a western boundary inertial recirculation. Eddy fluxes associated with zonal jets modify the baroclinic structure and lower the saturation transport value. Inertial effects increase the transport, although this effect is mainly limited to smaller domains.

The structure of Taylor's constraint in three dimensions

In a 1963 edition of Proc. R. Soc. A , J. B. Taylor (Taylor 1963 Proc. R. Soc. A 9 , 274–283) proved a necessary condition for dynamo action in a rapidly rotating electrically conducting fluid in which viscosity and inertia are negligible. He demonstrated that the azimuthal component of the Lorentz force must have zero average over any geostrophic contour (i.e. a fluid cylinder coaxial with the rotation axis). The resulting dynamical balance, termed a Taylor state, is believed to hold in the Earth's core, hence placing constraints on the class of permissible fields in the geodynamo. Such states have proven difficult to realize, apart from highly restricted examples. In particular, it has not yet been shown how to enforce the Taylor condition exactly in a general way, seeming to require an infinite number of constraints. In this work, we derive the analytic form for the averaged azimuthal component of the Lorentz force in three dimensions after expanding the magnetic field in a truncated spherical harmonic basis chosen to be regular at the origin. As the result is proportional to a polynomial of modest degree (simply related to the order of the spectral expansion), it can be made to vanish identically on every geostrophic contour by simply equating each of its coefficients to zero. We extend the discussion to allow for the presence of an inner core, which partitions the geostrophic contours into three distinct regions.