Geostrophic Contours Research Articles

Asymmetry of Free Circulations in Closed Ocean Gyres

Abstract Steady flows in regions of closed geostrophic contours, such as in ocean basins or over seamounts, are examined by calculating solutions to the nonlinear quasigeostrophic and shallow-water equations with topography. For oceanically realistic choices of parameters, the solutions are asymmetric in that those with cyclonic circulation resemble the topography while those with anticyclonic circulation exhibit small-scale structure and cross-isobath flow. These small-scale structures reflect topographic wave modes, which are stationary with the anticyclonic circulation. The implication of the asymmetry is that random wind forcing is much more likely to excite persistent cyclonic than anticyclonic flow. This may explain why the circulation in the Norwegian and Greenland Gyres is most often cyclonic.

Connections between surface fluxes and the deep circulation in the Sea of Japan

The extent to which seasonably variable surface fluxes and bottom friction can exert a control on the abyssal circulation above localized bottom topography is analyzed in the Japan Sea region through the use of a three‐dimensional eddy‐resolving ocean model. Our simulations show that the bottom friction exerts a first‐order control on the magnitude of the eddy‐driven deep circulation over f/H geostrophic contours, which is inversely dependent on the bottom drag, in accordance with theory. Seasonal surface flux variability acts as a modifier to this theory, depending on the timescale of active forcing relative to bottom friction spin‐down time. Possible physical mechanisms for a varying bottom drag coefficient are proposed. Winter ventilation of isopycnals during deep convection is followed by enhanced drain energy to small‐scale turbulence and strong energy dissipation in intermediate layers leading to a weakening of deep circulation that contradicts the classic ventilation theory.

Low-Frequency Basin Modes in a Two-Layer Quasigeostrophic Model in the Presence of a Mean Gyre Flow*

Abstract The spectrum of baroclinic basin modes is investigated in a two-layer wind-driven quasigeostrophic model through weakly nonlinear multiple time-scale expansion in the Burger number. The baroclinic basin modes are mainly advected by a barotropic steady Sverdrup flow. Emphasis is given to the regularizing influence of dispersion rather than to dissipation. In the inviscid large-scale limit, that is, for basin scale considerably larger than the Rossby radius of deformation, all of the basin modes are neutral. Their typology is then numerically examined (with some necessary dissipation), and their frequency and spatial properties are discussed. Three types of modes arise for some wind forcing strong enough to produce a recirculating gyre with closed geostrophic contours: the classical Rossby basin modes deformed by the mean flow (shadow modes), stationary modes, and recirculating pool modes, the two latter being trapped in the closed-contours pool. Focus is made here on the recirculating modes that could have very low frequencies for moderate recirculating gyres. Strong gyres lead to higher frequencies, and recirculating modes resonate with deformed Rossby basin modes.

Buoyancy-forced circulations in shallow marginal seas

The properties of water mass transformation and the thermohaline circulation in shallow marginal seas with topography and subject to surface cooling are discussed in the context of an eddy-resolving primitive equation model and an analytic planetary geostrophic model. A unique and important aspect of the model configuration is that the geostrophic contours, or characteristics of the system, extend from a region where temperature is restored toward a uniform value, providing a source of heat, through the cooling region. This removes a degree of symmetry that has often been imposed in previous studies of deep convection. The heat loss within the marginal sea is balanced by lateral advection from the restoring region. The planetary geostrophic model shows that the basic temperature distribution can be well predicted by integrating along geostrophic contours from their entry into the marginal sea to their exit. Scaling estimates for the exchange rate and density of the waters formed within the marginal sea are derived and compare well with a series of numerical model calculations. In contrast to many previous buoyancy-forced deep convection problems, basin-scale cooling is balanced mainly by the mean flow, with mesoscale eddies serving primarily to restratify locally but not to provide a net heat flux to balance cooling. However, eddy fluxes and the mean flow are locally of comparable importance for cases with a localized patch of surface cooling.

Abyssal currents driven by a local wind forcing through deep mixed layer: implication to the east sea

A simple analytical model is considered in an attempt to demonstrate a formation mechanism of the abyssal current in the East Sea. In this model, the abyssal currents are driven by wind through an outcrop region and flow along closed geostrophic contours. A rough estimate of the abyssal currents, arrived at by applying this model to the region of deep mixing in the East Sea, gives currents comparable to those observed, although there is an uncertainty in the surface area of the outcrop region. It seems that the spin-up of deep water by wind forcing through the region of deep winter mixing is, at least partly, an important contribution to the formation of the abyssal currents in the East Sea.

A geostrophic-like model for large-Hartmann-number flows

A flow of electrically conducting fluid in the presence of a steady magnetic field has a tendency to become quasi-two-dimensional, i.e. uniform in the direction of the magnetic field, except in thin so-called Hartmann boundary layers. The condition for this tendency is that of a strong magnetic field, corresponding to large values of the dimensionless Hartmann number ( explains why the flow expected at large Hartmann number was not observed in experiments. The second problem exemplifies a situation where an analytical solution had been obtained in the past Walker & Ludford (J. Fluid Mech. vol. 56, 1972, p. 481) for the so-called ‘M-shaped’ velocity profile, which is here understood as an aspect of general quasi-two-dimensional magnetohydrodynamics.

The dynamical balance, transport and circulation of the Antarctic Circumpolar Current

The physical elements of the circulation of the Antarctic Circumpolar Current (ACC) are reviewed. A picture of the circulation is sketched by means of recent observations from the WOCE decade. We present and discuss the role of forcing functions (wind stress, surface buoyancy flux) in the dynamical balance of the flow and in the meridional circulation and study their relation to the ACC transport. The physics of form stress at tilted isopycnals and at the ocean bottom are elucidated as central mechanisms in the momentum balance. We explain the failure of the Sverdrup balance in the ACC circulation and highlight the role of geostrophic contours in the balance of vorticity. Emphasis is on the interrelation of the zonal momentum balance and the meridional circulation, the importance of diapycnal mixing and eddy processes. Finally, new model concepts are described: a model of the ACC transport dependence on wind stress and buoyancy flux, based on linear wave theory; and a model of the meridional overturning and the mean density structure of the Southern Ocean, based on zonally averaged dynamics and thermodynamics with eddy parametrization.

Potential vorticity dynamics in a domain with closed geostrophic contours. I: Steady linear flows

Potential vorticity dynamics in a domain with closed geostrophic contours. I: Steady linear flows

Baroclinic Modes in a Two-Layer Basin

The objective of this study is to investigate the time-dependent circulation in a closed basin where the steady circulation is included and long Rossby wave speeds are consistent with observations. Specifically, the large-scale baroclinic eigenmodes of a two-layer rectangular basin forced by surface wind stress in the limit of small dissipation are examined. Low-frequency modes with small decay rates independent of friction result when the constraint of mass conservation is enforced. The magnitude of the wind stress is found to be critical to the eigenspectrum. For all forcing magnitudes, including forcings with closed geostrophic contours, oscillatory modes with decay rates independent of friction emerge. For forcings with closed geostrophic contours, two important classes of eigenmodes with comparable decay rates emerge: purely decaying modes confined to the region of closed contours, and basin-scale oscillatory modes. The purely decaying modes also exist without the constraint of total mass conservation but their decay rates depend on the magnitude of friction to leading order.

Sources of Eddy Kinetic Energy in the Labrador Sea

Experiments with a suite of North Atlantic general circulation models are used to examine the sources of eddy kinetic energy (EKE) in the Labrador Sea. A high-resolution model version (112°) quantitatively reproduces the observed signature. A particular feature of the EKE in the Labrador Sea is its pronounced seasonal cycle, with a maximum intensity in early winter, as already found in earlier studies based on altimeter data. In contrast to a previously advanced hypothesis, the seasonally varying eddy field is not related to a forcing by high-frequency wind variations but can be explained by a seasonally modulated instability of the West Greenland Current (WGC). The main source of EKE in the Labrador Sea is an energy transfer due to Reynolds interaction work (barotropic instability) in a confined region near Cape Desolation where the WGC adjusts to a change in the topographic slope: Geostrophic contours tend to converge upstream of Cape Desolation, such that the topographically guided WGC narrows as well and becomes barotropically unstable. The eddies spawned from the WGC instability area, dominating the EKE in the interior Labrador Sea, are predominantly anticyclonic with warm and saline cores in the upper kilometer of the water column, while the few cyclones originating as well from the instability area show a more depth-independent structure. Companion experiments with a ⅓° model exhibit the strength of the WGC, influenced by either changes in the wind stress or heat flux forcing, as a leading factor determining seasonal to interannual changes of EKE in the Labrador Sea

Thermohaline and Wind Forcing of a Circumpolar Channel withBlocked Geostrophic Contours

Abstract The Antarctic Circumpolar Current is governed by unique dynamics. Because the latitude belt of Drake Passage is not zonally bounded by continents, the Sverdrup theory does not apply to the Antarctic Circumpolar Current. However, most of the geostrophic contours are blocked at Drake Passage, which provides an important dynamic constraint for the vorticity equation of the depth averaged flow. This study addresses the effects of thermohaline and wind forcing on the large-scale transport of a circumpolar current with blocked geostrophic contours. Various numerical experiments with three different idealized model geometries were conducted. Based on the results and theoretical arguments, the authors promote an indirect wind effect on the circumpolar current: while the direct effects of the wind in driving the circumpolar current through a vertical transfer of the applied wind stress are of minor importance, the wind does substantially influence the circumpolar current transport through its effects on the density field. This indirect wind effect is discussed in two steps. First, at the latitudes of the circumpolar current and longitudes where the geostrophic contours are blocked, the meridional gradient of the mass transport streamfunction is to leading order balanced by the meridional gradient of the baroclinic potential energy. This balance implies that the total transport is to leading order baroclinic and that the deep transport is small. For this statement, some theoretical arguments are offered. Second, a simplified analytical model is used to obtain the distribution of the baroclinic potential energy. Assuming an advective–diffusive balance for the densities in the deep downwelling northern branch of the Deacon cell, this model reproduces the qualitative dependence of the circumpolar current transport on the imposed wind and thermohaline forcing as well as on the turbulent diffusivities.

Thermohaline and Wind Forcing of a Circumpolar Channel withBlocked Geostrophic Contours

Thermohaline and Wind Forcing of a Circumpolar Channel withBlocked Geostrophic Contours

Determination of wind-driven ocean circulation inside closed characteristics

Using two-layer quasigeostrophic equations neglecting relative vorticity, it is shown that part of the lower layer flow inside closed geostrophic contours in the Sverdrup interior is determined neither by applying the integral condition nor by matching with the frictional western boundary layer. This flow is a higher approximation than might be supposed, so that the problem reduces to a perturbation one related to a local forcing-dissipation balance with flow paths being prescribed. A significant correction to this interior flow comes from the vorticity balance south of the closed region, so that to what degree the interior circulation is influenced by the western coast depends on the meridional size of the closed region. The extension of the theory to a 2(½)-layer model is immediate. Thus the present analysis strongly suggests that on shallow isopycnal surfaces the flow pattern and the associated potential vorticity distribution are not affected by the frictional western boundary current. Our asymptotic argument may partly be applied to more general cases provided that no O(1) external forcing acts on the lower layer.

Ventilation of the North Pacific Ocean: Water exchange between subtropical and tropical gyres

Ventilation or water exchange between the subtropical and tropic Pacific is studied with a simple none-thermodynamic two-and-half layer model. The shallow upper layer is assumed to communicate with its lower counterpart by entrainment and detrainment at ratesW e andW d. Trenberth wind stress data (Trenberth Data Center, 1995) are chosen to drive the upper moving ocean to obtain a stable state. The results show that the subtropical and tropic Pacific exchange water in two ways. One is the direct exchanging by which the surface water in the mid-latitude goes down and moves to the tropical region in the subsurface layer and upwells back to the Ekman layer and finally moves northward to complete its journey; and the other is the way of detour, by which water in the subtropical Pacific moves first to the western boundary region along geostrophic flow contours and goes down to the tropic region as southward boundary currents. These two ways contribute almost the same amount to the water exchange between the subtropical and tropic Pacific gyres although the spatial scale in the latter is ten times greater than that of the former. LPS's (Luyten et al., 1983) ventilation theory is reviewed to give a clear picture of how the water exchange in large scale has been studied and the numerical results in this paper are compared with both the conclusions of such analysis theory and some previous observation (tritium survey) reports.

Three-Dimensional Structure of Thermohaline Circulation Steered by Bottom Topography

An investigation based on the expansion in terms of diffusive vertical modes is made on the effect of an isolated seamount on the three-dimensional structure of thermohaline circulation driven by an inflow of deep water. While the circulation has a relatively simple structure dominated by the first baroclinic mode in a flat ocean, it becomes rather complicated in an ocean with a seamount. Nevertheless its three-dimensional structure is reconstructed and understood well by analyzing the dynamics of the vertical modes. It is shown that the vertical modes respond to the topography-induced stretching in a similar way irrespective of the mode number. When synthesized in the deep layer, therefore, the vertical modes interfere constructively to yield the same pattern of circulation as a single vertical mode or the diffusive reduced-gravity model. It is thus confirmed that the abyssal circulation certainly has the features predicted by the diffusive reduced-gravity model such as cyclonic circulation over the mountain or downwelling in the geostrophic island, in which geostrophic contours close on themselves. Close to the surface, however, different modes of different vertical structures interfere destructively so that the horizontal distribution of topography-induced circulation in the deep layer decays, upward shifting its center westward.

The rectification of wind-driven flow due to its instabilities

Within a quasi-geostrophic two-layer model of the wind-driven ocean circulation, an idealized symmetric double gyre flow is considered. When lateral friction is large enough, this flow is steady and characterized by a motionless lower layer. As friction is decreased, the flow undergoes a transition to time-dependence through a Hopf bifurcation, associated with a mixed barotropic/baroclinic instability. It is shown that the nonlinear self-interaction of this oscillatory unstable mode induces a nonzero time mean response in the lower layer. The origin of this deep flow is clarified through a weakly nonlinear analysis near critical conditions. It is explained how the perturbation is associated with both fluxes of anomalous layer thickness and Reynolds' stresses, due to vertical and horizontal phase lags, respectively. Furthermore, it is explained how the patterns of vorticity input, integrated over a cycle of the perturbation, induce a forcing of the second layer. Results deduced from computed trajectories at supercritical conditions support the conclusions from the weakly nonlinear analysis. This time-dependent view of the origin of the deep circulation is complementary to the classical (steady) picture based on the closure of geostrophic contours and forcing by interfacial friction, and may help to interpret results of eddy-resolving numerical models.

Bifurcation of the Kuroshio Extension at the Shatsky Rise

A 1/16° six‐layer Pacific Ocean model north of 20°S is used to investigate the bifurcation of the Kuroshio Extension at the main Shatsky Rise and the pathway of the northern branch from the bifurcation to the subarctic front. Upper ocean‐topographic coupling via a mixed barotropic‐baroclinic instability is essential to this bifurcation and to the formation and mean pathway of the northern branch as are several aspects of the Shatsky Rise complex of topography and the latitude of the Kuroshio Extension in relation to the topography. The flow instabilities transfer energy to the abyssal layer where it is constrained by geostrophic contours of the bottom topography. The topographically constrained abyssal currents in turn steer upper ocean currents, which do not directly impinge on the bottom topography. This includes steering of mean pathways. Obtaining sufficient coupling requires very fine resolution of mesoscale variability and sufficient eastward penetration of the Kuroshio as an unstable inertial jet. Resolution of 1/8° for each variable was not sufficient in this case. The latitudinal extent of the main Shatsky Rise (31°N–36°N) and the shape of the downward slope on the north side are crucial to the bifurcation at the main Shatsky Rise, with both branches passing north of the peak. The well‐defined, relatively steep and straight eastern edge of the Shatsky Rise topographic complex (30°N–42°N) and the southwestward abyssal flow along it play a critical role in forming the rest of the Kuroshio northern branch which flows in the opposite direction. A deep pass between the main Shatsky Rise and the rest of the ridge to the northeast helps to link the northern fork of the bifurcation at the main rise to the rest of the northern branch. Two 1/16° “identical twin” interannual simulations forced by daily winds 1981–1995 show that the variability in this region is mostly nondeterministic on all timescales that could be examined (up to 7 years in these 15‐year simulations). A comparison of climatologically forced and interannual simulations over the region 150°E–180°E, 29°N–47°N showed greatly enhanced abyssal and upper ocean eddy kinetic energy and much stronger mean abyssal currents east of the Emperor Seamount Chain (about 170°E) in the interannual simulations but little difference west of 170°E. This greatly enhanced the upper ocean‐topographic coupling in the interannual simulations east of 170°E. This coupling affected the latitudinal positioning of the eastward branches of the Kuroshio Extension and tended to reduce latitudinal movement compared to the climatologically forced simulation, including a particularly noticeable impact from the Hess Rise. Especially in the interannual simulations, effects of almost all topographic features in the region could be seen in the mean upper ocean currents (more so than in instantaneous currents), including meanders and bifurcations of major and minor currents, closed circulations, and impacts from depressions and rises of large and small amplitudes.

Deep water properties, velocities, and dynamics over ocean trenches

Observations of water properties and deep currents over several trenches in the Pacie c Ocean central basins give consistent evidence for recent ventilation of water below the trench sills and cyclonic sense of circulation over the trenches. A dynamical argument for this pattern is advanced. First, a review of previous analyses of hydrographic data shows that the trenches are well ventilated by dense bottom water, that within the trenches this bottom water generally spreads away from its source, and that a cyclonic sense of circulation is suggested over some trenches. Then, this cyclonic sense of circulation over the trenches is further documented using deep current meter and e oat data. Finally, bathymetry is used to motivate a simple dynamical framework for e ow over trenches. If the trench sides are sufficiently steep and the trench is sufficiently removed from the equator to ensure a region of closed geostrophic contours, then any upwelling over that region will drive a strong deep cyclonic recirculation in the weakly-stratie ed abyss through vortex stretching. The magnitude of this recirculation is limited by bottom drag. Ageostrophic e ow in a bottom Ekman layer into the trench balances the water upwelled over the trench. The cyclonic recirculation is much stronger than the upwelling-driven e ow predicted across blocked geostrophic contours by the linear planetary geostrophic balance.

Hydraulically Drained Flows in Rotating Basins. Part II: Steady Flow

Abstract The slow, horizontal circulation in a deep, hydraulically drained basin is discussed within the context of reduced-gravity dynamics. The basin may have large topographic variations and is fed from above or from the sides by mass sources. Dissipation is provided by bottom friction. To the order of the appromixations made (weak forcing and dissipation), the nonlinear hydraulic control is found to influence only the mean level of the interface separating upper and lower layers, and not the horizontal circulation. For the case of forcing from above the interior basin flow is anticyclonic about closed geostrophic contours and feeds into diffusive boundary layers leading to the draining strait and sill. With sidewall forcing, the interior is motionless and flow is channeled directly to the strait in boundary layers. The latter may circle the basin cyclonically or anticyclonically depending on the source distribution, and a circulation integral is shown to predict the sense of the overall swirl velocity...

Dynamic impact of oscillating sources on the North Atlantic deep circulation: A process study

In this process study the dynamic effects of fluctuating deep water sources on the deep circulation of the North Atlantic are examined by means of a 1½‐layer model. The model is used with a realistic topography of the Atlantic Ocean between 65°N and 25°S and has an open southern boundary. According to observations, the northern inflow of deep water is subject to variability on timescales between days and decades. The same holds for the Deep Western Boundary Current (DWBC), which acts as a link between the deep water inflow and the interior circulation. The timescales of the observed variability motivate the forcing functions used in the model. They determine the nature of the models response. The flow response relative to the local mean flow can be considerably larger than the original perturbation at the source. Normalizing the perturbed flow with the local steady state flow leads to the identification of sensitive areas. Their location and shape are determined by the difference between the characteristic travel paths of the perturbation and the streamlines of the steady state circulation. In the eastern equatorial Atlantic a forcing with periods between 1 and 3 months gives rise to larger flow perturbations than a forcing with periods between half a year and 1 year. Forcing with the latter periods leads to a stronger response in the western equatorial Atlantic and in the interior ocean. Changes in the direction of the deep equatorial flow are driven by low‐frequency oscillations of the DWBC in the model. This is consistent with observations in the area. Perturbations radiate into the interior away from the eastern boundary as long Rossby waves. As this propagation is along geostrophic contours, consequently large parts of the abyssal interior are inaccessible. The results support the notion that the area where the DWBC encounters the equator is not only a key region for the “slow” interhemispheric exchange of heat and tracers but also for the transport of information by “fast” internal waves along the equator.