Zonal Momentum Balance Research Articles

On the Steadiness of Separating Meandering Currents

Abstract The existence of inertial steady currents that separate from a coast and meander afterward is investigated. By integrating the zonal momentum equation over a suitable area, it is shown that retroflecting currents cannot be steady in a reduced gravity or in a barotropic model of the ocean. Even friction cannot negate this conclusion. Previous literature on this subject, notably the discrepancy between several articles by Nof and Pichevin on the unsteadiness of retroflecting currents and steady solutions presented in other papers, is critically discussed. For more general separating current systems, a local analysis of the zonal momentum balance shows that given a coastal current with a specific zonal momentum structure, an inertial, steady, separating current is unlikely, and the only analytical solution provided in the literature is shown to be inconsistent. In a basin-wide view of these separating current systems, a scaling analysis reveals that steady separation is impossible when the interior flow is nondissipative (e.g., linear Sverdrup-like). These findings point to the possibility that a large part of the variability in the world’s oceans is due to the separation process rather than to instability of a free jet.

The dynamics of zonal current variations in the central equatorial Indian Ocean

This paper examines the depth integrated zonal momentum balance in the central equatorial Indian Ocean (0°, 80.5°E) for two periods in 1993–1994 and 2004–2006 using a combination of in‐situ and satellite observations. One‐ to two‐year record length mean balances are approximately linear and steady state. Monthly to seasonal time scale variations are also governed by linear dynamics, with imbalances between the pressure gradient force and surface wind stress leading to zonal mass transport variations along the equator. Interannual variations in zonal transports along the equator associated with Indian Ocean Dipole events in 1994 and 2006 are likewise consistent with linear dynamics. These results provide a valuable benchmark for evaluating models of equatorial Indian Ocean circulation on seasonal time scales.

Eddy-Mediated Regime Transitions in the Seasonal Cycle of a Hadley Circulation and Implications for Monsoon Dynamics

Abstract In a simulation of seasonal cycles with an idealized general circulation model without a hydrologic cycle and with zonally symmetric boundary conditions, the Hadley cells undergo transitions between two regimes distinguishable according to whether large-scale eddy momentum fluxes strongly or weakly influence the strength of a cell. The center of the summer and equinox Hadley cell lies in a latitude zone of upper-level westerlies and significant eddy momentum flux divergence; the influence of eddy momentum fluxes on the strength of the cell is strong. The center of the cross-equatorial winter Hadley cell lies in a latitude zone of upper-level easterlies and is shielded from the energy-containing midlatitude eddies; the influence of eddy momentum fluxes on the strength of the cell is weak. Mediated by feedbacks between eddy fluxes, mean zonal winds at upper levels, and the mean meridional circulation, the dominant balance in the zonal momentum equation at the center of a Hadley cell shifts at the transitions between the regimes, from eddies dominating the momentum flux divergence in the summer and equinox cell to the mean meridional circulation dominating in the winter cell. At the transitions, a feedback involving changes in the strength of the lower-level temperature advection and in the latitude of the boundary between the winter and summer cell is responsible for changes in the strength of the cross-equatorial winter cell. The transitions resemble the onset and end of monsoons, for example, in the shift in the dominant zonal momentum balance, rapid shifts in the latitudes of maximum meridional mass flux and of maximum convergence at lower levels, rapid changes in strength of the upward mass flux, and changes in direction and strength of the zonal wind at upper and lower levels. In the monsoonal regime, the maximum upward mass flux occurs in an off-equatorial convergence zone located where the balance of the meridional geopotential gradient in the planetary boundary layer shifts from nonlinear frictional to geostrophic. Similar dynamic mechanisms as at the regime transitions in the simulation—mechanisms that can act irrespective of land–sea contrasts and other inhomogeneities in lower boundary conditions—may be implicated in large-scale monsoon dynamics in Earth’s atmosphere.

On the fast response of the Southern Ocean to changes in the zonal wind

Abstract. Model studies of the Southern Ocean, reported here, show that the Antarctic Circumpolar Current responds within two days to changes in the zonal wind stress at the latitudes of Drake Passage. Further investigation shows that the response is primarily barotropic and that, as one might expect, it is controlled by topography. Analysis of the results show that the changes in the barotropic flow are sufficient to transfer the changed surface wind stress to the underlying topography and that during this initial phase baroclinic processes are not involved. The model results also show that the Deacon Cell responds to changes in the wind stress on the same rapid time scale. It is shown that the changes in the Deacon Cell can also be explained by the change in the barotropic velocity field, an increase in the zonal wind stress producing an increased northward flow in shallow regions and southward flow where the ocean is deep. This new explanation is unexpected as previously the Deacon Cell has been thought of as a baroclinic feature of the ocean. The results imply that where baroclinic processes do appear to be involved in either the zonal momentum balance of the Southern Ocean or the formation of the Deacon Cell, they are part of the long term baroclinic response of the ocean's density field to the changes in the barotropic flow.

A Zonal Momentum Balance on Density Layers for the Central and Eastern Equatorial Pacific

Abstract Brown et al. analyzed the kinematics of flow in the equatorial Pacific Ocean, along time-varying isopycnals in a three-dimensional eddy-permitting model. Here the dynamics of these flows is explored in the same model via the zonal momentum equation (ZME). Previous work has shown that the dominant terms of the ZME, on and near the equator, are the pressure gradient, wind stress, and Coriolis term. In one model study, the nonlinear and friction terms were significant but negated each other. In this study, with a higher-resolution model and more realistic friction scheme it is shown that the nonlinear term is important along and north of the equator, while the explicit friction term is negligible. The part of the nonlinear term derived from high-frequency eddy flows acts like a friction on the Equatorial Undercurrent, while the remaining part of the nonlinear term from smooth flows enhances it. In density coordinates, meridional tropical cells lie on either side of the equator in the first half of the year (January–June) as expected. In July–December, a continuous southward surface flow appears from 4°N into the Southern Hemisphere and arises from variations in the geostrophic flow and the nonlinear term. Variations in the geostrophic flow are due to both seasonal variability in the thermocline and a surface bolus effect arising from baroclinic instability. The nonlinear term increases in the surface layers at the same time assisting the southward flow, most likely because of tropical instability waves.

Intraseasonal Variability of Equatorial Indian Ocean Zonal Currents

Abstract New satellite and in situ observations show large intraseasonal (10–60 day) variability of surface winds and upper-ocean current in the equatorial Indian Ocean, particularly in the east. An ocean model forced by the Quick Scatterometer (QuikSCAT) wind stress is used to study the dynamics of the intraseasonal zonal current. The model has realistic upper-ocean currents and thermocline depth variabilities on intraseasonal to interannual scales. The quality of the simulation is directly attributed to the accuracy of the wind forcing. At the equator, moderate westerly winds are punctuated by strong 10–40-day westerly wind bursts. The wind bursts force swift, intraseasonal (20–50 day) eastward equatorial jets in spring, summer, and fall. The zonal momentum balance is between local acceleration, stress, and pressure, while nonlinearity deepens and strengthens the eastward current. The westward pressure force associated with the thermocline deepening toward the east rapidly arrests eastward jets and, subsequently, generates (weak) westward flow. Thus, in accord with direct observations in the east, the spring jet is a single intraseasonal event, there are intraseasonal jets in summer, and the fall jet is long lived but strongly modulated on an intraseasonal scale. The zonal pressure force is almost always westward in the upper 120 m, and changes sign twice a year in the 120–200-m layer. Transient eastward equatorial undercurrents in early spring and late summer are associated with semiannual Rossby waves generated at the eastern boundary following thermocline deepening by the spring and fall jets. An easterly wind stress is not necessary to generate the undercurrents. Experiments with a single westerly wind burst forcing show that apart from the intraseasonal response, the zonal pressure force and current in the east have an intrinsic 90-day time scale that arises purely from equatorial adjustment.

A finite-difference convective model for Jupiter's equatorial jet

AbstractWe present results of a numerical model for studying the dynamics of Jupiter's equatorial jet. The computed domain is a piece of spherical shell around the equator. The bulk of the region is convective, with a thin radiative layer at the top. The shell is spinning fast, with a Coriolis number = ΩL/V on the order of 50. A prominent super-rotating equatorial jet is generated, and secondary alternating jets appear in the higher latitudes. The roles of terms in the zonal momentum equation are analyzed. Since both the Reynolds number and the Taylor number are large, the viscous terms are small. The zonal momentum balance is primarily between the Coriolis and the Reynolds stress terms.

Tropical Zonal Momentum Balance in the NCEP Reanalyses

Abstract The seasonal cycle of the zonal-mean zonal momentum balance in the Tropics is investigated using NCEP reanalysis data. It is found that the climatological stationary waves in the tropical upper troposphere, which are dominated by the equatorial Rossby wave response to tropical heating, produce an equatorward eddy flux of westerly momentum in the equatorial belt. The resulting westerly acceleration in the tropical upper troposphere is balanced by the advection of easterly momentum associated with the cross-equatorial mean meridional circulation. The eddy momentum fluxes and the cross-equatorial flow both tend to be strongest during the monsoon seasons, when the maximum diabatic heating is off the equator, and weakest during April–May, the season of strongest equatorial symmetry of the heating. The upper-level Rossby wave pattern exhibits a surprising degree of equatorial symmetry and follows a similar seasonal progression. Solutions of the nonlinear shallow water wave equation also show a predominantly equatorially symmetric response to a heat source centered off the equator.

Zonal Momentum Balance, Potential Vorticity Dynamics, and Mass Fluxes on Near-Surface Isentropes

AbstractWhile it has been recognized for some time that isentropic coordinates provide a convenient framework for theories of the global circulation of the atmosphere, the role of boundary effects in the zonal momentum balance and in potential vorticity dynamics on isentropes that intersect the surface has remained unclear. Here, a balance equation is derived that describes the temporal and zonal mean balance of zonal momentum and of potential vorticity on isentropes, including the near-surface isentropes that sometimes intersect the surface. Integrated vertically, the mean zonal momentum or potential vorticity balance leads to a balance condition that relates the mean meridional mass flux along isentropes to eddy fluxes of potential vorticity and surface potential temperature. The isentropic-coordinate balance condition formally resembles balance conditions well known in quasigeostrophic theory, but on near-surface isentropes it generally differs from the quasigeostrophic balance conditions. Not taking the intersection of isentropes with the surface into account, quasigeostrophic theory does not adequately represent the potential vorticity dynamics and mass fluxes on near-surface isentropes—a shortcoming that calls into question the relevance of quasigeostrophic theories for the macroturbulence and global circulation of the atmosphere.

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.

Estimation of the low-latitude reflectivity of stationary waves in a GCM simulation

Propagation of stationary waves induced by isolated orographic forcing in high latitudes was simulated in a long-term GCM run. The purpose of the study was to establish to what degree these waves are reflected from low latitudes. In this simulation, a broad unbroken belt of tropical easterlies prevents wave propagation into the southern hemisphere, and the waves are efficiently absorbed in low latitudes. The ratio of the northward to southward stationary wave activity flux can be estimated by studying the meridional distribution of the correlation between the stationary eddy horizontal velocity components. In middle latitudes of the northern hemisphere the ratio was 0.2 ± 0.04. A large proportion of the rather weak northward flux component is induced by low-latitude transient eddy forcing associated with the baroclinic instability of the flow, while reflection from the nonlinear critical layer (CL) seems to be small. This paper presents a method of partitioning the horizontal stationary wave activity flux into contributions due to various forcing functions. In the longitude belt where the mountain-induced wave train encounters the time-mean zero wind line, one can find indications of nonlinear wave breaking. In contrast to several previous simulations, wave breaking does not involve significant reflection. This may be explained by the existence of the Hadley circulation, which allows the zonal momentum balance to be maintained even under wave absorption. In the present GCM runs the reflectivity of the CL was found to be low; however, further GCM experiments are needed to assess whether this conclusion holds universally in the atmosphere.

Dynamic and energetic coupling in the equatorial ionosphere and thermosphere

A three‐dimensional coupled model of the global ionosphere and thermosphere has been used to examine the importance of ion drag parallel to the geomagnetic field, on the equatorial wind and temperature structure. Simulations performed at equinox, moderate solar activity (F10.7 = 150), and geomagnetically quiet condition (Ap = 7) show that the model reproduces the general observed structures of the global ionosphere and thermosphere. Comparison between the model results and satellite observations confirms that ion drag plays a significant role in the zonal momentum balance and superrotation of the Earth's upper atmosphere at equatorial latitudes. The results also suggested that ion drag parallel to the field lines, in the vicinity of a pronounced Equatorial Ionization Anomaly, has a significant impact on the latitudinal structure of the equatorial neutral wind and temperature structure. Note that the impact of parallel ion drag on the wind and temperature structure has not been evaluated previously. The model simulations show that the ion motion parallel to the field lines acts as a source of momentum to the neutral atmosphere. It is well established that after being transported upward by electric fields at the magnetic equator, plasma falls along the inclined field lines either side. The simulations indicate that collisions between the falling plasma and neutrals impart a small momentum source forcing poleward winds away from the magnetic equator. The neutral wind in turn transports momentum and energy and produces adiabatic changes that alter the meridional temperature structure. The results show that the impact of parallel ion drag must be considered in any comprehensive analysis of dynamics and energy coupling of the equatorial ionosphere and thermosphere and is important when interpreting observations of equatorial wind and temperature features, such as ETWA or MTM.

On the meridional circulation and balance of momentum in the Southern Ocean of POP

The circulation of the Southern Ocean is studied in the eddy-resolving model POP (Parallel Ocean Program) by an analysis of zonally integrated balances. The TEM formalism (Transformed Eulerian Mean) is extended to include topography and continental boundaries, thus deviations from a zonally integrated state involve transient and standing eddies. The meridional circulation is presented in terms of the Eulerian, eddy-induced, and residual streamfunctions. It is shown that the splitting of the meridional circulation into Ekman and geostrophic transports and the component induced by subgrid and Reynolds stresses is identical to a particular form of the zonally integrated balance of zonal momentum. In this balance, the eddy-induced streamfunctions represent the interfacial form stresses by transient and standing eddies and the residual streamfunction represents the acceleration of the zonal current by density fluxes in a zonally integrated frame. The latter acceleration term is directly related to the surface flux of density and interior fluxes due to the resolved and unresolved eddies. The eddy-induced circulation is extremely vigorous in POP. In the upper ocean a shallow circulation, reversed in comparison to the Deacon cell and mainly due to standing eddies, appears to the north of Drake Passage latitudes, and in the Drake Passage belt of latitudes a deep-reaching cell is induced by transient eddies. In the resulting residual circulation the Deacon cell is largely cancelled and the residual advection of the zonal mean potential density is balanced by diapycnal eddy and subgrid fluxes which are strong in the upper few hundred meters but small in the ocean interior. The balance of zonal momentum is consistent with other eddy-resolving models; a new aspect is the clear identification of density effects in the zonally integrated balance. We show that the wind stress and the stress induced by the residual circulation drive the eastward current, whereas both eddy species result in a braking. Finally, we extend the Johnson–Bryden model of zonal transport to incorporate all relevant terms from the zonal momentum balance. It is shown that wind stress and induction by the residual circulation carry an eastward transport while bottom form stress and the stress induced by standing eddies yield westward components of transport.

Intense surface currents in the tropical Pacific during 1996–1998

Tropical Pacific Ocean near‐surface currents and their momentum and temperature balances are investigated using several data sets, including drifting buoy velocities and TOPEX/Poseidon altimetry. The data sets are combined to produce monthly surface current estimates on a uniform grid for the 6‐year period 1993–1998, using multivariate optimal interpolation. The analysis shows dramatic changes in current from December 1996 through August 1998 in response to the recent El Niño‐Southern Oscillation event. Eastward current anomalies of ∼1 m s−1 were recorded in December 1996 in the western Pacific, generated by sporadic westerly wind bursts. By April 1997 these equatorial anomalies reached the eastern boundary, and in the summer of 1997 a band of strong eastward flow formed across the basin. This circulation pattern persisted until the beginning of 1998, when a westward equatorial jet appeared in January‐April. Interestingly, the reversal of flow occurred prior to the restoration of the trade winds. The timing of these events as well as the results of previous dynamical studies raise questions about the relative importance of terms in the zonal momentum and temperature balances. We address the first of these questions by examining the applicability of a three‐term linear zonal momentum balance on the equator. In all cases we focus on anomalies from the time mean. Our results show that local acceleration is reasonably well balanced by the difference between zonal pressure gradient anomaly and wind‐induced momentum flux. This three‐term balance displays significant basin‐wide variations and is consistent with the conclusion that the equatorial Pacific is not in equilibrium with local wind forcing due to the presence of propagating waves. Examination of the temperature balance shows that at the beginning of El Niño the warming in the central Pacific is mainly supported by horizontal temperature transport, while the vertical heat exchange and transport become important in the eastern half of the equatorial Pacific during the transition from El Niño to La Niña.

Wind-Forced Reversing Jets in the Western Equatorial Pacific*

Upper-ocean zonal currents in the western equatorial Pacific are remarkably variable, changing direction both with time and depth. As a part of the Tropical Ocean and Global Atmosphere Coupled Ocean‐Atmosphere Response Experiment, an enhanced monitoring array of moorings measured the upper-ocean velocity, temperature, salinity, and, surface meteorological conditions in the western equatorial Pacific for two years (March 1992‐April 1994). Data from this array are used to evaluate the zonal momentum balance. Although nonlinear terms (zonal, meridional, and vertical advection) were at times large, reversing jets were primarily due to an interplay between wind forcing and compensating pressure gradients. In the weakly stratified surface layer, the flow is to a large extent directly forced by local winds. Eastward acceleration associated with westerly wind bursts and westward accelerations associated with easterly trades lead to frequent reversals in the surface-layer flow. However, pressure gradients set up by the wind bursts partially compensate the local wind forcing in the surface layer. Below the surface layer, these pressure gradients tend to accelerate the upper-thermocline flow in a direction opposing the local winds. Consequently, during westerly wind bursts, a reversing jet structure can develop, with a surface eastward current overlying a westward intermediate layer flow, overlaying the eastward Equatorial Undercurrent.

A theoretical reason to expect inviscid western boundary currents in realistic oceans

The conventional picture of an ocean gyre, based on an ocean with vertical sidewalls, assumes a balance between an input of vorticity by wind stress curl, and a viscous flux of vorticity through the boundary at the same latitude, resulting from a viscous western boundary current which may be significantly modified by nonlinear terms. Potential interactions with topography are also commonly acknowledged as a possible complicating factor. In this idealized picture, the zonal momentum balance is taken to be geostrophic, as numerous model analyses confirm. A theoretical argument is given here which shows that, in an ocean with sloping sidewalls, this geostrophic balance results in bottom pressure torques which balance the wind stress curl at each latitude. This removes the requirement for a viscous western boundary current at each latitude suggesting that the dynamics within a western boundary current may be essentially inviscid. While inviscid western boundary currents have already been found in certain idealized systems, and in one set of diagnostics from an eddy permitting model, the generality of the argument presented here gives a strong reason to believe that these are not special cases. Inviscid western boundary currents are in fact the rule, and the vertical sidewall case is an unrealistic exception.

Dynamics of the equatorial undercurrent in a high‐resolution ocean model

In this study, we investigate the sensitivity of the equatorial circulation simulated with the high‐resolution World Ocean Circulation Experiment (WOCE) Community Modeling Effort (CME) model to the specification of eddy viscosity. In one of two simulations the coefficient of vertical viscosity is tripled. We focus on the dynamics associated with the anomalous eastward surface flow found in the simulation results. We find, in agreement with other studies, that close to the western boundary, the equatorial undercurrent is dominated by a large positive pressure gradient. In the top layer, for the low‐viscosity case, the balance in the western part of the basin is everywhere between the horizontal pressure gradient and vertical viscosity with the advective terms playing a secondary role. In the high‐viscosity zonal momentum budget analysis the advective terms are less significant in the surface layers in the west. Toward the east the advective terms become more important in the low‐viscosity experiment, whereas in the high‐viscosity case the balance is still predominantly between the horizontal pressure gradient and vertical diffusion terms. It is found that in the CME, horizontal viscosity plays a very minor role in the zonal momentum balance. Changes in the vertical viscosity lead to changes in the nonlinear advective terms. These, in turn, contribute to the unusual eastward surface flow.

The Surface Branch of the Zonally Averaged Mass Transport Circulation in the Troposphere

The near-surface branch of the overturning mass transport circulation in the troposphere, containing the equatorward flow, is examined in isentropic and geometric coordinates. A discussion of the zonal momentum balance within isentropic layers shows that the equatorward flow at a given latitude is confined to isentropic layers that typically intersect the surface at that latitude. As a consequence of mass transport within the surface mixed layer, much of the equatorward flow occurs in layers with potential temperatures below the mean surface potential temperature. In the conventional transformed Eulerian mean formulation for geometric coordinates, the surface branch of the overturning circulation is represented in an unrealistic manner: streamlines of the residual circulation do not close above the surface. A modified residual circulation is introduced that is free from this defect and has the additional advantage that its computation, unlike that of the conventional residual circulation, does not require division by the static stability, which may approach zero in the planetary boundary layer. It is then argued that cold air advection by the residual circulation is responsible for the formation of surface inversions at all latitudes in idealized GCMs with weak thermal damping. Also included is a discussion of how a general circulation theory for the troposphere must be built upon a theory for the near-surface meridional mass fluxes.

The Zonal Momentum Balance of the Equatorial Undercurrent in the Central Pacific

Current velocity data from an array of subsurface moorings deployed during the Tropical Instability Wave Experiment from May 1990 to June 1991 are used to diagnose the upper-ocean zonal momentum balance at 0°, 140°W. The flow field and associated zonal momentum flux divergence are fully three-dimensional over the upper 250 m, consistent with the earliest descriptions and theoretical ideas of the Equatorial Undercurrent (EUC). Estimates of the vertical stress divergence show dynamical flow regimes that change between the surface and the base of the EUC, being essentially linear (modified by nonlinearity) near the surface, weakly nonlinear at the EUC core, and fully nonlinear below the core. The vertical stress divergence is much larger over the lower portion of the EUC than previously reported, but this is consistent with the observed downstream deceleration of the EUC and the idea that vertical mixing is important in maintaining the thermostad. Nonlinearity becomes increasingly important with decreasing frequency, but tends to cancel upon vertical integration.

The zonal momentum balance in an eddy-resolving general-circulation model of the Southern Ocean

The momentum balance in the zonally unbounded region of the Southern Ocean is examined using an eddy-resolving ocean general-circulation model (namely FRAM). Momentum, which is input at the surface and accelerates the Antarctic Circumpolar Current, is transferred down the water column and removed by topographic form stress. Bottom friction and lateral eddy viscosity are found to be negligible. the poleward flux of eastward momentum has a small effect in redistributing momentum. In spite of this, below the wind-driven surface layer and above the level of topography, the poleward momentum-flux divergence provides the main balance along with the ageostrophic flux of planetary vorticity (although the magnitude of these terms is an order of magnitude smaller than the wind stress). Below the Ekman layer, standing eddies produce a drag on the flow whilst transient eddies accelerate the flow. However, the impact of transient eddies is smaller. the downward transfer of momentum is achieved by interfacial form stress. This can be understood in terms of a poleward density (heat) flux. the main contribution comes from standing eddies, with a smaller contribution from transient eddies. Both contributions assist the transfer. the flux of density (heat) from the neighbouring oceans (to the north and south of the Drake Passage latitudes) influences the depth penetration of zonal momentum, particularly in the upper 1000 m. the Johnson-Bryden theory is generalized to give an additional term which is proportional to the stream function for the residual circulation associated with Eliassen-Palm cross-sections.