Transport Streamfunction Research Articles

Decomposing Barotropic Transport Variability in a High‐Resolution Model of the North Atlantic Ocean

AbstractA method using a linear shallow water model is presented for decomposing the temporal variability of the barotropic stream function in a high‐resolution ocean model. The method is based on the vertically averaged momentum equations and is applied to the time series of annual mean stream function from the model configuration VIKING20 for the northern North Atlantic. An important result is the role played by the nonlinear advection terms in VIKING20 for driving transport. The method is illustrated by examining how the Gulf Stream transport in the recirculation region responds to the winter North Atlantic Oscillation (NAO). While no statistically significant response is found in the year overlapping with the winter NAO index, there is a tendency for the Gulf Stream transport to increase as the NAO becomes more positive. This becomes significant in lead years 1 and 2 when the mean flow advection and eddy momentum flux contributions, associated with nonlinear momentum advection, dominate. Only after 2 years, does the potential energy term, associated with the density field, start to play a role and it is only after 5 years that the transport dependence on the NAO ceases to be significant. It is also shown that the potential energy contribution to the transport stream function has significant memory of up to 5 years in the Labrador and Irminger Seas. However, it is only around the northern rim of these seas that VIKING20 and the transport reconstruction exhibit similar memory. This is due to masking by the mean flow advection and eddy momentum flux contributions.

An Analytical Solution for Nearshore Circulation Driven by Focused/Defocused Waves

An offshore shoal or bar refracts ocean surface waves and causes wave focusing/defocusing on the adjacent beach. Wave focal patterns characterized by alongshore variations in wave height, wave angle, and breaking location induce alongshore non-uniformities of wave setup and nearshore circulation, e.g., rip currents and alongshore currents, in the surfzone. A simplified analytic model for nearshore circulation generated by focused/defocused waves on a planar beach is developed and theoretical solutions are obtained using transport stream function and perturbations in alongshore distributions of wave height and wave angle at the breaker line. The analytic model suggests that alongshore currents are strongly affected by a pair of counter-rotating vortices generated shoreward of the wave focal zone. The vortices are persistent, and their strengths depend on the amplitudes of alongshore variations in wave height and wave angle. The alongshore gradient in wave height tends to intensify the vortices while the convergence of wave angle tends to weaken the vortices. Divergent flows associated with the vortices in the surfzone are intense, strengthening alongshore currents in the downstream of the wave focal zone and weakening alongshore currents or causing flows reversal in the upstream. Alongshore currents are modulated by rip currents associated with the wave focusing/defocusing patterns.

The Island Rule with lateral and bottom friction

The Island Rule, derived from the Sverdrup theory, is widely used to estimate and analyze water transport through a strait. Previous studies presented single- or multi-island rules with either lateral or bottom friction. In this paper, an analytical model of wind-driven circulation is assumed based on linear dynamics. Considering both lateral and bottom friction, the analytic solutions of the transport streamfunction around the islands are derived and the volume transport through the channel is presented. The results are similar to those of Wajsowicz, but the frictional constants represent different values. The analytic solution shows that the relationship between the lateral frictional and bottom frictional dissipation is complex in terms of the frictional constants. To understand the interaction between the two friction types, lateral and bottom friction values were randomly chosen on a barotropic beta plane. The result shows an approximately linear relationship between the lateral and bottom friction in consisting of the combined frictional constants. We studied the effect of the channel width on the transport through the channel. The results show that the friction enhances the flow under some widths, which is similar to the flow behavior when only the lateral friction is considered. We also compared the transport through the channel at different depths and founded that the deeper the water, the smaller the transport reduction ratio when the horizontal eddy viscosity coefficient and the bottom drag coefficient remained constants. To further present the combined role of lateral frictional and bottom frictional dissipation, we compared our model with the model of Wajsowicz for two islands, where only the lateral or bottom friction were considered, with different channel widths. The results showed that the effect of the lateral friction is greater than the bottom friction when the channel is narrow, especially in the Munk boundary layer thickness. When the channel is much wider than the Munk boundary layer thickness, the role of the bottom friction is greater than that of the lateral friction. The model was applied to the Indonesian throughflow and yielded a reduction of approximately 20% in the transport.

Eddy Subduction and the Vertical Transport Streamfunction

Abstract Subduction—the transport of fluid across the base of mixed layer—exchanges water masses and tracers between the ocean surface and interior. Eddies can affect subduction in a variety of ways. First, eddies shoal the mixed layer by restratifying water columns through baroclinic instabilities. Second, eddies induce an isopycnic transport that leads to the entrainment of warm waters and subduction of cold waters, which effectively counters the wind-driven overturning circulation. In this study, the authors use an idealized model to examine these two mechanisms by which eddies influence subduction and to discuss how eddy subduction may be better approximated using the concept of vertical transport streamfunction than the conventional meridional transport streamfunction.

Subtropical Mode Water Variability in a Climatologically Forced Model in the Northwestern Pacific Ocean

Abstract A climatologically forced high-resolution model is used to examine variability of subtropical mode water (STMW) in the northwestern Pacific Ocean. Despite the use of annually repeating atmospheric forcing, significant interannual to decadal variability is evident in the volume, temperature, and age of STMW formed in the region. This long time-scale variability is intrinsic to the ocean. The formation and characteristics of STMW are comparable to those observed in nature. STMW is found to be cooler, denser, and shallower in the east than in the west, but time variations in these properties are generally correlated across the full water mass. Formation is found to occur south of the Kuroshio Extension, and after formation STMW is advected westward, as shown by the transport streamfunction. The ideal age and chlorofluorocarbon tracers are used to analyze the life cycle of STMW. Over the full model run, the average age of STMW is found to be 4.1 yr, but there is strong geographical variation in this, from an average age of 3.0 yr in the east to 4.9 yr in the west. This is further evidence that STMW is formed in the east and travels to the west. This is qualitatively confirmed through simulated dye experiments known as transit-time distributions. Changes in STMW formation are correlated with a large meander in the path of the Kuroshio south of Japan. In the model, the large meander inhibits STMW formation just south of Japan, but the export of water with low potential vorticity leads to formation of STMW in the east and an overall increase in volume. This is correlated with an increase in the outcrop area of STMW. Mixed layer depth, on the other hand, is found to be uncorrelated with the volume of STMW.

Effects of Mesoscale Eddies on Subduction and Distribution of Subtropical Mode Water in an Eddy-Resolving OGCM of the Western North Pacific

Abstract The effects of mesoscale eddies on the subduction and distribution of the North Pacific Subtropical Mode Water (STMW) are investigated using an eddy-resolving ocean general circulation model (OGCM). First, the subduction rate is calculated and the contribution of eddies to the subduction of STMW is estimated. It is found that eddy subduction significantly contributes to the total subduction of STMW. Second, eddy thickness transport and diapycnal flux are directly diagnosed to investigate the large-scale eddy-induced transport process of STMW. The large southward eddy thickness transport in the STMW core density is consistent with eddy subduction. The eddy transport on the isopycnal surface of STMW is directed down the thickness gradient and traverses the mean flow. The meridional eddy transport streamfunction indicates two eddy circulation cells south of 30°N, associated with the circulation of STMW. These cells flatten density surfaces, similar to the effect of the Gent and McWilliams (GM) scheme. The subducted STMW is gradually dissipated to lower or higher densities in the main thermocline, basically by vertical diffusion. Finally, local processes of eddy subduction and transport of STMW are explored using an anticyclonic eddy. Results imply two possible local processes of the eddy subduction of STMW. One is the destruction of a potential vorticity (PV) gradient by eddy mixing, where the PV gradient is due to winter deep mixed layer formation. The other is the southward translation of anticyclonic eddies that accompany low PV.

A boundary-value problem for the parameterized mesoscale eddy transport

We present a physically and numerically motivated boundary-value problem for each vertical ocean column, whose solution yields a parameterized mesoscale eddy-induced transport streamfunction. The new streamfunction is a nonlocal function of the properties of the fluid column. It is constructed to have a low baroclinic mode vertical structure and to smoothly transition through regions of weak stratification such as boundary layers or mode waters. It requires no matching conditions or regularization in unstratified regions; it satisfies boundary conditions of zero transport at the ocean surface and bottom; and it provides a sink of available potential energy for each vertical seawater column, but not necessarily at each location within the column. Numerical implementation of the methodology requires the solution of a one-dimensional tridiagonal problem for each vertical column. To illustrate the approach, we present an analytical example based on the nonlinear Eady problem and two numerical simulations.

Modelling the circulation and exchange of Kingston Basin and Lake Ontario with FVCOM

An unstructured grid, finite-volume, 3-dimensional primitive equation, sigma-coordinate terrain following ocean model (FVCOM) has been applied to Lake Ontario to investigate its monthly climatological circulation with a focus on Kingston Basin. Kingston Basin, in the northeastern end of Lake Ontario, sits between the main body of the lake and the outflowing St. Lawrence River and is adjacent to the Bay of Quinte Area of Concern designated by the International Joint Commission. The focus of this study is to use the unstructured model FVCOM to model the mean circulation in the Basin. Results showed that the FVCOM model can take up to 3 years to spin-up from rest for a wind-forced, almost fully enclosed lake model. The model accurately reproduced the current flow field within the main body of the lake and compared favourably to the flow field observed during the International Field Year for the Great Lakes (IFYGL) in Kingston Basin. Transport streamfunction results show that the structure of the flow into Kingston Basin from the main body of the lake changes throughout the year.

The effect of Antarctic Circumpolar Current transport on the frontal variability in Drake Passage

The Antarctic Circumpolar Current (ACC) is composed of three major fronts: the Sub-Antarctic Front (SAF), the Polar Front (PF), the Southern ACC Front (SACCF). The locations of these fronts are variable. The PF can shift away from its historical (mean) location by as much as 100 km. The transport of the ACC in Drake Passage varies from its mean (134 Sv) by as much as 60 Sv. A regional numerical circulation model is used to study frontal variability in Drake Passage as affected by a range of volume transports (from 95 Sv to 155 Sv with an interval of 10 Sv). Large transport shifts the fronts northward while the smaller transport causes a southward shift. The mean shifting distance of the PF from the historical mean location is minimum with 135 Sv transport. The SAF and the SACCF are confined by northern and southern walls, respectively, while the PF is loosely controlled by the topography. Due to impact of the eddies and meanders on the PF at several regions in Drake Passage, the PF may move northward to join the SAF or move southward to combine with the SACCF, especially in central Scotia Sea. The SAF and PF are more stable with higher transport. The SAF behaves as a narrow, strong frontal jet with large transport while displaying meanders with smaller transport. In the model simulations, the Ertel Potential Vorticity (EPV) is strongly correlated with the volume transport stream function. EPV at depths between 1000 and 2500 m is correlated with the transport stream function with a coefficient above 0.9. Near the bottom, the correlation is about 0.6 due to the disruptive influence of bottom topography. Within 750 m of the surface, the correlation is much reduced due to the effect of K-Profile Parameterization (KPP) mixing and eddy mixing.

Inverse solution for pentadal variability in the North Atlantic

[1] Seven pentads (1960–1964 to 1990–1994) of the North Atlantic climatology by Lozier et al. (1995) are analyzed with the help of an inverse finite-element ocean circulation model. The model solves for temperature and salinity fields that are close to observations and respect stationary dynamical balances, and produces estimates of the circulation. The first two EOF's of transport streamfunction variability (39% and 26% of the explained variance) are found to have a high correlation with the North Atlantic Oscillation (NAO) index averaged over pentads and lagged negatively by three years (first EOF) and between zero and one years (second EOF). The spatial pattern of the first EOF corresponds to an anticyclonic anomaly (in the positive NAO phase) located between 20 and 45°N with the largest variability between 30 and 45°N, and much weaker cyclonic anomalies in the subpolar gyre. The second EOF shows a sharp anticyclonic anomaly along the Gulf Stream and its extension and a wide cyclonic cell over most of subtropical gyre. The anomaly in the meridional overturning streamfunction is characterized by a single positive cell which poorly correlates with the NAO index.

Wind‐driven circulation for the eastern North Atlantic Subtropical Gyre from Argo data

A trans‐oceanic section at 24.5°N in the North Atlantic has been sampled at a decadal frequency. This work demonstrates that the wind‐driven component of the Meridional Overturning Circulation (MOC) may be monitored using autonomous profiling floats deployed in the eastern North Atlantic Subtropical Gyre. More than 500 CTD vertical profiles from the surface to 2000 m depth, spanning one year (from April 2002 to March 2003), are used to compute the geostrophic transport stream function at 24.5°N. The baroclinic transport obtained from the autonomous profiling floats is not statistically different than that from three hydrographic cruises carried out in 1957, 1981 and 1992. A good agreement is found between the geostrophic transport stream function and the transport derived from the wind field through the Sverdrup relation.

Isopycnal Averaging at Constant Height. Part I: The Formulation and a Case Study

Abstract Simple Eulerian averaging of velocities, density, and tracers at constant position is the most natural way of averaging. However, Eulerian averaging gives incorrect watermass distributions and properties as well as spurious diabatic circulations such as the Deacon cell. Instead of averaging at constant height, averaging along isopycnals removes such fictitious mixing and diabatic circulations. Such isopycnal averaging is normally performed at constant latitude, that is, averaging along isopynals as they heave up and down. As a result, height information is lost and the sea surface becomes much warmer (or lighter) than with simple Eulerian averaging. In fact, averaging can be performed along arbitrarily aligned surfaces. This study considers a particular case in which isopycnal averaging is performed at constant height. Thus, this new isopycnal averaging follows isopycnals as they meander horizontally at constant z. Height information is now retained at the cost of losing latitudinal information. The advantage of this averaging is that it avoids the problem of giving a surface that is too warm. Associated with this new isopycnal averaging, a “vertical” transport streamfunction in (ρ, z) space can be defined, in analogy to the conventional meridional overturning streamfunction in (y, ρ) space. Here in Part I, this constant-height isopycnal averaging is explained and illustrated in an idealized zonal channel model. In Part II the relationship between the two different isopycnal averagings and the Eulerian mean eddy flux divergence is explored.

Isopycnal Averaging at Constant Height. Part II: Relating to the Residual Streamfunction in Eulerian Space

Abstract In Part I, the “vertical” transport streamfunction was defined as resulting from isopycnic averaging at constant height in the same way that the meridional streamfunction results from averaging at constant latitude. Part II here discusses the relationship between these two isopycnic streamfunctions and the Eulerian residual streamfunction that arises from the transformed Eulerian mean (TEM). It is known that the meridional isopycnic streamfunction can be approximated by a Taylor expansion to give an Eulerian residual streamfunction involving the horizontal eddy flux. This Taylor expansion approximation works well in the interior, removing the spurious mixing associated with the simple Eulerian-averaged streamfunction. However, it fails near the surface where isopycnals outcrop to the surface. It can be shown in a similar way that the vertical isopycnic streamfunction can formally be approximated by a residual streamfunction involving the vertical eddy flux. However, if horizontal isopycnal displacements are large, this approximation fails even in the ocean interior. Inspired by the two different residual streamfunctions, a more general form of TEM formulation is explored. It is shown that the different TEM residual streamfunctions arise from decomposing the eddy flux into a component along isopycnals, which leads to advective flow, and a remaining diffusive component, which is oriented either vertically or horizontally. In theory the diffusive flux can be oriented in any direction, although in practice the orientation should be such that neither the advective flow nor the diffusive flux cross any boundary (surface, sidewalls, and bottom). However, it is not clear how to merge the continuously changing orientation in a physically meaningful way. A variety of approaches are discussed.

Upper ocean temperature and the baroclinic transport stream function relationship in Drake Passage

Repeat hydrographic sections across the Antarctic Circumpolar Current (ACC) in Drake Passage are used to derive an empirical relationship between upper ocean temperature and the baroclinic transport stream function. Cross validation shows this relationship can be used to infer baroclinic transport (above and relative to 2500 m) from expendable bathythermograph (XBT) temperature measurements with an error of a few per cent. Transport errors of less than 2 Sv are obtained if temperature at depths between 600 and 1600 m is used to define the relationship. Temperature at depths above 300 m provides an unreliable index of transport because of variability in temperature‐salinity (T‐S) properties produced by air‐sea interaction. The scatter in the relationship between temperature and stream function from repeat observations along a single line is similar in magnitude to the scatter observed when data from the broader Drake Passage area are considered. In both cases, variability about the mean temperature‐stream function relationship reflects advection of water with anomalous T‐S properties. The tight relationship between temperature and stream function in Drake Passage and south of Australia suggests baroclinic transports can be inferred from XBT temperatures with high accuracy in the Southern Ocean, providing a cost‐effective means of monitoring ACC variability. However, care must be taken at the end points, particularly in the Drake Passage where the strong flow of the Subantarctic Front sometimes lies over the continental slope.

Sea surface height and transport stream function of the South China Sea from a variable-grid global ocean circulation model

A fine-grid model (1/6°) covering the South China Sea (SCS), East China Sea and Japan/East Sea, which is embedded into a coarse-grid (3°) global model, was established to study the SCS circulation. In the present paper, we report the model-produced monthly and annual mean transport stream functions and sea surface heights(SSH) and their anomalies of the SCS. Comparison to the TOPEX/Poseidon data shows that the model-produced monthly sea surface height anomalies (SSHA) are in good agreement with altimeter measurements. Based on the results, the circulation of the SCS, especially the upper layer circulation, is discussed. In the surface layer, the western Philippine Sea water intrudes into the SCS through the Luzon Strait in autumn, winter and spring, but not in summer. However, as far as the whole water column is concerned, the water intrudes into the SCS through the Luzon Strait all the year round. This indicates that in summer the water still intrudes into the SCS in the subsurface and intermediate layers. The area near the northern continental slope of the SCS is dominated by a cyclonic circulation all the year round. The SCS Southern Anticyclonic Gyre, SE Vietnam Off-Shore Current in summertime and SCS Southern Cyclonic Gyre in wintertime are reproduced reasonably. The difference between the monthly averaged SSH and SSHA is significant, indicating the importance of the mean SSH in the SCS circulation.

Eddy mass transport for the Southern Ocean in an eddy-permitting global ocean model

The eddy-induced mass transport is diagnosed for the Southern Ocean in an eddy-permitting global ocean model (OCCAM). The focus is on the transport by transient eddies in the deep ocean. The transport streamfunction is calculated in four different combinations of coordinate system. Depending on the coordinate system employed, the strength of transient eddy transport varies from 6 Sv meridional transport in latitude-density coordinates to 20 Sv across-streamline transport in streamline-depth coordinates. It is shown that transient eddies as well as standing eddies are necessary for cancelling the Deacon cell. In the Antarctic bottom water density layer, the major contribution of the transient eddies towards net equatorward transport occurs (a) as a strong transport over the narrow Drake Passage and (b) as a weaker but systematic transport over a broader region in the southeast Pacific where the Antarctic circumpolar current breaks up into multiple jets. In contrast, in the North Atlantic deep water density layer the net poleward eddy transport is spread out almost everywhere. This suggests that attention to eddies should not be restricted to places where the eddy transport has large magnitude.

A 6 year record of baroclinic transport variability of the Antarctic Circumpolar Current at 140°E derived from expendable bathythermograph and altimeter measurements

Repeat hydrographic sections across the Antarctic Circumpolar Current are used to derive an empirical relationship between upper ocean temperature and the baroclinic transport stream function. Cross validation shows this relationship can be used to infer baroclinic transport (above and relative to 2500 dbar) from temperature measurements with an error of a few per cent. The mean transport distribution derived from 31 austral summer expendable bathythermograph (XBT) sections over a 6 year period consists of westward flow immediately south of Tasmania, a broad band of strong eastward flow between 50° and 55°S, and three cores of eastward flow south of 55°S. By defining a second empirical relationship between surface dynamic height and cumulative transport a continuous time series of baroclinic transport is derived from altimeter measurements of sea surface height. Transports derived from altimetry in this way agree well with simultaneous in situ estimates (root mean square error in net transport is 4 × 106 m3 s−1), suggesting sea level anomalies largely reflect baroclinic changes above 2500 dbar. The 10 day sampling of the altimeter transport time series shows the irregular XBT sampling aliases variability at unresolved timescales. The standard deviation of net transport above and relative to 2500 m is 4.3 × 106 m3 s−1. The variability in net transport is largest (2.7 × 106 m3 s−1) in the quasi‐annual band (periods of 4 months to 1.5 years), slightly smaller (2.3 × 106 m3 s−1) in the mesoscale band (<4 months), and smallest in the interannual band (>1.5 years, 1.5 × 106 m3 s−1). Changes in transport are correlated with local changes in both wind stress and wind stress curl in the quasi‐annual and interannual bands, but the transport time series is too short to draw significant conclusions.

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.

A Modified Sverdrup Model of the Atlantic and Caribbean Circulation

Abstract An analytical model of the mean wind-driven circulation of the North Atlantic and Caribbean Sea is constructed based on linear dynamics and assumed existence of a level of no motion above all topography. The circulation around each island is calculated using the island rule, which is extended to describe an arbitrary length chain of overlapping islands. Frictional effects in the intervening straits are included by assuming a linear dependence on strait transport. Asymptotic expansions in the limit of strong and weak friction show that the transport streamfunction on an island boundary is dependent on wind stress over latitudes spanning the whole length of the island chain and spanning just immediately adjacent islands, respectively. The powerfulness of the method in enabling the wind stress bands, which determine a particular strait transport, to be readily identified, is demonstrated by a brief explanation of transport similarities and differences in earlier numerical models forced by various cl...

Absolute geostrophic velocity within the Subantarctic Front in the Pacific Ocean

Velocity measurements from a shipboard acoustic Doppler current profiler (ADCP) are used as a reference for geostrophic current calculations on six sections across the Subantarctic Front (SAF) in the Pacific Ocean. The resulting cross‐track velocity estimates near the bottom range from 4 to 10 cm s−1 to the east in the eastward jet at the SAF; in adjacent regions of westward surface flow, the near‐bottom velocity is usually to the west. On one section where simultaneous lowered ADCP velocity profiles are available, they confirm the results from the shipboard ADCP. Annual mean velocity sections from the Parallel Ocean Program numerical model also show near‐bottom velocities exceeding 5 cm s−1, with the same tendency for the zonal velocity component near the bottom to match the direction of the surface jets. Transport across the entire Antarctic Circumpolar Current (ACC) cannot be estimated accurately from ADCP‐referenced geostrophic sections because even a very small cross‐track bias integrates to a large error. A preliminary look at the 1992 model transport stream function shows that the effect of bottom‐referencing varies from section to section; it can cause 40‐Sv recirculations to be missed, and can cause net transport to be underestimated or overestimated by O (30 Sv).