In April 2010, full-depth hydrographic and direct velocity measurements across a solitary meander in the Agulhas Current were collected at nominally 34∘S. During a second cruise in November 2011, a transect across the nonmeandering Agulhas Current was captured. These data provide the first full-depth, in situ picture of the meandering Agulhas Current and allow us to investigate how the velocity structure and transport of the meandering current differs from its nonmeandering state. An analysis of the horizontal momentum equations show that the meander is in geostrophic balance. However, sampling bias causes large differences between geostrophic and direct velocity measurements during meandering, especially near the surface. As the current meanders offshore, its core speed weakens by more than 70 cm s−1 and its width broadens by almost 40 km. These two effects compensate so that the southwestward transport of the Agulhas current is largely unchanged during meandering. At the same time, the meander generates a strong inshore counterflow, which weakens the net Eulerian transport across the 300-km line by almost 20 Sv.
The Agulhas Current (AC) is the strongest western boundary current (WBC) in the Southern Hemisphere with an average transport of 70 Sv (1 Sv = 106 m3 s−1) at 32°S [Bryden et al., 2005]. North of approximately 34°S, the AC is relatively stable while attached to the South African continental slope. Once detached, the southern AC is characterized by frequent eddies, plumes, and meanders [Lutjeharms and Connell, 1989]. Solitary meanders (so-called Natal pulses) have been seen to form in the north and propagate the length of the current, connecting these two regions.
Solitary meanders are more than dynamical curiosities; they have broader implications both regionally and climatically. Meanders affect shelf circulation [Gründlingh, 1992; Lutjeharms et al., 1989], alter coastal rainfall patterns [Lutjeharms and De Ruijter, 1996; Jury et al., 1993], and significantly correlate with Agulhas ring shedding events [van Leeuwen et al., 2000]. Agulhas rings transport water between the Indian and Atlantic oceans, carrying most of the so-called Agulhas leakage. This leakage of warm salty water forms the warm-water route of the thermohaline circulation as described by Gordon . Several studies confirm the relationship between meanders and Agulhas rings [Schouten et al., 2002; Lutjeharms et al., 2003; Pichevin et al., 1999; Penven et al., 2006], suggesting that meanders are an important part of the climate system.
Solitary meanders manifest themselves as a paired inshore cyclone with an offshore anticyclone. The inshore cyclone is used to determine the meander's speed and size. These inshore cyclonic eddies typically have diameters between 30 and 200 km and propagate downstream within the current at 10–20 km day−1 [de Ruijter et al., 1999]. Satellite observations show that meanders induce an inshore northeastward counter-current at the surface [Lutjeharms et al., 2001]. Models show that this counter-current connects with the Agulhas Undercurrent (AUC) at depth [Biastoch et al., 2009]. The question of how meanders affect the full-depth velocity structure and transport of the current remains unknown. Model studies show that meanders increase AC transport [Biastoch et al., 2009], while a transport time series at 32∘S showed AC transports reducing by 15–25 Sv during a meander [Bryden et al., 2005]. Here, we present high-resolution, full-depth, in situ observations of a solitary meander within the AC. These are compared with observations of the nonmeandering AC at the same latitude. We aim to understand how the velocity structure and transport of the meandering current differs from its nonmeandering state.
2 Data and Methodology
Observations were collected across the AC at nominally 34°S (Figure 1, left). This paper presents data from four separate occupations of this line: two across the meandering AC in April 2010, and two across the nonmeandering AC in November 2011. Data were collected using a CTD (Conductivity, Temperature, Depth), and lowered acoustic Doppler current profilers (LADCP). The LADCP configuration consisted of dual 300 kHz instruments during the April 2010 cruise, and a hybrid configuration, with 300 kHz upward-looking, and 150 kHz downward-looking instruments during the November 2011 cruise. The CTD system included a 12 bottle rosette, and a Sea-Bird SBE9–11 with an altimeter and dual temperature, conductivity, and oxygen sensors.
The first CTD-LADCP line across the solitary meander was spread out over 9 days of mooring operations from 7 to 15 April 2010, and the second was sampled continuously over 3 days from 17 to 19 April 2010. We will concentrate on the second more synoptic line which we refer to as the meander line. Two further occupations of the same line were conducted in November 2011, the first collected over 10 days from 10 to 19 November 2011 during mooring operations and the second over 4 days from 20 to 23 November 2011. Again we concentrate here on the more synoptic dataset, which will be referred to as the nonmeander line. Each line of hydrographic data consists of 20 stations, with station spacing a minimum 6 km over the shelf and up to 24 km over deep water. Cast depths range from 50 m inshore to greater than 4500 m offshore (Figure 1, right). April 2010 data were sampled inshore to offshore, while November 2011 data were sampled offshore to inshore. Station locations for the meander and nonmeander lines are labeled in the right plot of Figure 1: stations 21–40 for the meander line, and stations 31–50 for the nonmeander line.
We use complementary satellite data to describe the surface characteristics of the solitary meander: sea surface temperature (SST) data from the group for high-resolution SST (GHRSST), and mapped absolute dynamic topography (MADT) data from Archiving, Validation, and Interpretation of Satellite Oceanographic Data (AVISO). The GHRSST product is a daily, 1.5 km resolution, gridded SST. The AVISO product is a daily, 1/3° resolution MADT. MADT is calculated as sea level anomaly plus a mean sea surface derived from altimetry, in situ measurements, and GRACE data [Rio et al., 2011].
3.1 Meander Surface Characteristics
Rapidly changing SST and MADT fields coincident with our hydrographic occupations in April 2010 emphasize the dramatic effect of the passing meander (Figures 2a and 2b). Using the MADT data, we estimate that the inshore cyclonic anomaly that marks the solitary meander averages 100 km in diameter and propagates across the hydrographic line at 15 km day−1. These estimates were acquired by using the 50 cm MADT contour to define the inshore cyclonic anomaly. We determined the diameter of the meander by approximating a circle using this contour. The meander's propagation speed was determined by evaluating the period of time needed for this closed contour to propagate across our observation line. These values result in a propagation timescale of less than 7 days and are typical of previously reported Agulhas solitary meanders (so-called Natal Pulses) [Lutjeharms and Roberts, 1988; de Ruijter et al., 1999]. The 7-day propagation timescale is comparable to the duration of occupation, which is 9 days for the first occupation and 3 days for our meander line.
The top plots of Figure 2 trace the development of the sea surface during the sampling of our asynoptic meander line. On April 7, the AC adjoins the continental slope, as evidenced by the large inshore velocity vectors, strong inshore MADT gradient, and warm inshore SST. There is also a clear region of diffluence along the observation line, concurrent with the passage of the solitary meander's trough. By April 11, the current core has moved to approximately 130 km offshore, creating an aliased double-core in the asynoptic in situ velocity vectors. The inshore cyclonic eddy's leading edge abuts the hydrographic line, and a filament of warm water stretches into its center. By the end of the asynoptic meander line's collection, the crest of the solitary meander is only slightly upstream of our line. The maximum MADT gradient that marks the location of the AC weakens slightly as the inshore cyclonic eddy becomes more distinct.
The sea surface characteristics during meander line collection are shown in the middle plots (Figure 2b). Since the meander line was collected in just 3 days, it is more synoptic, but some changes are evident. The inshore cyclonic eddy propagates from slightly upstream to downstream of the line between April 17 and April 20. The warm SSTs that mark the AC's core are noticeably cooler on April 20. The AC has narrowed, as compared to the top plots of Figure 2, consistent with confluence accompanying the passage of the solitary meander's crest.
For comparison, the sea surface characteristics during the nonmeander line are shown in Figure 2c. Here, the AC is found directly against the slope in a narrow band whose path does not change over the course of the 3 day occupation. In conclusion, the nonmeander line is highly synoptic, while data collection during the two meander lines was on timescales comparable to that of the propagating meander.
3.2 Sampling Bias
It is clear from the rapid evolution of the meander during the in situ occupations that sampling bias could be a serious issue in this data set. To investigate this, we compared LADCP and geostrophic shear profiles from the meander line and found some large differences (Figure 3, top). These differences are greatest near the core of the meandering current: a difference as large as 150 cm s−1 is found 160 km offshore above 1000 m depth along the AC's offshore edge. In contrast, the bottom plot of Figure 3 shows that LADCP and geostrophic shears match well in the nonmeandering current. Here the AC is in geostrophic balance, except at the surface where wind-driven Ekman velocities become important [Beal and Bryden, 1999]. In this section, we look carefully at the attribution of the geostrophic departures in the meander line, which could be due in whole or part to sampling bias, ageostrophic acceleration of the flow around the meander, or measurement error. We first consider the amplitude of measurement error.
Random measurement errors are a product of LADCP inverse processing [Visbeck, 2002]. In the meander line, these formal errors average ±11 cm s−1 throughout the domain. Large as they are, these errors cannot account for the geostrophic departures seen in Figure 3. For the nonmeander line, measurement errors average ±7 cm s−1 throughout the domain. Since errors within each line are comparable, they cannot explain the differences in geostrophic departures between the meander and nonmeander lines. Moreover, Thurnherr  show that true LADCP velocity errors are significantly smaller than these formal estimates. The strong agreement between geostrophic and LADCP velocity shear profiles in the nonmeander line support this (Figure 3, bottom), and suggest that errors are likely small and random. Next, we consider ageostrophic flow as a possible explanation for the geostrophic departures in the meander line.
Gradient wind balance is considered the dominant balance for a flow that is accelerated around a radius of curvature such as the velocities in our meander line. This balance is given by:
where v is the gradient velocity (taken as LADCP), R is the radius of curvature, f is the Coriolis force, and vg is the geostrophic velocity. For the meander line, the gradient wind balance yields maximum ageostrophic velocities of order 15 cm s−1. This value is a full order of magnitude too small to explain the differences seen in Figure 3. Next, we perform a full momentum balance analysis to further investigate ageostrophic flow as an explanation for the observed geostrophic departures.
In a rotated coordinate system, with x the along stream or cross-track direction (rotated 64∘, positive to the northeast) and y the cross-stream or along-track direction (positive inshore, to the northwest), the horizontal momentum equations are given by:
where f is the Coriolis term, P is pressure, u and v are the downstream and cross-stream velocities, z is the local vertical, and w is the vertical velocity. Eddy stresses are neglected. These terms, excepting the absolute pressure gradient, can be calculated using our direct LADCP velocities and some scaling arguments. We assume a quasigeostrophic approximation, so that the terms involving vertical velocity can be neglected compared to the horizontal velocity in both equations (2) and (3). Since we are unable to measure it, we also assume that the downstream change in velocity is small and neglect in equation (2) and in equation (3). This is justified since we assume the downstream gradients are much smaller than the cross-stream gradients. We are left with the following equations for the along-stream and cross-stream horizontal momentum balance where every term on the left hand side is directly measurable from our data:
The local time derivative is calculated from the difference in u and v between each of the two occupations in April 2010 and November 2011 and dividing them by the time between occupations in a manner similar to Joyce et al. . Since we expect the largest geostrophic deviations to be close to the surface, Figure 4 shows all terms averaged only over the top 150 m of the water column from the left hand side of equations (4) (left plots) and (5) (right plots). For the meander line (Figure 4, top plots), the Coriolis term dominates everywhere in both the across- and along-stream momentum balances. The Coriolis term is 4 times larger than the inertial terms for the along stream, and 15 times larger for the cross-stream balances. For the nonmeander line, the domination of the Coriolis term is similar except in the along-stream momentum budget within 50 km of the coast, which is dominated by the nonlinear terms. This is on the inshore, cyclonic side of the current where the cross-stream shears are very large over the continental slope. Therefore, our momentum analysis suggests that the meander line is in geostrophic balance, since the unmeasured pressure gradient term likely balances the dominant Coriolis term in this case. Surprisingly, it is the nonmeandering AC which shows a small departure from geostrophic balance, but only in the along-stream momentum budget, where acceleration is significant over the continental slope. Looking back at Figure 3, the large differences between direct (LADCP) and geostrophic velocities (cross-stream momentum balance) during the meander event are clearly not explained by geostrophic departures in the momentum balance of the flow. Most notably, there are no significant accelerations in the case of the meander, despite the curvature and rapid evolution of flow.
We now consider sampling bias as a possible explanation for the geostrophic departures in the meander line. As an integrated value, geostrophic velocities are particularly sensitive to the movement of sloping isopycnals during meandering. Depending on the length of occupation, this can lead to large sampling biases. Johns et al.  quantify the fractional error in geostrophic velocities across a meandering current as the ratio between the current's lateral velocity and the ship's cross-sectional velocity offshore. Hence, we calculate the fractional error of the geostrophic velocity as:
where is the difference between our geostrophic and LADCP velocities, Vc is the current's lateral velocity as the meander advects across the line, and Vs is the ship's velocity along the sampling line. During meander passage, the AC's lateral velocity varies between about 16 and 26 km day−1, as estimated from the movement of the warmest SST contour along the observation line in the daily GHRSST data. The ship's average velocity along the line varies between 39 and 76 km day−1, largely dependent on CTD sampling depth. Hence, the resulting fractional error due to sampling bias is between 21% and 67% of the geostrophic velocity. In the core of the meandering Agulhas current, velocities reach over 150 cm s−1, implying a sampling bias up to 100 cm s−1. This bias is large enough to explain the discrepancy we see in our geostrophic velocities from the meander line. The lateral motion of the current along our line during the meander event is comparable to the speed at which we can occupy the line and this distorts the horizontal density gradients from which geostrophic velocity is calculated.
3.3 Velocity Structure
We have shown that our geostrophic velocities are biased by the fast evolution of the flow during the meander line occupation. However, we can use direct velocities from LADCP to examine the velocity structure of the solitary meander. Comparing cross-track direct velocities from the meandering AC and the more common nonmeandering case, shown in Figures 5a and 5b, reveals that the Agulhas current weakens and broadens as it meanders offshore.
During meandering, the AC core moves 89 km offshore from the 600 m isobath to the 4200 m isobath (Figures 5a and 5b). This offshore shift significantly alters the circulation along the slope. During the meander, an inshore, strongly barotropic countercurrent develops at the typical location of the nonmeandering AC's core. The along-track area of this northeastward countercurrent is two orders of magnitude larger than the northeastward flow during the nonmeandering line ( versus 0.3 km3), which is restricted to below 1000 m as the Agulhas Undercurrent. The development of an inshore countercurrent during solitary meander passage is well-established from the literature [Lutjeharms and Connell, 1989; Bryden et al., 2005]. Here, we find that this anomaly reaches throughout the full depth of the water column, and occupies the space of the nonmeandering AC core.
The development of an inshore countercurrent is reflected in the location and direction of isopycnal slopes. We use neutral density surfaces as defined by Jackett and McDougall  and overlain in yellow on Figure 5 to illustrate these changes. The maximum neutral density gradient is found at 30 km when the Agulhas Current is attached to the slope, while it is found 120 km offshore when it is detached. Approaching the slope, the neutral density surface dips sharply downward for the meander line indicating northeastward flow. In contrast, the neutral density surface in the nonmeander line dips gradually upward at the slope, indicative of the southwestward-flowing AC. The overlain neutral density contours also show a dramatic thinning of neutral density layers during meandering. This is especially apparent over the shelf, and along the slope between and . This thinning of neutral density layers during the meander has large implications for the overall potential vorticity structure, as described in the next section.
Meandering of the AC is accompanied by a broadening and weakening of its core. Cross-track velocities weaken by 72 cm s−1 from −208 to −136 cm s−1, and the current's width, defined by the outcropping of the −50 cm s−1 cross-track isotach, increases by 37 km, from 88 to 125 km. We note that the meandering flow is also weaker in the local direction of flow, but we can approximate that its width may be similar. The maximum speed is 191 cm s−1 at a heading of 200 degrees T (45 degrees to the east of cross-track) for the meander and is 213 cm s−1 at a heading of 225 degrees T (15 degrees east of cross-track) for the nonmeander line. Using these angles, we can approximate the width of the current (defined by the 50 cm s−1 cross-track isotachs) in the local direction of flow in each case as 88 km in the meander and 85 km in the nonmeander line.
To quantify changes in the structure of the current, we calculate its relative vorticity, defined as the cross-stream gradient of the down-stream velocity ( ) measured at the surface. Note that given the angle of the meander flow to the ACT line, the relative vorticity could be as much as double this in the true local direction of flow. We find that the relative vorticity structure of the AC changes significantly during a meander. The amplitude of the inshore relative vorticity of the nonmeandering current is more than three times greater than its offshore side: versus , while for the meandering current relative vorticity on either side of its front is more comparable, versus . In the next section, we explore the vorticity structure of the meandering current in more detail by calculating the full Ertel's potential vorticity [Pedlosky, 1986].
3.4 Vorticity Structure
To further explore the structure of the current, we calculate the full Ertel's potential vorticity. We find that differences in planetary vorticity dominate the total difference in cross-sectional potential vorticity structure between the meandering and nonmeandering currents. Hence, the largest changes in total potential vorticity are due to variations in isopycnal layer thickness.
To calculate the full Ertel's potential vorticity (Q) equation [Pedlosky, 1986], we follow Beal and Bryden  and rewrite Q such that all terms can be calculated using our CTD-LADCP data:
where the total potential vorticity (Q) is shown as the sum of the planetary vorticity (Qp), relative vorticity from horizontal shear (Qhs), and relative vorticity from vertical shear (Qvs). Note that again we neglect the downstream gradient when calculating the Qhs term since our dataset limits us to cross-stream gradients only. Since the local direction of flow for the meander line is 45 degrees east of the cross-track direction, the unmeasured downstream gradient term could potentially double the calculated relative vorticity term. We find, however, that the relative vorticity term is small when considering the total potential vorticity such that this difference does not change our main results. The top plots of Figure 6 show the total Q, as well as the components Qp, and Qhs. We exclude the Qvs term because it is an order of magnitude smaller than the other two components. The reader interested in the full Q structure of the nonmeandering current is directed to Beal and Bryden .
The Qp of the meander line looks remarkably similar to the total Q, because it makes up the bulk of the signal (Figure 6b). The meander Q signal saturates at the surface due to high stratification (Figure 6a). Q is largely homogeneous along isopycnal layers that do not outcrop, except between and where the magnitude of Q decreases offshore of the current core. Qhs contributes significantly to Q above 250 m, where it alternates in the offshore direction from positive to negative and back to positive. The velocity contours reveal that the changes in sign of Qhs correspond to the core of the northeastward-flowing countercurrent above the shelf break approximately 40 km offshore, and to the core of the meandering AC found approximately 130 km offshore. The Q, Qp, and Qhs of the nonmeandering current have a similar structure, but are shifted inshore [e.g., Beal and Bryden, 1999].
The bottom plots of Figure 6 show the differences, meander minus nonmeander, in Q, Qp, and Qhs. Changes in Qhs can be attributed to the input of cyclonic relative vorticity inshore of the meandering current. These changes are comparable in size to changes in Qp only over the top 150 m of the water column. The total change in Q is dominated by isopycnal layer thickness changes. The largest fractional differences in Q are positive and found along the continental slope. These positive changes are indicative of uplifting and thinning of isopycnal layers during the meander, associated with the cyclone inshore of the meandering current. A less significant positive difference 250 km offshore at 650 m depth can be attributed to a homogeneous region of low amplitude Qp (Figures 6a and 6b) between and in the meander. This is Subantarctic Mode Water (SAMW) as described by Hanawa and Talley . This SAMW signature is absent in the nonmeander case. Since the meander line was collected in April and the nonmeander line in November, this difference could be due to seasonality of SAMW in the region. In summary, below outcropping density layers which may be dominated by seasonal differences, the bulk of the difference in Q is due to thinning isopycnal layers over the continental slope during the meander. This is the result of enhanced cyclonic vorticity inshore of the current during a meander.
3.5 Volume Transport
A previous study based on 1 year of mooring data at 32∘S showed that the transport of the Agulhas Current decreases up to 25 Sv during meander events [Bryden et al., 2005]. However, the limited length of their mooring array means that transport may have been missed during offshore excursion of the current. Here, we are able to calculate the transport of the Agulhas Current using a line of stations that fully capture the displaced current. Volume transports are calculated as across-track LADCP velocities multiplied by the cross-sectional area between each station, ignoring bottom triangles. A new method for determining transport error estimates was derived by randomly setting a posteriori velocity errors from the LADCP linear inverse method from Visbeck  to be positive or negative. Once the errors were randomly set to be positive or negative, the total error was summed. This process was repeated until the average total error stabilized (approximately 1000 times). Total errors in transport for the AC, AUC, and interior were summed separately. We assume each region is independent, so that the total transport error across the line was calculated as the square root of the sum of the squares of the errors for each region.
The results of our transport calculations are shown in Figure 7. The AC transport, defined as the total southwestward transport, is 120 ± 1.1 Sv for the meander and 125 ± 0.5 Sv for the nonmeander lines. These transport values are larger than the 70 Sv mean calculated by Bryden et al.  at 32∘S, which is consistent with the known increase in transport downstream due to entrainment [Casal et al., 2009]. The 5 Sv difference between our transport measurements is less than 20% of the standard deviation of the transport at 32∘S [Bryden et al., 2005]. Note that transport accumulates out to 250 km for both the meander and nonmeander lines, confirming that the WBC transport is fully captured within our 300 km hydrographic line. The northeastward transport across the line increases more than threefold during meandering. This difference in northeastward transport, rather than a change in the transport of the AC, is responsible for a 20 Sv net Eulerian transport difference between the two lines.
The right plot of Figure 7 reveals that the transport per unit depth for each line is markedly similar. Hence, our results show that solitary meanders represent a lateral shift of the AC, with little change in the depth structure and transport of the current.
The transport of the meandering Agulhas current is conserved due to the compensating effects of the broadening and weakening of its core. The Eulerian transport, however, decreases substantially due to the development of an inshore countercurrent. This inshore countercurrent represents a barotropic change to the AC since the transport per unit depth is unchanged.
As the Agulhas current meanders, its velocity structure loses the asymmetry that is characteristic of its nonmeandering state. When the AC is against the continental slope, the relative vorticity of its inshore side is much greater than its offshore side. During the meander, these values are more comparable. Differences in the potential vorticity fields of the meandering and nonmeandering current are dominated by thinning isopycnal layers over the continental slope owing to the development of cyclonic vorticity inshore of the current during a meander.
There are significant differences between the geostrophic and LADCP profiles of the meandering current. However, careful analysis of the horizontal momentum equations confirms the meander is in geostrophic balance and that these differences are caused by sampling bias owing to the rapid evolution of the solitary meander compared to the occupation time. Therefore, LADCP measurements are essential to capture the structure of the meandering current.
The authors would like to thank the officers and crew of RV Knorr and RV Melville, as well as the mooring technician group at Rosenstiel School. This study was supported by NSF grant OCE0850891. The altimeter products were produced by SSALTO/Duacs and distributed by Aviso, with support from CNES (http://www.aviso.oceanobs.com/duacs/) CTD data used in this analysis is available through the CLIVAR and Carbon Hydrographic Data Office (http://cchdo.ucsd.edu), or by request to Lisa Beal (email@example.com).