## 1. Introduction

The Agulhas Current (AC), the western boundary current of the south Indian subtropical gyre, flows along the coast of South Africa from approximately 27° to 34°S (e.g., Lutjeharms 2006). Along its length, it sporadically undergoes dramatic offshore excursions or solitary meanders, the so-called Natal pulses (Lutjeharms and Roberts 1988), which propagate downstream. Typically, solitary meanders are diagnosed by in situ or remote data as a cyclonic circulation inshore of the core of the current, which cools water at the coast by upwelling (Lutjeharms and Roberts 1988; Bryden et al. 2005; Leber and Beal 2014). Thus, propagating meanders affect waters along the entire South African east coast, possibly influencing the ecosystem of the region (e.g., Jackson et al. 2012). They may also play an important role in linking upstream anomalies from the Mozambique Channel (MC) and East Madagascar Current (EMC) to the Agulhas retroflection region (Schouten et al. 2002; Biastoch et al. 2008b,a). Meanders have been traced to the retroflection, where they appear to destabilize the flow and cause the shedding of Agulhas rings (van Leeuwen et al. 2000; Dijkstra and de Ruijter 2001).

Solitary meanders of the Agulhas Current are thought to be its dominant mode of variance, although this has not been formally shown. Previous observations, from the Agulhas Current Experiment (ACE) array at 32°S, show that meander events perturb the flow field of the Agulhas Current in a consistent pattern for a duration of 7 to 10 days (Bryden et al. 2005). The Agulhas Current moves offshore and a barotropic, northeastward flow and strong upwelling develop over the slope and shelf. At the peak of a meander, strong cyclonic flow is present over the entire mooring array, with low sea surface height inshore of the displaced jet. There appears to be no significant change in Agulhas Current transport during a meander because weakening of the jet is accompanied by a broadening (Leber and Beal 2014). This modification of the jet during a meander is consistent with linear theory for barotropic instability (van der Vaart and de Ruijter 2001). Van der Vaart and de Ruijter (2001) found that during the growth of a meander, Reynolds stresses generate a momentum flux that decelerates the inshore side of the jet and accelerates the offshore side, such that the jet becomes slower and broader. This process ultimately stabilizes the jet because cross-stream shear is reduced, limiting the growth of the meander. Experiments in a numerical model also point to the importance of barotropic instability for the growth of meanders (Tsugawa and Hasumi 2010), which are found to be initiated by the interaction of eddies with the offshore edge of the Agulhas jet. The role of barotropic instability has yet to be substantiated with observations.

The frequency and along-stream persistence of propagating solitary meanders and their significance as a link between upstream anomalies and Agulhas ring–shedding events remains unclear. Observations close to 32°S have suggested 3–6 meanders per year, similar to the number of Agulhas rings, supporting a dynamical link (de Ruijter et al. 1999; Lutjeharms 2006). At the ACE array, five meanders were observed within 1 yr (Bryden et al. 2005). Meanders appear to originate where offshore anomalies impinge on the western boundary (de Ruijter et al. 1999; Schouten et al. 2002; Tsugawa and Hasumi 2010), and these anomalies can be traced to both the Mozambique Channel and the southern tip of Madagascar (Schouten et al. 2002; de Ruijter et al. 2005). Anomalies have been linked farther upstream to westward-propagating Rossby waves at latitudes 12° and 27°S (Schouten et al. 2002). Individual meander events have been traced all the way downstream from near the Natal Bight to the retroflection (van Leeuwen et al. 2000; Lutjeharms 2006). Schouten et al. (2002) used 6 yr of satellite sea surface height data to find that 4–5 anomalies per year interact with the northern Agulhas Current, propagate downstream (noted by anticyclonic anomalies at the offshore edge of the current), and link with 4–5 Agulhas rings per year.

More recent studies have questioned this link. In the first numerical model to simulate Agulhas meanders, Biastoch et al. (2008b) found there were fewer meanders per year on average (2–5) than Mozambique eddies (5–6) and postulated that anomalies were a necessary but not sufficient condition for the generation of meanders. Farther downstream at 34°S, Rouault and Penven (2011) used satellite data to find only 1.6 meanders per year on average and suggested that the difference in number observed at 32° versus 34°S may result from dissipation or merging of meander events on their passage downstream. They noted that satellite studies of meanders, particularly farther north, are subject to uncertainty because of the proximity of the current to the coast, to cloudiness, and to dependency on temporal filtering and arbitrary thresholds. Ground truthing with in situ data could improve their estimates. Breaking the link between upstream anomalies and Agulhas rings altogether, Weijer et al. (2013) suggested that the phase of Agulhas ring shedding is set by a Rossby basin mode, which is amplified in the retroflection region by barotropic instabilities of the shear zone between the Agulhas Current and Agulhas Return Current. The basin mode has a frequency of 6.6 yr^{−1}.

In this study, we are able to gain new insight on Agulhas meander events using a new 34-month time series of the cross-sectional velocity structure of the Agulhas Current (Beal et al. 2015), together with 20 yr of altimeter data. We characterize meander events locally, in terms of rectilinear and rotating modes of current variance, to find two different meander types: small, stable perturbations of the Agulhas Current and larger, mesoscale perturbations that grow through the extraction of energy from the mean flow, consistent with barotropic instability. Expanding our analysis in time, using in situ observations of meanders at 32° and 34°S to ground truth altimeter signals, we take another look at the downstream propagation of anomalies and their origins upstream. We find that while all meanders at 34°S are linked to westward-propagating anomalies upstream, only a fraction of incoming anomalies instigate a meander, and of these, about two-thirds of meanders propagate the full length of the African coast to result in Agulhas ring–shedding events. Importantly, most Agulhas rings are shed independently of meandering.

## 2. Data and methods

The Agulhas Current Time-Series Experiment (ACT) array consists of seven moorings equipped with current meters (A to G) and three current- and pressure-recording inverted echo sounders (CPIES), forming two pairs (P3–P4 and P4–P5) (Fig. 1; Table 1). From these, a gridded velocity dataset at 12-h intervals is derived, from April 2010 to February 2013, on a vertical section from the coast to 300 km offshore. Instrumentation and data processing methods are described in detail in Beal et al. (2015). The altimetry data we use are the absolute dynamic topography (ADT) merged, delayed time, updated, mapped product with a 7-day interval on a ⅓° Mercator grid. We also use sea level anomalies (SLA), calculated here as the ADT minus the 2009–13 time mean. We filter the SLA time series at each grid point to remove periods longer than 1 yr in order to focus on mesoscale variability.

Mooring location, distance from coast, and number of days that the AC core was located at each mooring. The distances for CPIES pairs P3–P4 and P4–P5 are the midpoint distances.

To study the spatiotemporal structure of the horizontal velocity variance at ACT, and hence characterize meandering, we apply empirical orthogonal function (EOF) analyses. We first apply a standard EOF analysis (e.g., Preisendorfer and Mobley 1988) on the along-track and cross-track velocity components, hereinafter called Cartesian EOF analysis. Second, we apply an EOF analysis on the time domain rotary components of the horizontal velocity (Lilly and Gascard 2006) and recombine the resulting rotary modes to reveal elliptical motions, a novel method hereinafter called rotary EOF. Past observations have shown that velocity vectors rotate cyclonically during the passage of an Agulhas meander (van der Vaart and de Ruijter 2001; Bryden et al. 2005). A rotary EOF can capture this pattern of variance. As our results will subsequently show, the rotary EOF method is able to capture the meandering of the Agulhas jet in a single mode, while the Cartesian EOF method can only represent rectilinear motions and thus multiple modes are needed to represent a meander. Our rotary EOF method is expounded in the appendix. It has similarities to the method of Denbo and Allen (1984), who applied an EOF analysis on specific frequency bands of velocity rotary spectra.

To investigate the upstream origins and downstream fates of meanders that pass through the ACT array, we look for propagation pathways in SLA data using both the Pearson product-moment correlation coefficient, hereinafter standard correlation, and its analytic counterpart as described in the appendix [(A5)], hereinafter analytic correlation. The latter integrates all phase lags of SLA signals. Starting at a grid point at 33.6°S, 28°E, close to mooring C on the ACT line (Fig. 1), we look “upstream” for the grid point with the largest magnitude correlation among the adjacent points with azimuth ranging from north to southeast going clockwise. From this new point, we repeat the same search and so on. A similar procedure is used to look for a “downstream” path, instead searching among adjacent points with azimuth ranging from south to northwest going clockwise. We expect that both the standard and analytic correlations [(A5)] will capture local, spatially coherent SLA signals, while the analytic correlation will capture propagating SLA signals. Note that these paths are not based on feature tracking, as used in a previous analysis by Schouten et al. (2003), which is inhibited owing to proximity to the coast. We further constrain correlation pathways by requiring that they do not cross shoreward of the 750-m isobath, avoiding the data-sparse region with large errors close to the coast (e.g., Vignudelli et al. 2011). Varying the depth of this isobath between 400 and 1000 m does not change our results significantly.

## 3. Results

### a. Definition and occurrences of Agulhas Current meanders

Meandering at the ACT array can be diagnosed as sporadic offshore shifts of the Agulhas Current core. Figure 2a shows a time series of AC core positions, defined as the offshore location of the minimum (maximum southwestward) velocity at 200-m depth (this depth is more continuously sampled than the surface). For 90% of the record (946 days out of 1039 days), the AC core is found at moorings A, B, or C, above the continental slope and within 60 km of the coast (Fig. 1; Table 1). The AC core is found most often (80%) at mooring B. We define the AC as meandering when its velocity core is at mooring D (88 km) or offshore, which occurs for 93 days of the record or 9% of the time. The ACT array successfully captured the AC jet at all times, as the velocity core was never observed beyond 227 km offshore (P3–P4).

(a) Distance from coast of the cross-track velocity minimum at 200-m depth. Black triangles indicate ring shedding at the Agulhas retroflection. Labels 1 to 4 indicate the mesoscale meanders and gray bands indicate when the velocity minimum is offshore of mooring C (meandering times). (b) Cross-track velocity minimum at 200-m depth *υ*, corresponding along-track component *u*, and current speed [(*u*^{2} + *υ*^{2})^{1/2}]. The mean value of each variable is indicated by a horizontal dashed line. The *u* component and therefore the total speed are not known when the cross-track velocity minimum is located offshore of mooring G. (c) Snapshots of ADT at the dates indicated above each panel, approximately during the mesoscale events. Mean ADT for the time period 2009–13 is indicated by black contours with labels in cm.

Citation: Journal of Physical Oceanography 45, 9; 10.1175/JPO-D-14-0254.1

(a) Distance from coast of the cross-track velocity minimum at 200-m depth. Black triangles indicate ring shedding at the Agulhas retroflection. Labels 1 to 4 indicate the mesoscale meanders and gray bands indicate when the velocity minimum is offshore of mooring C (meandering times). (b) Cross-track velocity minimum at 200-m depth *υ*, corresponding along-track component *u*, and current speed [(*u*^{2} + *υ*^{2})^{1/2}]. The mean value of each variable is indicated by a horizontal dashed line. The *u* component and therefore the total speed are not known when the cross-track velocity minimum is located offshore of mooring G. (c) Snapshots of ADT at the dates indicated above each panel, approximately during the mesoscale events. Mean ADT for the time period 2009–13 is indicated by black contours with labels in cm.

Citation: Journal of Physical Oceanography 45, 9; 10.1175/JPO-D-14-0254.1

(a) Distance from coast of the cross-track velocity minimum at 200-m depth. Black triangles indicate ring shedding at the Agulhas retroflection. Labels 1 to 4 indicate the mesoscale meanders and gray bands indicate when the velocity minimum is offshore of mooring C (meandering times). (b) Cross-track velocity minimum at 200-m depth *υ*, corresponding along-track component *u*, and current speed [(*u*^{2} + *υ*^{2})^{1/2}]. The mean value of each variable is indicated by a horizontal dashed line. The *u* component and therefore the total speed are not known when the cross-track velocity minimum is located offshore of mooring G. (c) Snapshots of ADT at the dates indicated above each panel, approximately during the mesoscale events. Mean ADT for the time period 2009–13 is indicated by black contours with labels in cm.

Citation: Journal of Physical Oceanography 45, 9; 10.1175/JPO-D-14-0254.1

We find two distinct periods of variability during ACT (Fig. 2a); during the first year of the experiment (April 2010–April 2011) there are four mesoscale meanders, while during the last 2 yr none occurred. Of the mesoscale events, two feature core displacement over 100 km (first and third) and two over 180 km (second and fourth), with each associated with inshore negative and offshore positive anomalies of ADT (Fig. 2c). The first mesoscale meander occurred during the initial ACT deployment cruise and is only partially captured by the array (see Leber and Beal 2014). The three subsequent events (starting on 5 June 2010, 12 August 2010, and 5 January 2011) lasted for 21, 28, and 39 days, respectively. The longest and last event was accompanied by a trailing meander of smaller amplitude, a feature noted previously by Rouault and Penven (2011). About 2 weeks prior to each meander, the core speed decreases by more than 1 m s^{−1}, corresponding to an inshore anomaly of the along-track velocity and a weakening of the cross-track velocity (Fig. 2b). Over the final 2 yr of the experiment there are five small offshore displacements of the AC core, each less than 50 km (Fig. 2a). These events are not associated with inshore negative SLA (not shown), and we characterize them as submesoscale meanders.

Mesoscale meanders of the AC have been linked to Agulhas ring shedding downstream (van Leeuwen et al. 2000). During ACT, 14 ring-shedding events occurred, as shown by the triangles in Fig. 2a. The timing of these events was noted by visual inspection of ADT maps, with an estimated accuracy of ±2 weeks. Each of the four mesoscale meanders appears to coincide with a ring-shedding event, while the submesoscale meanders do not. However, many ring-shedding events occur independently of mesoscale meanders, and we expect an advective time lag between a meander at the ACT array and ring shedding. We explore the relationship between meanders and ring shedding further in section 3d.

### b. Characterizing the spatiotemporal structure of meanders

In this section, we characterize the velocity structure of Agulhas meanders, examine their kinematics and dynamics, and quantify their impact on transport. We consider a transport *T*_{c}, defined as the minimum (maximum southwestward) of the cumulative transport from the shore. Hence, *T*_{c} includes the inshore northeastward flows that are characteristic of the velocity structure during a meander. Transport *T*_{c} is correlated at 0.66 with the jet transport defined by Beal et al. (2015).

#### 1) Rectilinear modes of variance

The first four Cartesian EOF modes of the Agulhas Current explain 74% of the total covariance of the *u* and *υ* fields (Figs. 3, 4). The first three EOFs represent meandering of the jet (Figs. 3, 4), while EOF4 (11% of the variance) represents a strengthening or weakening of the flow across the whole array and has a strong correlation with transport (0.85; Fig. 4).

Cartesian EOFs 1 to 4 of the cross-track *υ* and along-track *u* velocity components. The EOFs are dimensionalized to represent velocity anomalies in m s^{−1} for an amplitude of 1 of their respective PC time series shown in Fig. 4. For each EOF, the *υ* component is contoured with the colors as indicated by the color bar. At a number of grid points, the *u* and *υ* components of the EOFs are combined into horizontal velocity vectors represented on the plane of the paper, with a scale given by the gray arrow on the left of each panel. The arrows are colored red when the *u* component is positive (i.e., pointing offshore) and colored blue when negative (onshore). In each panel, the time-mean *υ* component is drawn with gray contours at 0.2 m s^{−1} intervals. The squared fraction covariance (sfc) of each mode is indicated in the inset of each panel.

Citation: Journal of Physical Oceanography 45, 9; 10.1175/JPO-D-14-0254.1

Cartesian EOFs 1 to 4 of the cross-track *υ* and along-track *u* velocity components. The EOFs are dimensionalized to represent velocity anomalies in m s^{−1} for an amplitude of 1 of their respective PC time series shown in Fig. 4. For each EOF, the *υ* component is contoured with the colors as indicated by the color bar. At a number of grid points, the *u* and *υ* components of the EOFs are combined into horizontal velocity vectors represented on the plane of the paper, with a scale given by the gray arrow on the left of each panel. The arrows are colored red when the *u* component is positive (i.e., pointing offshore) and colored blue when negative (onshore). In each panel, the time-mean *υ* component is drawn with gray contours at 0.2 m s^{−1} intervals. The squared fraction covariance (sfc) of each mode is indicated in the inset of each panel.

Citation: Journal of Physical Oceanography 45, 9; 10.1175/JPO-D-14-0254.1

Cartesian EOFs 1 to 4 of the cross-track *υ* and along-track *u* velocity components. The EOFs are dimensionalized to represent velocity anomalies in m s^{−1} for an amplitude of 1 of their respective PC time series shown in Fig. 4. For each EOF, the *υ* component is contoured with the colors as indicated by the color bar. At a number of grid points, the *u* and *υ* components of the EOFs are combined into horizontal velocity vectors represented on the plane of the paper, with a scale given by the gray arrow on the left of each panel. The arrows are colored red when the *u* component is positive (i.e., pointing offshore) and colored blue when negative (onshore). In each panel, the time-mean *υ* component is drawn with gray contours at 0.2 m s^{−1} intervals. The squared fraction covariance (sfc) of each mode is indicated in the inset of each panel.

Citation: Journal of Physical Oceanography 45, 9; 10.1175/JPO-D-14-0254.1

(top to bottom) PC time series for EOFs 3, 1, 2, and 4 (colored curves). The curves are organized as such to highlight the order of their local maxima during meanders. Each PC time series is normalized to have a variance of 1. For each axis the background black curve is the negative of the normalized time series of minimum cumulative transport anomaly at the ACT array [*ρ* is the correlation between the PC time series and −*T*_{c}.

Citation: Journal of Physical Oceanography 45, 9; 10.1175/JPO-D-14-0254.1

(top to bottom) PC time series for EOFs 3, 1, 2, and 4 (colored curves). The curves are organized as such to highlight the order of their local maxima during meanders. Each PC time series is normalized to have a variance of 1. For each axis the background black curve is the negative of the normalized time series of minimum cumulative transport anomaly at the ACT array [*ρ* is the correlation between the PC time series and −*T*_{c}.

Citation: Journal of Physical Oceanography 45, 9; 10.1175/JPO-D-14-0254.1

(top to bottom) PC time series for EOFs 3, 1, 2, and 4 (colored curves). The curves are organized as such to highlight the order of their local maxima during meanders. Each PC time series is normalized to have a variance of 1. For each axis the background black curve is the negative of the normalized time series of minimum cumulative transport anomaly at the ACT array [*ρ* is the correlation between the PC time series and −*T*_{c}.

Citation: Journal of Physical Oceanography 45, 9; 10.1175/JPO-D-14-0254.1

In its positive phase, the eigenmode pattern for EOF4 is that of a surface-intensified baroclinic strengthening and convergence of the mean jet, with maxima on both the onshore and offshore sides of the mean jet (Fig. 3). Superimposing this mode onto the mean velocity field leads to patterns of velocities similar to the high and low transport composites shown by Beal et al. (2015, their Fig. 7). The convergent pattern of along-track anomalies appears to be a result of topographic steering since the large-scale orientation of the isobaths rotates from approximately 11° east of the cross-track direction (244° T) to 10° west of it at the point of convergence (Fig. 1). Mesoscale meander events project weakly onto this transport mode, with minima in the principal component (PC) time series during each fully captured event (Fig. 4).

The meander modes, EOFs 1, 2, and 3 (Fig. 3), are all surface intensified with little rotation with depth of the current anomalies. There is a localized change of sign of *u* at 1500 m above the continental slope, corresponding to the core of the Agulhas Undercurrent (Beal 2009; Beal et al. 2015). This suggests a coupling of variability between the meandering Agulhas jet and the undercurrent, causing localized convergence and divergence of the flow. The primary meander mode EOF1 exhibits one zero crossing near 130 km, EOF2 has two zero crossings implying a wavelength of about 300 km, and EOF3 has three zero crossings and an implied wavelength of 200 km. Mesoscale meander events project strongly onto EOFs 1, 2, and 3, always in the same temporal sequence (Fig. 4). PC3 leads, peaking at the onset of the meander, and represents an initial onshore shift of the AC core, a phenomenon also observed by Bryden et al. (2005). Subsequently, PC1 increases and the current moves offshore and finally PC2 ramps up, representing the maximum displacement (Fig. 3). The mesoscale meander is not exactly represented by consecutive occurrences of EOF3, EOF1, and then EOF2 but by an overlap of the three patterns, which peak successively.

Submesoscale meander events project onto EOFs 2 and 3 (Fig. 4). For example, during the submesoscale event of November 2011 (Figs. 2a, 4), PC1 is near zero, while PC2 is positive and PC3 is strongly negative. During the second period of ACT, PC1 and PC2 are anticorrelated at −0.6;^{1} given the structures of EOF1 and EOF2, their velocity anomalies tend to cancel each other such that the variability of the velocity field outside of meandering is dominated by small-scale oscillations represented by only EOF3 and the pulselike behavior of EOF4.

#### 2) Rotary modes of variance

Next we conduct a rotary EOF analysis, which can account for phase and rotation of the velocity field during meandering and thus can capture meandering in a single mode of variance. Since the variance of the first year (four mesoscale meanders) and following 2 yr (only submesoscale meanders) of ACT are so distinct, we analyze these periods separately to find those modes that correspond to mesoscale and submesoscale meanders (Table 2; Figs. 5, 6). For the first period, the first rotary EOF (REOF1) represents 55% of the variance and captures mesoscale meanders. For the second period, the second rotary EOF (REOF2) captures submesoscale meanders and represents 21% of the variance.

Percentage of covariance of the REOFs and analytic correlation [absolute value |*ρ*|, complex argument Arg(*ρ*), and estimated *p* value] with the transport time series −*T*_{c} for the first period from April 2010 to April 2011 and the second period from April 2011 and February 2013. In each case, the probability of obtaining by chance an absolute correlation as large as the one obtained from the data is *p*. The cases indicated in bold text are represented in Figs. 5 and 6.

(a) REOF1 of horizontal velocity for the period April 2010–April 2011. The ellipses drawn correspond to standard deviation ellipses for this mode but also to instantaneous velocity hodographs with velocity vectors at times when the phase of RPC1 is 0 and the normalized amplitude is 1. The phase and amplitude of REOF1 are further illustrated as colors, where the saturation of the colors is proportional to ellipse amplitude (maximum amplitude, 0.68 m s^{−1}). The color scale is doubly periodic to show the continuity of the phase. The scale of the ellipses is drawn on the left. Rectilinear motions past P3–P4 are drawn as anticyclonic flat ellipses. (b) RPC1. The terms |*ρ*| and Arg(*ρ*) are the absolute value and phase of the analytic correlation between the RPC time series and −*T*_{c}. The vertical gray bands indicate the meandering times when the core of the AC is offshore of mooring C.

Citation: Journal of Physical Oceanography 45, 9; 10.1175/JPO-D-14-0254.1

(a) REOF1 of horizontal velocity for the period April 2010–April 2011. The ellipses drawn correspond to standard deviation ellipses for this mode but also to instantaneous velocity hodographs with velocity vectors at times when the phase of RPC1 is 0 and the normalized amplitude is 1. The phase and amplitude of REOF1 are further illustrated as colors, where the saturation of the colors is proportional to ellipse amplitude (maximum amplitude, 0.68 m s^{−1}). The color scale is doubly periodic to show the continuity of the phase. The scale of the ellipses is drawn on the left. Rectilinear motions past P3–P4 are drawn as anticyclonic flat ellipses. (b) RPC1. The terms |*ρ*| and Arg(*ρ*) are the absolute value and phase of the analytic correlation between the RPC time series and −*T*_{c}. The vertical gray bands indicate the meandering times when the core of the AC is offshore of mooring C.

Citation: Journal of Physical Oceanography 45, 9; 10.1175/JPO-D-14-0254.1

(a) REOF1 of horizontal velocity for the period April 2010–April 2011. The ellipses drawn correspond to standard deviation ellipses for this mode but also to instantaneous velocity hodographs with velocity vectors at times when the phase of RPC1 is 0 and the normalized amplitude is 1. The phase and amplitude of REOF1 are further illustrated as colors, where the saturation of the colors is proportional to ellipse amplitude (maximum amplitude, 0.68 m s^{−1}). The color scale is doubly periodic to show the continuity of the phase. The scale of the ellipses is drawn on the left. Rectilinear motions past P3–P4 are drawn as anticyclonic flat ellipses. (b) RPC1. The terms |*ρ*| and Arg(*ρ*) are the absolute value and phase of the analytic correlation between the RPC time series and −*T*_{c}. The vertical gray bands indicate the meandering times when the core of the AC is offshore of mooring C.

Citation: Journal of Physical Oceanography 45, 9; 10.1175/JPO-D-14-0254.1

(a) REOF2 of horizontal velocity for the period April 2011–February 2013. The ellipses drawn correspond to standard deviation ellipses for this mode but also to instantaneous velocity hodographs with velocity vectors at times when the phase of RPC1 is 0 and the normalized amplitude is 1. The phase and amplitude of REOF2 are further illustrated as colors, where the saturation of the colors is proportional to ellipse amplitude (maximum amplitude, 0.39 m s^{−1}). The color scale is doubly periodic to show the continuity of the phase. The scale of the ellipses is drawn on the left. Rectilinear motions past P3–P4 are drawn as anticyclonic flat ellipses. (b) RPC2. The terms |*ρ*| and Arg(*ρ*) are the absolute value and phase of the analytic correlation between the RPC time series and −*T*_{c}. The vertical gray bands indicate the meandering times when the core of the AC is offshore of mooring C.

Citation: Journal of Physical Oceanography 45, 9; 10.1175/JPO-D-14-0254.1

(a) REOF2 of horizontal velocity for the period April 2011–February 2013. The ellipses drawn correspond to standard deviation ellipses for this mode but also to instantaneous velocity hodographs with velocity vectors at times when the phase of RPC1 is 0 and the normalized amplitude is 1. The phase and amplitude of REOF2 are further illustrated as colors, where the saturation of the colors is proportional to ellipse amplitude (maximum amplitude, 0.39 m s^{−1}). The color scale is doubly periodic to show the continuity of the phase. The scale of the ellipses is drawn on the left. Rectilinear motions past P3–P4 are drawn as anticyclonic flat ellipses. (b) RPC2. The terms |*ρ*| and Arg(*ρ*) are the absolute value and phase of the analytic correlation between the RPC time series and −*T*_{c}. The vertical gray bands indicate the meandering times when the core of the AC is offshore of mooring C.

Citation: Journal of Physical Oceanography 45, 9; 10.1175/JPO-D-14-0254.1

(a) REOF2 of horizontal velocity for the period April 2011–February 2013. The ellipses drawn correspond to standard deviation ellipses for this mode but also to instantaneous velocity hodographs with velocity vectors at times when the phase of RPC1 is 0 and the normalized amplitude is 1. The phase and amplitude of REOF2 are further illustrated as colors, where the saturation of the colors is proportional to ellipse amplitude (maximum amplitude, 0.39 m s^{−1}). The color scale is doubly periodic to show the continuity of the phase. The scale of the ellipses is drawn on the left. Rectilinear motions past P3–P4 are drawn as anticyclonic flat ellipses. (b) RPC2. The terms |*ρ*| and Arg(*ρ*) are the absolute value and phase of the analytic correlation between the RPC time series and −*T*_{c}. The vertical gray bands indicate the meandering times when the core of the AC is offshore of mooring C.

Citation: Journal of Physical Oceanography 45, 9; 10.1175/JPO-D-14-0254.1

REOF1 (Fig. 5a) consists of a cyclonic elliptical rotation out to 150 km offshore (mooring F). Beyond 150 km, the ellipses change polarity and there is anticyclonic rotation, opposing in sign the inshore circulation. The linear ellipses point to velocity variance predominantly oriented along isobaths over the shelf and slope. The variance gradually becomes more isotropic offshore, with cross-shore variance increasing, but this tendency is reversed at 100 km or so and the variance again becomes more linear. Overall REOF1 can be described as two surface-intensified, counterrotating, baroclinic cells of horizontal shear flow. The ellipses also represent instantaneous hodographs (Fig. 5a) at a time when the phase of the first rotary PC time series (RPC1) is zero at the onset of each mesoscale meander event (Fig. 5b). The corresponding stick vectors show the initial northeastward and onshore velocity anomalies within the cyclonic cell and the southwestward velocity anomalies within the anticyclonic cell. As the phase of RPC1 and the velocity field progress by 90°, the meander fully develops and velocity anomalies rotate, so that between 50 and 225 km there are offshore and downstream anomalies, displacing the AC core offshore. A further phase progression by 90° brings back nonmeandering conditions. The phase of the ellipses (parameter *T*_{c} (|*ρ*_{+}| = 0.41; Fig. 5b) with a phase of 146°, implying that the southwestward transport would marginally weaken after the onset of a mesoscale meander event.^{2}

The first rotary mode of the second period (not shown) consists of velocity anomalies that are focused outside the mean jet (offshore mooring G). This velocity variance is due to mesoscale anomalies impinging on the array from offshore, as noted by Beal et al. (2015). The peaks of the RPC time series of this mode do not coincide with the submesoscale meanderings of this period, as diagnosed from the time series of AC core position. Hence, we focus on REOF2, which does peak at the times of submesoscale meanders, when the phase of the second rotary PC time series (RPC2) is zero (Fig. 6). This mode captures an anomalous cyclonic rotation of the velocity, spanning the entirety of the mean jet but restricted to the top 1500 m. The variance appears constrained by bathymetry, as the orientation of the ellipses follows the large-scale pattern of the isobaths (Fig. 1), with the largest amplitude at the shelf break where they are strongly linear. Velocity anomalies have an offshore component within the entire mean jet and a positive–negative–positive pattern of cross-track anomalies from the shore out to about 220 km, the mean offshore edge of the jet. Thus, REOF2, reminiscent of Cartesian EOF3 (Fig. 3), captures small offshore displacements of the AC core, now seen to be manifested by a cyclonic rotation of the horizontal velocity that commences just offshore of the jet core, in line with the foot of the continental slope (as indicated by the phase pattern). We note that REOF2 sometimes has large amplitude when no offshore displacement of the AC core is detectable (e.g., July 2012), which implies that other modes of variance must also be important at these times. The principal component time series of REOF2 has the strongest (yet moderate) correlation with transport (|*ρ*_{+}| = 0.53) of all the rotary modes (Table 2). The phase of *ρ*_{+} between RPC2 and −*T*_{c} is 67°, implying a marginal increase of the southwestward transport prior to submesoscale meanderings.

### c. Energetics of Agulhas meander events

The Agulhas meanders that we observe must grow through a transfer of energy from the mean flow to the meander, either through barotropic or baroclinic processes or a mixture of both. Past theoretical and numerical studies have shown that the onset and evolution of meander events are strongly associated with the extraction of kinetic energy (rather than potential energy) from the mean flow, pointing to the importance of barotropic instability in the AC (de Ruijter et al. 1999; Tsugawa and Hasumi 2010). This is in contrast to the separated Gulf Stream, where baroclinic instability is more important. De Ruijter et al. (1999) estimated the kinetic energy transfer in the AC to be two orders of magnitude greater than the potential energy transfer.

The time mean

(a) Time average of the barotropic conversion rate *T*_{BT}. The contributions to *T*_{BT} from the three terms (b) *u* in (b) and (d), and the time-mean across-track component *υ* in (c). The term *T*_{BT} and its contributions are not estimated beyond mooring G where the *u* component is not measured. Note the change of color scale for each panel.

Citation: Journal of Physical Oceanography 45, 9; 10.1175/JPO-D-14-0254.1

(a) Time average of the barotropic conversion rate *T*_{BT}. The contributions to *T*_{BT} from the three terms (b) *u* in (b) and (d), and the time-mean across-track component *υ* in (c). The term *T*_{BT} and its contributions are not estimated beyond mooring G where the *u* component is not measured. Note the change of color scale for each panel.

Citation: Journal of Physical Oceanography 45, 9; 10.1175/JPO-D-14-0254.1

(a) Time average of the barotropic conversion rate *T*_{BT}. The contributions to *T*_{BT} from the three terms (b) *u* in (b) and (d), and the time-mean across-track component *υ* in (c). The term *T*_{BT} and its contributions are not estimated beyond mooring G where the *u* component is not measured. Note the change of color scale for each panel.

Citation: Journal of Physical Oceanography 45, 9; 10.1175/JPO-D-14-0254.1

To quantify the time-varying

(a) Vertical area-integrated barotropic energy conversion term *T*_{BT} across the AC jet. The black curve is the sum of the three colored curves as indicated in the legend. (b) Cumulative time integral of each of the four curves in (a). Two curves are added to this plot that correspond to *T*_{BT}, calculated only from the velocity anomalies from the rotary EOF mode REOF1 and REOF2. In both panels, the vertical gray bands indicate the meandering times when the core of the AC is offshore of mooring C.

Citation: Journal of Physical Oceanography 45, 9; 10.1175/JPO-D-14-0254.1

(a) Vertical area-integrated barotropic energy conversion term *T*_{BT} across the AC jet. The black curve is the sum of the three colored curves as indicated in the legend. (b) Cumulative time integral of each of the four curves in (a). Two curves are added to this plot that correspond to *T*_{BT}, calculated only from the velocity anomalies from the rotary EOF mode REOF1 and REOF2. In both panels, the vertical gray bands indicate the meandering times when the core of the AC is offshore of mooring C.

Citation: Journal of Physical Oceanography 45, 9; 10.1175/JPO-D-14-0254.1

(a) Vertical area-integrated barotropic energy conversion term *T*_{BT} across the AC jet. The black curve is the sum of the three colored curves as indicated in the legend. (b) Cumulative time integral of each of the four curves in (a). Two curves are added to this plot that correspond to *T*_{BT}, calculated only from the velocity anomalies from the rotary EOF mode REOF1 and REOF2. In both panels, the vertical gray bands indicate the meandering times when the core of the AC is offshore of mooring C.

Citation: Journal of Physical Oceanography 45, 9; 10.1175/JPO-D-14-0254.1

During the passage of a mesoscale meander at the ACT array, kinetic energy is suddenly and strongly extracted from the mean flow through all three barotropic conversion terms. The value

### d. Census, origins, and fates of mesoscale meanders

Here, we use SLA, together with the in situ ACT data, to investigate the upstream origins and downstream fates of Agulhas meanders. In the past, anomalies within the Agulhas Current have been linked to westward-propagating anomalies upstream, at latitudes 12° and 27°S (Schouten et al. 2002), and downstream to Agulhas ring shedding (van Leeuwen et al. 2000; Biastoch et al. 2008b).

We find two pathways (Figs. 9a,b) from the Indian Ocean, through the ACT array and into the Agulhas retroflection region, using standard (Path I) and analytic (Path II) correlation analyses on SLA fields for the time period 2009–13 (see section 2). Repeating our analysis for the entire altimeter record leads to very similar paths. Both paths are defined by large correlation magnitudes, typically greater than 0.8, for distances in the range −2 to 11 (×10^{3}) km (Fig. 9c), which suggests that they represent highly probable propagating routes for SLA.

(a) ADT in the Agulhas Current system and in the south Indian Ocean averaged for the time period January 2009–August 2013. (b) Close-up of the box delineated by a dashed line in (a). The thin white lines are the 750-m isobaths from the seafloor topography database version 15.1 of Smith and Sandwell (1997). The gray and black curves are the correlation path (Path I) and analytic correlation path (Path II); see text for definitions. Along those paths, the distances from the origin at the ACT array are written at 1000-km intervals, positive upstream of ACT and negative downstream. In (b), the 90-cm contour is drawn with a dashed line. (c) Correlation magnitude along Path I (gray) and along Path II (black).

Citation: Journal of Physical Oceanography 45, 9; 10.1175/JPO-D-14-0254.1

(a) ADT in the Agulhas Current system and in the south Indian Ocean averaged for the time period January 2009–August 2013. (b) Close-up of the box delineated by a dashed line in (a). The thin white lines are the 750-m isobaths from the seafloor topography database version 15.1 of Smith and Sandwell (1997). The gray and black curves are the correlation path (Path I) and analytic correlation path (Path II); see text for definitions. Along those paths, the distances from the origin at the ACT array are written at 1000-km intervals, positive upstream of ACT and negative downstream. In (b), the 90-cm contour is drawn with a dashed line. (c) Correlation magnitude along Path I (gray) and along Path II (black).

Citation: Journal of Physical Oceanography 45, 9; 10.1175/JPO-D-14-0254.1

(a) ADT in the Agulhas Current system and in the south Indian Ocean averaged for the time period January 2009–August 2013. (b) Close-up of the box delineated by a dashed line in (a). The thin white lines are the 750-m isobaths from the seafloor topography database version 15.1 of Smith and Sandwell (1997). The gray and black curves are the correlation path (Path I) and analytic correlation path (Path II); see text for definitions. Along those paths, the distances from the origin at the ACT array are written at 1000-km intervals, positive upstream of ACT and negative downstream. In (b), the 90-cm contour is drawn with a dashed line. (c) Correlation magnitude along Path I (gray) and along Path II (black).

Citation: Journal of Physical Oceanography 45, 9; 10.1175/JPO-D-14-0254.1

Downstream from the ACT array, Paths I and II follow each other closely until the tip of the Agulhas Bank (38°S, 22°E), where they separate; Path I leaves the Agulhas retroflection south at that longitude, while Path II heads westward to leave the retroflection toward the Atlantic (Fig. 9b). These could represent the divergent pathways of cyclonic (Path I) and anticyclonic (Path II) anomalies drifting on a beta plane after separation from the retroflection (Boebel et al. 2003; Morrow 2004); although, the high levels of variance in the retroflection region introduce strong uncertainties in these pathways and their interpretation.

Going upstream from the ACT array, Paths I and II follow each other closely within the AC and beyond the Natal Bight. At the southern end of the MC, where the time-mean AC originates at approximately 28°S, the two paths diverge. Path I continues north through the MC with at first relatively lower correlation magnitudes (Fig. 9c), maybe indicating a weaker or more variable route at the southern end of the channel. Path I continues east and north into the tropical gyre, then toward Sumatra and Java and into the Indonesian Throughflow. This last portion of Path I appears to capture eastward-propagating equatorial and coastal Kelvin wave processes (e.g., Drushka et al. 2010). Within the MC, Path I is very similar to the region of maximum SLA variance found by Schouten et al. (2002), representing the southward drift of Mozambique eddies. The possible connection between these eddies and variability upstream in the South Equatorial Current (SEC) has also been noted before (Backeberg and Reason 2010). The frequency of MC eddies may be modified on interannual time scales through its connection with these westward-propagating anomalies in the South Equatorial Current (Backeberg and Reason 2010; Schouten et al. 2003) and the Indian Ocean dipole (Palastanga et al. 2006).

Path II heads eastward, following approximately the 100-cm time-mean ADT toward the southern tip of Madagascar. This pathway is the corridor for Madagascar dipoles, originating from the separated, southward-flowing EMC (de Ruijter et al. 2005; Schouten et al. 2002; Siedler et al. 2009). This path does not turn upstream into the EMC as might be expected (Biastoch and Krauss 1999) but instead continues east and slightly north across the basin to eventually reach the 750-m isobath off the west Australian coast near 26°S. Once it reaches this isobath, it turns northward and into the Indonesian Throughflow. The transbasin portion of Path II corresponds to a region of higher SLA variance noted before within the south Indian Ocean basin (de Ruijter et al. 2005) and may be associated with an eddy corridor formed by long-lived nonlinear features (>100 weeks) (Chelton et al. 2011) emanating from the Leeuwin Current (Feng et al. 2005; Fang and Morrow 2003; Chelton et al. 2011) at a rate of three to nine anomalies per year. Baroclinic instabilities of the South Indian Countercurrent may also inject variability at frequencies of 3.5–6 yr^{−1} (Palastanga et al. 2007). All these anomalies may be modified at interannual time scales by variations in Pacific equatorial wind energy, which travels down the Papuan–Australian shelf break and radiates Rossby waves into the south Indian Ocean (Wijffels and Meyers 2004; Potemra 2001) along these latitudes.

A clearer idea of the significance of these pathways for individual meander events is gained by studying space–time diagrams of SLA along Paths I and II and ground truthing with in situ array data (Fig. 10). We use the entire altimeter period available at the time of this study, from late 1992 to late 2013, and look for propagating SLA on both paths toward and through the Agulhas Current System. We find that during ACT, all mesoscale events are associated with a propagating SLA signal, while submesoscale events are not. The trailing meander after the fourth and largest mesoscale meander event is an exception in that it has an SLA signal upstream of ACT (although not downstream). All mesoscale meanders observed at the ACT array are associated with SLA < −20 cm and can be traced both upstream to the northern end of the Natal Bight (1000 km) and downstream to the center of the Agulhas retroflection at 23°E (−1000 km; Figs. 9b, 10a). Over this range the propagation speed along Path I (calculated from the SLA space–time diagram by a Radon transform analysis) averages 14 km day^{−1} and is faster upstream of the array (17 km day^{−1}) than downstream (12 km day^{−1}), corroborating previous studies that noted a deceleration of Natal pulses from north to south (e.g., Lutjeharms 2006). The first and fourth mesoscale meanders are traceable beyond the Natal Bight to the southern end of the MC (2000 km), where positive SLA signals represent anticyclonic eddies (Fig. 10a).

Space–time diagram of SLA along (a) Path I and SLA_{+} along (b) Path II. SLA_{+} is displayed as a hue–saturation–value color with hue representing phase, value representing absolute value as shown in the inset panel, and the saturation kept at 1. Horizontal dashed lines show the beginning and end of ACT. The vertical dashed line in both panels indicate the distance from the origin where the two paths diverge (see Figs. 9a,b). Plus signs indicate the times when the AC is meandering during ACT. The circles indicate the times when the SLA at the origin is equal to or less than −20 cm.

Citation: Journal of Physical Oceanography 45, 9; 10.1175/JPO-D-14-0254.1

Space–time diagram of SLA along (a) Path I and SLA_{+} along (b) Path II. SLA_{+} is displayed as a hue–saturation–value color with hue representing phase, value representing absolute value as shown in the inset panel, and the saturation kept at 1. Horizontal dashed lines show the beginning and end of ACT. The vertical dashed line in both panels indicate the distance from the origin where the two paths diverge (see Figs. 9a,b). Plus signs indicate the times when the AC is meandering during ACT. The circles indicate the times when the SLA at the origin is equal to or less than −20 cm.

Citation: Journal of Physical Oceanography 45, 9; 10.1175/JPO-D-14-0254.1

Space–time diagram of SLA along (a) Path I and SLA_{+} along (b) Path II. SLA_{+} is displayed as a hue–saturation–value color with hue representing phase, value representing absolute value as shown in the inset panel, and the saturation kept at 1. Horizontal dashed lines show the beginning and end of ACT. The vertical dashed line in both panels indicate the distance from the origin where the two paths diverge (see Figs. 9a,b). Plus signs indicate the times when the AC is meandering during ACT. The circles indicate the times when the SLA at the origin is equal to or less than −20 cm.

Citation: Journal of Physical Oceanography 45, 9; 10.1175/JPO-D-14-0254.1

Along Path II, the four solitary meanders during ACT manifest as ridges of SLA_{+} [analytic transform of SLA; (A1)] and each can be traced over the same range as SLA (1000 km up and downstream; Fig. 10b). In this range, the average propagation speed along Path II is 15 km day^{−1}, decelerating from 19 km day^{−1} upstream of the ACT array to 10 km day^{−1} downstream. The phase of SLA_{+} at the ACT line at the time of a meander is near ±180°, which implies a negative SLA. In between each meander event, the phase of SLA_{+} progresses through 360°, reflecting an oscillatory behavior, similar to that seen for velocity (Fig. 5). In fact, the phase pattern of the SLA_{+} ridges remains organized up and down Path II, and it is possible to follow these ridges from the coast and out to the southern tip of Madagascar (2500 km). The second and third mesoscale meanders appear to originate here as EMC dipoles. Beyond Madagascar, SLA_{+} can continue to exhibit an organized pattern of phase, indicative of westward-propagating mesoscale features crossing the south Indian Ocean. The transbasin propagation speed is about 4.8 km day^{−1} (5.5 cm s^{−1}), similar to previous estimates at that latitude (Chelton et al. 2011, their Fig. 22).

Looking retrospectively from ACT, at the full 20 yr of SLA along Paths I and II (Fig. 10), leads to the conclusion that all mesoscale meanders, represented by SLA depressions < −20 cm at the ACT line, can be traced upstream for 1000 km to the source of the coherent AC. Many may be traced back to either MC eddies or to the tip of Madagascar. A few might be traced all the way to the eastern boundary along Path II. One striking example is an SLA_{+} ridge that emerges between 5000 and 6000 km upstream of the ACT array in early 2008 and appears as a meander event at ACT about 2 yr later, in late November 2009.

Using the SLA threshold for mesoscale meander events from the in situ data, we produce a time series of events at the ACT latitude for the 20-yr altimetry record (Fig. 11a). In all, we identify 31 mesoscale meanders, an average of 1.6 yr^{−1}. We do not count three events that exceed the SLA threshold but occur immediately on the heels of a preceding meander, such that SLA does not pass through zero in between. From our in situ data, we identify these as small trailing meanders and hence discount them as mesoscale meanders. Our number of meanders is the same as that obtained by Rouault and Penven (2011) 180 km downstream. The interannual variability of meanders is large, from 0 to 4 yr^{−1} (Fig. 11b). There is no annual signal detected. The ACT experiment covered one of the busiest and one of the calmest years of the altimetry period, including the longest interval on record (2 yr) without solitary meanders.

(a) Time series of SLA at 28°E, 33.6°S from 14 Oct 1993 to 7 Aug 2013. The horizontal dotted lines indicate the zero and the one negative standard deviation of SLA for the January 2009 to August 2013 time period. The downward triangles indicate when the SLA is equal to or less than −20 cm and thus a mesoscale meander. The white triangles indicate times when SLA time series did not return to zero since the last time it was equal to or less than −20 cm and thus represent a trailing meander. The right triangles indicate ring-shedding events at the retroflection (see text). The red symbols and dashed lines indicate possible downstream links between ACT meanders and ring sheddings. (b) Meander count in a 1-yr sliding window.

Citation: Journal of Physical Oceanography 45, 9; 10.1175/JPO-D-14-0254.1

(a) Time series of SLA at 28°E, 33.6°S from 14 Oct 1993 to 7 Aug 2013. The horizontal dotted lines indicate the zero and the one negative standard deviation of SLA for the January 2009 to August 2013 time period. The downward triangles indicate when the SLA is equal to or less than −20 cm and thus a mesoscale meander. The white triangles indicate times when SLA time series did not return to zero since the last time it was equal to or less than −20 cm and thus represent a trailing meander. The right triangles indicate ring-shedding events at the retroflection (see text). The red symbols and dashed lines indicate possible downstream links between ACT meanders and ring sheddings. (b) Meander count in a 1-yr sliding window.

Citation: Journal of Physical Oceanography 45, 9; 10.1175/JPO-D-14-0254.1

(a) Time series of SLA at 28°E, 33.6°S from 14 Oct 1993 to 7 Aug 2013. The horizontal dotted lines indicate the zero and the one negative standard deviation of SLA for the January 2009 to August 2013 time period. The downward triangles indicate when the SLA is equal to or less than −20 cm and thus a mesoscale meander. The white triangles indicate times when SLA time series did not return to zero since the last time it was equal to or less than −20 cm and thus represent a trailing meander. The right triangles indicate ring-shedding events at the retroflection (see text). The red symbols and dashed lines indicate possible downstream links between ACT meanders and ring sheddings. (b) Meander count in a 1-yr sliding window.

Citation: Journal of Physical Oceanography 45, 9; 10.1175/JPO-D-14-0254.1

An estimate of 1–2 mesoscale meanders per year corroborates the analysis of Rouault and Penven (2011) and significantly lowers the estimate of 3–5 yr^{−1} previously understood (de Ruijter et al. 1999; Lutjeharms et al. 2001; Schouten et al. 2002). This discrepancy may reflect sampling error, since previous estimates relied on short satellite records and cloudy SST data, or it may reflect real latitudinal dependence, since most prior estimates were made farther upstream, close to 32°S. To investigate this we quantify the number of meanders occurring farther upstream by using in situ data from the ACE array (Bryden et al. 2005) to ground truth the SLA signal there. We take SLA at the point closest to where our two correlation paths cross the ACE array and establish a threshold based on the four major meander events observed at this array in 1995 (Lutjeharms et al. 2001), in a similar manner to our analysis at ACT. This gives 40 mesoscale meanders at 32°S over the 20-yr satellite period, 29% more than at 34°S and an average 2 yr^{−1}. Thus, the frequency of mesoscale meanders in the Agulhas Current is much less than previously understood.

More than half of the meanders at 32°S can be detected downstream at the ACT array at a lag consistent with our estimated propagation speed. We estimate that 25% of meanders dissipate before reaching the retroflection region. Examples of dissipating events can be found in Fig. 10, where several negative SLA along Path I appear to originate from the southern end of the MC (2300 km), reach the Agulhas (1000 km), but disappear before reaching the ACT array. Similarly, some ridge patterns of SLA_{+} along Path II, emanating from the tip of Madagascar (≈2500 km), reach the coast and propagate downstream but disappear before reaching ACT. A few meander signals appear between 32° and 34°S, and these are likely related to the growth of trailing meanders (Rouault and Penven 2011; de Ruijter et al. 1999).

For the mesoscale meanders that do reach the retroflection, there are a few that can be traced along Path II to anomalies beyond 18°E (−1500 km), the westward extension of the retroflection (Fig. 10b) (Dencausse et al. 2010). This is an indication that some meanders are linked to Agulhas ring shedding (e.g., in late 2000 and 2006). However, the level of SLA variance is generally too high at the retroflection to link meanders directly to Agulhas ring–shedding events through these correlation pathways. We investigate the relationship between meanders at ACT and ring shedding by visually inspecting 20 yr of ADT fields for ring-shedding events. There are between three and nine shedding events per calendar year, averaging to six (Fig. 11a). We estimate a 2-week uncertainty in the timing of events owing to the spatiotemporal resolution of altimetry data and the subjectivity in identifying complete separation of the retroflection and a ring, particularly when there is remerging and splitting. We test whether these events could be related to a meander at the ACT array by considering their propagation speed downstream along Path II (Fig. 10b). Speeds are calculated by Radon transforms in 2-yr discrete windows for the entire 20-yr record and average 11 km day^{−1} with a standard deviation of 2 km day^{−1}. Accounting for the uncertainties in ring-shedding day and propagation speed gives a range of lags between 99 and 177 days for mesoscale anomalies at ACT to reach the tip of the retroflection at 18°E. Within that interval, 26 of the mesoscale meanders, or 84% of them, are consistent with subsequent ring-shedding events (Fig. 11a). Several meanders appear to lead to two ring-shedding events, and this is probably related to the occasional remerging and splitting of rings at the tip of the retroflection.

## 4. Conclusions

New velocity measurements across the Agulhas Current capture the full western boundary jet continuously over the course of 34 months, allowing an analysis of its modes of variance and energetics. Over the length of the ACT experiment, the variance of the velocity field was dominated by mesoscale meander events (Natal pulses). Meandering is described by the first three Cartesian eigenmodes, representing 63% of the variance. More concisely, mesoscale meanders can be captured by a single rotary eigenmode that accounts for both the rotation and phase of velocity variance.

The first year of ACT was marked by the passage of four mesoscale meanders, each displacing the core of the AC jet over 100 km from its mean position (43 km from the coast) and taking between 23 and 44 days to cross the array. Mesoscale meanders manifest as full-depth, surface-intensified, cyclonic circulation out to 150 km from the coast and anticyclonic circulation farther offshore, both causing anomalous flow across isobaths that otherwise constrain the mean flow. Hence, the meander can be described as two counterrotating, baroclinic cells of horizontal shear flow. There is an onshore propagation of the meander signal and the jet is first displaced onshore at the leading edge of each meander before proceeding offshore. During the latter 2 yr of ACT only smaller meander events occurred, characterized by offshore displacement of no more than 45 km and a cyclonic circulation spanning the entire width of the mean jet and confined to the top 1500 m. These cyclonic oscillations sometimes occurred without causing any displacement of the AC core.

Mesoscale meanders result in sudden and strong extraction of kinetic energy from the mean flow of the Agulhas Current during their passage, pointing to barotropic instability processes in agreement with previous theory (van der Vaart and de Ruijter 2001; Tsugawa and Hasumi 2010). In contrast, smaller meanders initially act to stabilize the mean flow and are not able to extract kinetic energy from the jet to grow. The strong energy input to meanders at the ACT array is consistent with the growth of meanders downstream, as observed previously (van Leeuwen et al. 2000) and seen here in the form of deepening negative SLA signals along correlation pathways. Outside meander events, the shear stress of the horizontal velocity field tends to feed energy into the mean flow, stabilizing the jet, while the normal stresses feed perturbations. The mean pattern of barotropic energy conversion suggests a barotropically unstable jet core, flanked by stabilizing regions where kinetic energy is feeding the mean flow.

Each of the mesoscale meanders observed at ACT can be traced upstream and downstream as propagating negative sea level anomalies, while smaller meanders are localized. Two of the mesoscale meanders appear to originate from anticyclones in the Mozambique Channel. The remaining two can be traced back to anomalies originating from the tip of Madagascar and maybe beyond. None can be reliably traced via SLA correlation pathways to Agulhas rings; however, given their propagation speeds into the retroflection, all the mesoscale meanders observed during ACT are temporally consistent with subsequent ring shedding events.

Using in situ data as ground truth, we expand our analysis over the 20-yr satellite record to find that all mesoscale meanders that pass through the ACT array can be traced upstream, beyond the Natal Bight, to where the flow of the Agulhas Current originates at about 28°S. Most meanders can be traced farther upstream to SLA propagating southward through the Mozambique Channel or propagating westward from the southern tip of Madagascar, in agreement with Schouten et al. (2002). Some can be traced eastward across the basin, beyond Madagascar and as far as Australia. An average two mesoscale meanders pass through 32°S per year, while only 1.6 pass through the ACT array at 34°S. Hence, at least 20% of meanders dissipate before reaching the retroflection. The relationship between meanders and ring shedding is less clear, owing to high levels of local SLA variance that mask the propagating anomalies. However, more than 80% of meanders at the ACT array are followed by a ring-shedding event between 3 and 6 months later, in a way consistent with the local meander propagation speed.

Our estimation of one or two Agulhas meanders per year corroborates the results of Rouault and Penven (2011) and is considerably less than previously understood. In the past, Mozambique eddies and East Madagascar dipoles have been thought to be strongly linked to the shedding of Agulhas rings via downstream propagation of meanders (van Leeuwen et al. 2000; Schouten et al. 2002; Penven et al. 2006; Biastoch et al. 2008b). With far fewer meanders, these upstream anomalies must be transmitted toward the retroflection outside the Agulhas Current or be dissipated at the western boundary, unable to influence ring shedding at all.

Within the Mozambique Channel, five to six eddies form on average per year at the narrows of the channel (van der Werf et al. 2010) and propagate southward toward the Agulhas Current (our Path I). From the eastern side of the Indian basin there are three to nine anomalies (Chelton et al. 2011) approaching the Agulhas per year (our Path II). Together, these observations imply that 8 to 15 anomalies are likely to arrive at the source region of the AC in an average year. Of these, only two form mesoscale meanders, of which two-thirds propagate along the entire coast and can be linked to Agulhas ring formation. Thus, the total number of ring-shedding events, 6 yr^{−1}, is far greater than the number of meander-driven events, which adds up to 1.3 yr^{−1}.

Hence, it appears that most anomalies hitting the African coast near the source region of the Agulhas are dissipated, effectively meeting their “western boundary graveyard” (Zhai et al. 2010). This leads to the conclusion that anomalies in the source flows of the Agulhas Current are unlikely to constrain ring-shedding events, overturning the paradigm of the last decade (Beal et al. 2011). Our results, together with those of Rouault and Penven (2011), Weijer et al. (2013), and Loveday et al. (2014) suggest that other local and remote mechanisms with intrinsic or external forcings—such as winds, Rossby basin modes, and coupled climate modes—are better candidates for the control of ring shedding and Agulhas leakage variability.

## Acknowledgments

The authors thank Adam Houk for the processing of the current meter data. This work was supported by the U.S. National Science Foundation through the ACT project, Award OCE-0850891. The altimetry data used are produced by SSALTO/Duacs and distributed by AVISO (http://www.aviso.oceanobs.com/duacs/).

## APPENDIX

### Methodology for Analytic Correlations and Rotary EOFs

#### a. Analytic signals and analytic correlation

*x*(

*t*) is a real-valued time series, its complex-valued analytic transform

*x*(

*t*) is

*x*(

*t*) =

*x*

_{0}cos(2

*πνt*), where

*x*

_{0}and

*ν*are constants, since the Hilbert transform of cos(

*x*) is −sin(

*x*), we find

*x*

_{a}(

*t*) and

*x*

_{b}(

*t*), with different phases

*ϕ*

_{a}and

*ϕ*

_{b}, as an example because of signal propagation. Thus,

*x*

_{a}(

*t*) and

*x*

_{b}(

*t*) is defined as the Pearson product-moment correlation coefficient between their analytic transforms:

*ϕ*

_{b}−

*ϕ*

_{a}, and the absolute value of

*π*/2, because in those cases the standard correlation has a value of almost zero.

#### b. Rotary empirical orthogonal functions

**w**(

*t*) be a vector variable function of time

*t*, with Cartesian components

*u*(

*t*) and

*υ*(

*t*), which in our case correspond respectively to along-track and cross-track components of velocity. The Cartesian pair of analytic signals

*u*

_{+}(

*t*) and

*υ*

_{+}(

*t*) associated with

*u*(

*t*) and

*υ*(

*t*), respectively, can be used to form another pair of rotary (analytic) signals (Lilly and Olhede 2010):

*a*

_{+}(

*t*) and

*a*

_{−}(

*t*) are real-valued amplitudes, and

*ϕ*

_{+}(

*t*) and

*ϕ*

_{−}(

*t*) are phases in radians. The Fourier components of

*w*

_{+}(

*t*) are zero for negative frequencies and equal to the Fourier components of

*w*(

*t*) for positive frequencies, while the Fourier components of

*w*

_{−}(

*t*) are also zero for negative frequencies but equal to the negative Fourier components of

*w*(

*t*) at the corresponding positive frequencies. Thus, an alternative representation of

*k*= 1, …,

*M*individual time series

*w*

_{k}(

*t*), from which we calculate the associated 2

*M*rotary time series

*w*

_{+k}(

*t*) and

*w*

_{−k}(

*t*). The rotary EOF analysis starts with building the complex-valued autocovariance matrix of

*w*

_{+k}(

*t*) and

*w*

_{−k}(

*t*), which has dimensions 2

*M*× 2

*M*. Then, using standard algebra for complex-valued matrices, the eigenvectors and the PCs, all complex valued, are calculated. Let us now consider

*n*th eigenvector rotary components for the

*k*th time series, and the corresponding

*n*th principal component time series

*a*

^{n}(

*t*), which can be written

*n*of the two

*k*th rotary component time series are

*k*th velocity time series in complex form for mode

*n*is

*n*, and have a spatially varying part or relative phase

*n*and index

*k*.

*n*are related by construction to the well-known variance or standard deviation ellipses (e.g., Emery and Thomson 2001) of the variability associated with that mode. The standard deviation ellipses for the

*n*.

*γ*

*(*

_{k}*t*) measured counterclockwise from the

*n*has a slowly varying angular frequency, and the phase of

Offshore of mooring G, only the cross-track geostrophic velocity component *υ* is obtainable from the CPIES, so the velocity variance there is rectilinear. To apply the rotary EOF analysis we need to ensure there are no discontinuities in the progression of the horizontal velocity vectors from two-dimensional to rectilinear between mooring G and CPIES pair P3–P4 (see Fig. 1). To do this we note that a rectilinear vector time series can be written as the sum of two counterrotating rotary time series with equal magnitude and phase. Therefore, we first calculate the equal-amplitude rotary components of the rectilinear *υ* profiles for the two CPIES pairs and then interpolate linearly in the horizontal direction each rotary component onto the regular grid of the array, instead of interpolating the Cartesian components as in Beal et al. (2015).

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^{1}

PC1 and PC2 are uncorrelated by construction over the whole time period of analysis (Preisendorfer and Mobley 1988).

^{2}

Since −*T*_{c} leads RPC1 by 146°, *T*_{c} lags RPC1 by 34°.