Lagrangian and Eulerian estimates of circulation in the lee of Kapiti Island, New Zealand

ARTICLE IN PRESS Continental Shelf Research 30 (2010) 515–532

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Lagrangian and Eulerian estimates of circulation in the lee of Kapiti Island, New Zealand Stephen M. Chiswell , Craig L. Stevens National Institute of Water and Atmospheric Research, PO Box 14-901, Kilbirnie, Wellington, New Zealand

a r t i c l e in fo

abstract

Article history: Received 16 April 2009 Received in revised form 27 October 2009 Accepted 6 January 2010 Available online 18 January 2010

Lagrangian drifters, moored acoustic Doppler current meters and hydrographic observations are combined with wind observations to describe the mean and variable nature of flow around Kapiti Island, New Zealand. Thirteen day-long deployments of up to six Lagrangian drifters show the mean flow is to the southwest, with evidence of stronger flows in the channel separating the island from the mainland, and an island wake in the lee of the island. Vortices in this island wake may be tidally driven. Scaling considerations suggest the flow is strong enough that tidal-generated vortices are shed on each tidal cycle. Both the drifters and mooring data suggest that the d’Urville Current around Kapiti Island has a significant wind-driven component. During north-westerlies, the drifters tend to hug the coast, and south-eastwards flows in the Rauoterangi Channel are accelerated. We suggest the observed correlation is the local expression of a South Taranaki basin scale response to the winds. & 2010 Elsevier Ltd. All rights reserved.

Keywords: Lagrangian drifters Kapiti Island Tidal rectification Larval dispersion Eddy diffusion

1. Introduction Kapiti Island in the South Taranaki Bight/Cook Strait region of New Zealand is 9.6 km long by 2.2 km wide and is separated from the North Island by the 5.6 km wide Rauoterangi Channel (Fig. 1). As well as being a popular recreational area, the Rauoterangi Channel contains the Kapiti Marine Reserve, which has been presumed to be a nursery for some species such as blue cod or butterfly fish (Stewart and MacDiarmid, 2003). The general characteristics of the coastal currents in the South Taranaki Bight were established some time ago from drift card measurements (Brodie, 1960; Heath, 1969) and sporadic radiotracked Lagrangian drifter measurements (Sanderson, 1979). Subtropical water in the d’Urville Current flows northwards along the west coast of the South Island and then into Cook Strait and retroflects, so that the mean flow around Kapiti Island is to the southwest into Cook Strait. Upwelling of cold water to the sea surface off west coast of the South Island was observed by Garner (1961) and this water appears in the d’Urville Current (Bowman et al., 1983a). Bowman et al. (1983b) observed the upwelling as an elongated cold-core plume extending northwards into the South Taranaki Bight. Cyclonic eddies in this upwelling plume appear to be stable for up to two weeks, allowing increased primary production, followed by increased zoo-plankton abundances and supporting higher trophic levels (primarily squid) (Foster and Battaerd, 1985). The d’Urville Current may be variable in time

 Corresponding author.

E-mail address: [email protected] (S.M. Chiswell). 0278-4343/$ - see front matter & 2010 Elsevier Ltd. All rights reserved. doi:10.1016/j.csr.2010.01.004

(Bowman et al., 1983b; Bowman et al., 1983c), and perhaps influenced by coastal trapped waves originating from wind forcing in Cook Strait (Cahill et al., 1991). The South Taranaki Bight and Cook Strait is a region known to have strong tides (Vennell, 1994). Tidal circulation in the region can be inferred from an existing numerical tidal model (Walters et al., 2001), although validation of this model has been limited (Stanton et al., 2001). There have been few systematic studies of the non-tidal circulation in the region, so that it would be safe to say that the exact nature of the flows in the region, and around the island in particular, is largely unknown. Studies elsewhere have shown that tidally-rectified eddies entrained in the lee of islands may be effective in entraining plankton and fish larvae (e.g., Furukawa and Wolanski, 1998; Wolanski et al., 1996), and in the summers of 2007 and 2008 a series of experiments was made around Kapiti Island using Lagrangian drifters to investigate possible entrainment of fish larvae in presumed tidally-generated vortices (Shima et al. in prep.). Up to six Lagrangian drifters were released near the island in 13 separate deployments over the two summers with each deployment lasting about one day. About half the drifters had larval traps attached that were designed to collect fish larvae during the hours of darkness. In addition to the drifters, two acoustic Doppler current profilers (ADCP) were moored near the island for a month, vertical profiles of temperature and salinity were made around the island on three separate days, and a limited number of vessel-based ADCP surveys were made. Lagrangian drifter studies are becoming more common in physical transport studies, and perhaps even more so in biophysical work (e.g., Rasmussen et al., 2009). The data

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Fig. 1. Left-hand panel: Map of study region showing the trajectories of all drifters released during the study (green lines). The locations of the Rauoterangi Channel and Tarapunga Shoal (‘T’) moorings have been marked with asterisks. Right-hand panel: Mean 2001–2005 February sea surface temperature (SST) from NOAA Pathfinder climatology. Inset shows New Zealand. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

presented here provide a better understanding of the mean and variability in the flow around Kapiti Island. The purpose of this article is to quantify Lagrangian and Eulerian flow statistics in the lee of an island. Questions posed include what are the mean, wind-driven and tidal flows during the experiments. Furthermore, we also document evidence of tidal vortices and make some estimate of the horizontal eddy diffusivity.

2. Methods 2.1. Drifters The Lagrangian drifters used in this study consist of a surface float containing two internally-recording GPS receivers and a radio-telemetry link attached to a holey-sock drogue 1 m in diameter, 5 m long, set about 1.5 m below the surface float. The surface floats were ballasted with lead weights so that they had minimal exposure to the wind. Slightly negatively buoyant larval light traps (Shima et al. in prep.) were attached above the drogue to some drifters during each experiment. A guide developed as part of the WOCE programme is to seek a 40:1 ratio of submerged to un-submerged cross-sectional area in order to minimise windage (Niiler et al., 1995). The present design had a slightly under-sized drogue for the surface floats. However, the addition of a light trap increased the area of the drag element. The drifters were deployed and recovered from an 8-m research vessel equipped to track the drifter telemetry. Because of the small size of the boat, deployments and recoveries were weather-dependent, and experiments were conducted only when the forecast winds were less than 25 knots. The first deployment of drifters took place near the southern end of Kapiti Island on 16 January 2007 (NZ Summer Time). All but one of the drifters were then redeployed in situ, and the drifters were finally retrieved on 18 January 2007 about 30 km offshore. This distance was judged too far offshore for safe boat operations, so in all further experiments, the drifters were recovered about 20 hours after deployment. Subsequently, drifters were deployed 6 more times in 2007, and 5 times in the summer of 2008. There were a total of

Table 1 Deployment times, durations, and number of drifters for the 12 drifter experiments. Deployment date (NZ Summer Time)

Duration (hours)

Number of drifters

16-Jan-2007 19:00 18-Jan-2007 10:20 24-Feb-2007 12:40 25-Feb-2007 12:05 28-Feb-2007 17:21 02-Mar-2007 10:11 03-Mar-2007 10:09 15-Jan-2008 10:08 17-Jan-2008 12:01 09-Feb-2008 14:48 12-Feb-2008 12:52 13-Feb-2008 12:42

37 23 21 20 15 23 22 23 20 21 21 20

6 4 6 4 6 6 5 2 4 6 6 6

13 deployments, the first two were combined to produce one experiment, whereas the remaining deployments are regarded as separate experiments—thus there were 12 experiments. Initial positions varied based on the requirements of the fish larvae tracking experiments. Data from the primary GPS unit were used when available. Occasionally the primary unit failed for various reasons, and data from the backup GPS unit were processed, although these are of lesser quality. The primary GPS data were recorded with a discretization interval of  8 m, which is larger than the inherent uncertainty in the GPS measurement ( 2–3 m), whereas the backup GPS data showed rms error of about 50 m. Some drifters went aground—these were excluded from this analysis, and in all there were a total of 61 useable drifter trajectories. Table 1 lists the start time, approximate duration and number of useable drifters in each experiment.

2.2. Vessel-mounted ADCP During 2–4 March 2007, vessel-based ADCP flow measurements were made with a RDI 3 kHz Workhorse Sentinel profiler.

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The ADCP was mounted on an swinging arm on the starboard side of the vessel and was configured to measure 4 m-range cells in bottom-tracking mode (Fong and Monismith, 2004) to determine accurate absolute velocity. 2.3. Moored ADCP Moored ADCPs were deployed at two sites from mid-January to mid-February 2008. The first site, which we designate the ‘Shoal’ mooring at 401 53.550 S, 1741 51.80 E was approximately 0.8 km from the southern tip of Kapiti Island near Tarapunga Shoal (Fig. 1). A 600 kHz Aanderaa RDCP was moored in approximately 58 m water depth from 12 January to 12 February 2008. The instrument was set to record 50 bins with a 2 m bin size, overlapped by 50%. The top bins were surface contaminated, and were removed so that final data set extends from 10 to 54 m below the surface. The second site, which we designate the ‘Channel’ mooring, at 401 53.30 S, 1741 56.20 E, was in the Rauoterangi Channel (Fig. 1). A 300 kHz RDI Workhorse Sentinel was deployed in approximately 60 m water depth from 12 January to 12 February 2008. The instrument was set to record 25 bins with a 2 m bin size at 5 min ensembles. The final data set extends from 8 to 54 m below the surface. 2.4. CTD An internally-recording Seabird SBE 19 + with conductivity, temperature and pressure sensors was deployed manually over the side of an 8 m boat in January 2008. The CTD records data at 4 Hz, and was lowered sufficiently slowly to give around 0.2 m vertical resolution—approximately the scale of the conductivity cell on the instrument. On 16 January, a section was made extending into the Rauoterangi Channel from the north-east tip of Kapiti Island. The following day, further CTD casts were made near the southern end of the island. 2.5. Mana Island winds Wind speed and direction measured every three hours at Mana Island (  20 km to the south of Kapiti Island, Fig. 1) are available from the NIWA climate database (http://www.niwa.co.nz/ser vices/clidb). Winds from Mana Island were considered to be more representative of the study area than nearby sites on the North Island because the island is relatively small and orographic effects on the island likely to be less than on the mainland.

3. Data 3.1. CTD CTD casts taken in January 2008 show large temporal and spatial differences in both salinity and temperature profiles. The casts can be clustered into two groups—those taken near the north end of Kapiti Island and those taken near the south end of the island. All the northern stations (Fig. 2) show a relatively-low-salinity surface layer, about 10 m thick, with surface salinities about 34.77. We presume this relatively-low-salinity surface layer is the result of fresh water inflow from the major rivers north of the study area, principally the Manawatu and Rangitikei Rivers (Fig. 1), although smaller local rivers might also contribute to this low salinity. Below this surface layer, deeper salinities close

517

to shore reach about 35.07, which is approximately the salinity of the dominant water mass in the South Taranaki Bight (Subtropical Water, Bradford-Grieve et al., 1991), however, the station closest to Kapiti Island (station 9) shows slightly fresher deep salinities of 35.02. Salinity shows some interleaving in the 20 m below the base of the low-salinity surface layer. Temperature in the low-salinity surface layer ranges between 19 and 20 1C with lower temperatures offshore, consistent with mean summertime SST (Fig. 1). Temperature decreases with depth generally showing a strong thermocline below the lowsalinity surface layer. Temperature increases monotonically across the channel with cooler temperatures offshore at all depths. The spatial range in temperature across the Rauoterangi Channel at depth is approximately 0.5 1C. In contrast, profiles to the south of Kapiti Island (Fig. 2) show much less evidence of a low-salinity surface layer, with salinities typically about 35.0–35.1 throughout the water column, although there is much more variability in salinity with depth compared to the northern stations. This deep variability in salinity may well indicate mixing downwards of the low-salinity surface layer as it progresses southwards, possibly due to tides and/or winds. Temperature profiles above 30 m are generally similar across this group of casts, showing surface values of about 19 1C and similar vertical gradients. Below 30 m, however, the heterogeneity in temperature is quite marked. Casts outside of the Rauoterangi Channel show strong thermal stratification all the way to the sea floor, whereas profiles within the channel (Station 6,) show mixed layers extending over 20 m vertical extent, presumably reflecting boundary layer mixing associated with stronger speeds in the channel (see later).

3.2. Drifters Drifter tracks from each of the 12 experiments are shown in Figs. 3 and 4. The first experiment was conducted on 16 January 2007 when six drifters were deployed about 1 km south west of the south-western tip of Kapiti Island in two arrays. Each array was about 250 m across, and the arrays were separated by about 2.5 km. The drifters were recovered 24 hours later, redeployed relatively quickly at their recovery locations, and finally recovered on 18 January 2007, about 24 km west of Kapiti Island. During this deployment, Mana Island winds were generally from the south and five of the drifters travelled to the west, although with large tidal excursions of about 10 km. One drifter separated from the rest of the group and travelled to the north. There was no indication on recovery that the drogue was different to any of the other drifters. The remaining experiments were for much shorter duration. Generally, the drifters were deployed in the late morning or afternoon, and recovered early the following morning. Deployment locations varied, but usually the drifters were deployed in a patch about 100 m across. For the experiments of 18 and 24 January, the drifters were deployed near the southern end of Kapiti Island. For the remaining experiments the drifters were deployed near the northern inshore end of Kapiti Island, in the Rauoterangi Channel, or in one case off the western shore of Kapiti Island (3 March 2007). Visual examination of the drifter trajectories gives some feel for the complicated flow structure associated with Kapiti Island. Since the different deployments were made both at different locations and at different phases of the tides, the structure and character of the drifter trajectories around the island is quite different. However, one can make some subjective assessment that gives clues to the possible flows around the island. For example, drifters that remained in the Rauoterangi Channel and

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16 January 2008 16 January 2008

0

48’

50’ 9 10 11 12 13

Depth (m)

10 20 30 9

40

13 12 11

50

52’

10

60 15

16

17 18 Temperature °C

54’

19

20

0 10 Depth (m)

56’

58’

20 30 9

40

13 12 11

50 41 °S

52’

54’

56’

58’

10

60 34.7

175 °E

34.8

17January2008

34.9 Salinity

35

35.1

17 January 2008

48’

0

51’

54’

5

Depth (m)

10 7

20 30 40 50

4

4

5

3

2

6

60

6

15

57’

16

17 18 Temperature °C

19

20

0 3 Depth (m)

41 °S

10

2

20 30 40 50

48’

50’

52’

54’

56’

58’ 175 °E

60 34.7

34.8

34.9

23

6 45

35

35.1

Salinity Fig. 2. (a) Locations, (b) temperature, and (c) salinity plotted as a function of depth, for CTD casts made on 16 January 2008. (d) Locations, (e) temperature, and (f) salinity plotted as a function of depth, for CTD casts made on 17 January 2008.

did not get close to the island tend to show little eddying so that the trajectories are relatively linear—(25 February 2007, 9 February 2008), whereas those that got close to the island often became entrained in small-scale eddies. There is clear evidence for such an eddy (or eddies) at the southern end of Kapiti Island (16 January 2007, 24 February 2007, 3 March 2007). Nine drifters during 4 deployments made at least one, (but usually only one), tight loop that was typically 1 to 2 km in diameter (Fig. 5). These loops are considerably smaller than the 15 km tidal excursions seen in Figs. 3 and 4. In one case (16 January 2007) only one drifter got entrained in the eddy even though the other drifters were close by (  700 m). In another case

(24 February 2007), all drifters in the group became entrained in the eddy. Rotation rates of the eddies estimated from the time it took for the drifter to make the loops range between 2 and 12 hours, but were typically 7 hours. The loops are both cyclonic and anticyclonic and appear to be linked to the phase of the tide as determined from the NIWA tidal model. Rotation is strongest at local high or low tide, although the rotation can be in either sense at high or low tide. For example, on 16 January 2007, at local high tide (the transition from red to blue in the Fig. 3), the rotation was cyclonic, whereas two days later, the rotation was anticyclonic at local high

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Fig. 3. Trajectories for Lagrangian drifters released near Kapiti Island during the study. The trajectories are colour coded to indicate the phase of the tide within the Rauoterangi Channel. Slack tide on the transition from northward to southward flowing tide in the channel is indicated by the transition between red and blue. The duration of each experiment varied, but was generally about 20 hours. The duration of the 16 January 2007 experiment was 48 hours. Wind velocity measured at Mana Island is shown as red vectors. Each wind vector is plotted at the mean location of the drifters at the time of the wind measurement. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

tide. Where the drifter was within the loop for both high and low tides, the rotation appears to be in the opposite sense for adjacent tidal extrema. For example, on 18 January 2007, two drifters were entrained in the region for nearly one tidal cycle, and the rotation appears to be cyclonic at low tide following anticyclonic rotation at the previous high tide. As a result, the drifters performed a figure-of-eight track. In the one experiment when drifters passed through the eddy region at mid-tide (12 February 2008), there is little curvature in the flow, and no sense of an eddy. There is also evidence for similar eddy-like structures near the reef protruding out into the Rauoterangi Channel from eastern end of Kapiti Island (18 January 2007, 15 January 2008). There

may be similar eddies near the northern tip of the island (28 February 2007). Even though all experiments were made with drifters having similar initial separation, there is a large range in the subsequent dispersal of the drifters. In some experiments (e.g., 25 February 2007, 28 February 2007, 17 January 2008), the drifters showed relatively little tendency to separate. For example, during a time of light winds (25 February 2007), the drifters stayed so close to one another that all tracks appear as one trajectory (Fig. 3). In other experiments (e.g., 16, 18 January 2007, 2 March 2007) the drifters were separated by relatively large distances on recovery. On one occasion the drifters remained close together initially but

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Fig. 4. As for Fig. 3, but for the final six experiments.

then separated when one or more of the drifters got entrained in eddies associated with the southern end of Kapiti (12 February 2008). The trajectories can be broadly categorised into two groups. One group (16 January 2007, 24 February 2007, 12 February 2008) consists of drifters that travelled to the west. Mana Island winds tended to be from the south for this group. The other group consists of drifters that stayed relatively close to the North Island coast (25 February 2007, 9 February 2008, etc.), and Mana Island winds tended to be from the north for this group.

3.3. Vessel-mounted ADCP Fig. 6 shows surface velocity vectors from the vessel-mounted ADCP survey made at the southern end of Kapiti Island after

redeploying drifters on 14 March 2007. The figure also shows tidal vectors coincident with the vessel sampling computed from the NIWA tidal model. The survey took approximately three hours to complete, during the southward-running phase of the tide, when substantial currents – reaching in excess of 1 m s  1 in places – were observed. The currents are primarily oriented along-channel (  451T), and so were rotated into along- and cross-channel components. Fig. 7 shows these along- and crosschannel components contoured in depth and time. Strongest velocities during the survey were in the Rauoterangi Channel, where speeds exceeded 1 m s  1, and to the west of the island, where speeds were about 0.8 m s  1. There was strong shear in the lee of the reef extending into the channel, so that speeds in the lee of the island were about 0.4 m s  1. Velocities from the tidal model, largely mimic the observed velocities, although model speeds in the lee of Kapiti Island tend to be less than observed. Both the observed and tidal-model currents show

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Fig. 5. Individual tracks for drifters that made loops in the lee of Kapiti Island. Colour coding is the same as for Fig. 3. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

horizontal shear in the flow as the currents are forced by continuity around the island into the island wake.

3.4. Moored ADCP Velocity records at both mooring sites are dominated by tidal flows superimposed on much lower amplitude low-

frequency variability. Along- and cross-axis axes for both Channel and Shoal mooring sites were determined by computing the principal axes of the detided low-pass filtered, verticallyaveraged flows (Fig. 8). As one might expect, flows at the Channel site are strongly constrained by the bathymetry, and both the low-frequency and mean flows are aligned along the axis of the channel. At the Shoal site, however, the lowfrequency flow is aligned approximately parallel with the local

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Fig. 6. Left-hand panel: Surface velocity vectors from ADCP transect data at the southern end of Kapiti Island recorded after redeploying drifters 4 March 2007. Right-hand panel: Tidal vectors from NIWA tidal model for the same times as the ADCP measurements were made.

Cross−channel 0

1

0

−0.2

0 0

.4

−0

0

.2

50

−0

60

−0.2

Depth (m)

−0 .2 0

40

70

Velocity (m s−1)

0.5

30

−0.2

0

20

0

−0.4 −0. 4

0

10

−0.5 80 90 −1

100 11

12 13 Time (hours local time)

14

Along−channel 0

1

0

−0. 2 −0. 6

70 80

Velocity (m s−1)

.6

−0.8

0.5

−0

0

−0.4 −0. 6 −0 .4

−0.6

−0.4

60

−0.4

−0.2

Depth (m)

50

2

40

−0.

−0. 4 .4 −0

30

−0.2

−0. 2 0. 2 −

20

−0.6

10

−0.5

90 −1

100 11

12 13 Time (hours local time)

14

Fig. 7. Along- and cross-channel sections of velocity from vessel-mounted ADCP transect plotted as a function of time (hours local time).

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Fig. 8. Detided and low-pass filtered vertically-averaged currents from the Rauoterangi Channel and Tarapunga Shoal moorings. Circles show the mooring locations, black axes show the principal axes, red vectors show the month-long mean currents. Green shows the low-pass filtered currents as vector arrows, but without the shafts; the base of the vectors is the mooring location. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

isobaths, but the mean flow is directed perpendicular to the isobaths. Vertically-averaged along-axis currents at the Channel site had a mean of 0.245 m s  1 to the southwest, and a total amplitude (including the tides) of about 1.2 m s  1, while cross-axis flows were much smaller in comparison (Fig. 9). These flows are strongly sheared in the vertical with the month-long averaged low-pass filtered along-axis flow having a value of about 0.3 m s  1 at 10 m depth and decreasing to about 0.1 m s  1 near the bottom. The across-axis mean circulation at this site shows surface flows directed towards Kapiti Island and a deeper return flow at 50 m directed towards the North Island. Vertically-averaged along-axis currents at the Shoal site had a amplitude of 0.7 m s  1 and a near-zero mean. In contrast, crossaxis currents had negligible amplitude yet had a mean of 0.12 m s  1 directed to the south-west (i.e., away from the island). There is large vertical shear in the along-axis direction with the surface flow directed towards the south-east while deeper flows were to the north-west. The cross-axis direction shows relatively less shear with a slight surface intensification.

3.5. Tidal model The NIWA tidal model is a high-resolution 2-dimensional finite element model for tides around New Zealand (Walters et al., 2001). The model is based on the 2-dimensional shallow water equations incorporating Boussinesq and hydrostatic approximations (Walters, 1992). The dependent variables, sea level and depth-averaged velocity, are expressed in terms of a harmonic

expansion of the tidal constituents. Non-linear terms are expressed as simple frequency sums and differences for the advection and wave drift terms, and by a series expansion for the quadratic bottom friction term. Both the equilibrium tide and the self-attraction/loading tide are included in the formulation. Continuity is included as a Helmholz equation. The finite element grid contains 32 065 nodes and 59 700 elements, with horizontal spacing between computational nodes varying from 98 km near the ocean boundaries to 300 m near the coast. Boundary conditions are zero normal flow at land boundaries and sea level specified at the open ocean boundary derived from TOPEX/Poseidon altimeter. The numerical simulations include eight tidal constituents—M2, N2, S2, K2, K1, O1, P1, and Q1. All the constituents interact non-linearly through friction.

4. Analyses 4.1. Tides The one-month duration of the two ADCP moorings is sufficient to extract the dominant diurnal and semi-diurnal amplitudes and Greenwich phase at each depth. Verticallyaveraged values for both sites, along with the NIWA tidal model values are listed in Table 2. The predicted and vertically-averaged observed tidal ellipses for the six major tides are plotted in Fig. 10, which also shows the observed tidal amplitudes as a function of depth. The dominant tide is the M2 tide (note the change of scale in the figure), and for this constituent, the observed

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Channel

Channel 0

3

−10 Depth (m)

Velocity (m s−1)

2 1 0 −1

−20 −30 −40 −50 −60 −0.4

−2

−0.3

−0.2

−0.1

0

0.1

0

0.1

−1

Velocity (m s ) Tarapunga

Tarapunga

3

0 −10 Depth (m)

Velocity (m s−1)

2 1 0 −1

−20 −30 −40 −50

−2 13

15

17

19

21

23

25

27

29

31 1

3

5

Jan

7

9

11

−60 −0.4

−0.3

−0.2

−0.1

Velocity (m s−1)

Feb 2008

Fig. 9. Left-hand panels: Vertically-averaged along- and across-axis flows from the Rauoterangi Channel and Tarapunga Shoal moorings, along with detided, low-pass filtered velocities. Right-hand panels: Vertical profile of the month-long averaged currents. Green lines are along-axis currents, blue lines are across-axis currents. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

Table 2 Tide constituents from the moorings and tidal model. Zonal Au (m s  1) Rauoterangi channel M2 0.30 0.08 S2 N2 0.07 K1 0.01 O1 0.02 P1 0.01

Meridional Au* (m s  1)

Au/Au*

Fu (1)

Fu* (1)

0.35 0.08 0.06 0 0.01 0

0.83 1.09 1.09 2.81 1.95 2.01

215 242 200 298 313 313

178 197 152 261 272 267

Tarapunga shoal mooring 0.20 0.14 M2 S2 0.05 0.02 0.03 0.02 N2 K1 0.01 0 O1 0.01 0 P1 0 1.89

1.38 2.02 1.20 3.85 1.85 141

6 37 344 102 141 112

336 353 312 106 117 0.01

Av (m s  1)

Av* (m s  1)

Av/Av*

Fv (1)

Fv* (1)

Fv  Fv*

37 45 48 37 41 36

0.56 0.14 0.13 0.02 0.04 0.01

0.63 0.14 0.12 0.02 0.04 0.01

0.88 1.01 1.10 1.23 1.12 1.14

216 236 195 299 304 304

210 226 184 306 318 312

6 10 11 7 14 8

30 44 32 106 117 112

0.41 0.08 0.08 0.01 0.02 0

0.13 0.02 0.02 0 0 0

3.17 3.56 4.03 4.64 7.34 7.47

193 221 146 350 301 301

156 173 132 286 297 292

37 48 14 64 4 9

Fu  Fu* (1)

Tidal amplitudes, A, and phases, F, from the Rauoterangi Channel and Tarapunga Shoal Moorings. Zonal and meridional values have subscripts u, and v, respectively. Model values have asterisk. The ratios of the observed to modelled amplitudes (Au/Au*) and (Av/Av*) and differences between observed and modelled phases (Fu  Fu*) and (Fv  Fv*) are also listed.

amplitudes tend to be relatively uniform in depth, except for a strong decrease in amplitude near the sea floor. M2 amplitudes are about 0.55 and 0.3 m s  1 for the zonal and meridional directions, respectively. The S2 and N2 amplitudes are about one-third the M2 values, and show more evidence of vertical

structure. The diurnal tides are much smaller than the semidiurnal tides, and show significantly more vertical structure, although with amplitudes of just a few millimetres, are probably very noisy. Observed phases (not shown) tend to be uniform with depth.

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M2

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Fig. 10. Tidal ellipses for the Rauoterangi Channel and Tarapunga Shoal mooring sites from both observations (blue= Channel, red = Shoal) and NIWA tidal model (green). Ellipses are shown for six major tidal constituents (M2, S2, N2, K1, O1, P1). Note the different scale for the M2 tide. Also shown are the observed tidal amplitudes as a function of depth from both sites (blue= Channel, red = Shoal). Zonal values are solid, meridional values are dashed lines. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

For the Channel site, the NIWA model amplitudes tend to agree with the vertically-averaged observed tides for all constituents as evidenced by the agreement in the major amplitudes of the ellipses. Model ellipses show the same orientation as the observed tides. However, the observed tides tend to be more rectilinear than the modelled tides, kinematically this occurs because model zonal and meridional phases are systematically about 301 and 101 different from the observed phases, respectively (not shown), but dynamically probably occurs because the model has limited resolution of the Kapiti Island and the Channel, so that topographic constraints are not as severe in the model as they are in reality. In contrast, the modelled tidal currents at the Shoal site tend to overestimate the observed currents, by as much as a factor of two.

The modelled ellipses tend to be larger, less rectilinear and oriented more meridionally than the observed ellipses. The model ellipse orientations are up to 451 different from the observed ellipses. It appears that the tidal model does not have enough resolution to resolve the small-scale spatial structure in the tides around the island.

4.2. Mean currents A common method to estimate pseudo-Eulerian mean currents from Lagrangian data is to average velocity estimates within regular latitude-longitude bins (e.g., Fratantoni, 2001). Here, we

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compute the mean velocity in 1/601 latitude-longitude bins from all 61 drifters by first removing a tidal velocity as predicted by the NIWA tidal model, and then computing the simple mean within each bin that had velocity estimates from four or more drifters. The choice of 4 estimates as a minimum was a compromise between trying to gain enough samples for statistically robust estimates, and gaining maximum spatial range for the mean. The resulting mean field (Fig. 11) shows mean currents towards the south/southwest (i.e., towards Cook Strait) with elevated speeds in the Rauoterangi Channel, reaching about 0.7 m s  1. There is some evidence of a wake in the lee of Kapiti Island where the mean currents suggest an anticyclonic loop just south-west of the southern tip of the island. Mean speeds in this wake region drop to as low as 0.2 m s  1. This is an area of convergence of trajectories, and so is reasonably well sampled in terms of the number of drifters contributing to these observations. The mean field computed from drifters is potentially biased because of spatial and temporal sampling variability in the drifter trajectories. Apart from the fact that all experiments were computed in summer months, and in relatively calm weather, there is a bias in speed caused by the fact that drifters that were in the flow at times of high velocity travelled further. Thus, for

example, the mean speed of drifters that travelled as far south as Mana Island (Fig. 1) is likely to be higher than the true mean for that region. To some extent, we have avoided this problem by computing the mean only where there were four or more drifters per bin. One can estimate the potential error uncertainty in the mean flow based on the number of drifters in each bin, but by almost any measure, the flows calculated here are unlikely to be statistically robust. Nevertheless, it is encouraging that mean speeds from the near-surface bins of the Channel and Shoal current meters are consistent with the drifter-derived mean flow, and we suggest that the fields depicted in Fig. 11 are representative of the structure, if not the details, of the summer time mean.

4.3. Wind-driven variability The drifter trajectories (Figs. 3 and 4) suggest that during northerly or north-westerly winds, the drifters tended to pass through the study area close to the North Island Coast (25 February 2007, 3 March 2008, 17 January 2008), whereas during southerly or south-easterly winds, the drifters tended to travel more offshore and to the west (25 February 2007, 12 February 2008).

Bin−averaged Drifter velocity 48’

1 m s−1

51’ 0.2

54’ 0.4

57’

41°S

3’

40’

44’

48’

52’

56’

175°E

Fig. 11. Mean velocity (blue vectors) and speed (colour) derived from averaging Lagrangian drifter velocities in 1 min (1/601) latitude-longitude bins (see text). Individual drifter trajectories are shown in red. Mean velocity from the two moorings is shown as black vectors. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

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One can test this observation more quantitatively by binaveraging the observed Mana winds at the drifter locations in the same manner as the mean field was computed, but by replacing the drifter velocities with the Mana wind velocities; i.e., the field at any location the average wind experienced by the drifters when they passed through that location. In order to gain some statistical reliability, this product was computed only when there were drifters from three or more days in each bin. Because of the requirement that this mean wind is only computed where there are at least three separate days of observations, the spatial extent of this field is limited compared to the overall drifter range (Fig. 12), but the results are consistent with the qualitative discussion above, and show that in the mean, northerlies were observed when drifters hugged the North Island coast, whereas southerlies were observed when the drifters were found to the west. Fig. 12 also shows a rose plot of the Mana Island winds. Winds are predominantly either from just east of south, or from the north-west with a principal axis along 1581T. The mooring data show wind-driven variability. On average, the low-passed along-axis flow at the Channel site was to the south, but the flow shows approximately 8-day periodicity with three periods when the flow briefly turned to the north (19, 25 January, 4 February 2008). In addition, there was an event of stronger than normal southward flow around 22 January 2008. The Shoal along-axis currents show similar oscillations, but delayed by about four days compared to the Channel events.

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These events appear to be correlated with wind events. For comparison with the currents, the winds were rotated into their principal axis components (i.e., the rotated x-axis is along 1581T, so that north-westerlies would have positive x-directed velocities and south-westerlies would have positive y-directed velocities). The winds were also scaled to have the same variance as the currents. When the low-pass filtered along-axis currents from the Channel site are overlaid on rescaled rotated wind from Mana Island (Fig. 13) there is a strong suggestion that the two time series are correlated with little lag. This apparent correlation comes about because of the approximately 8-day periodicity in the currents combined with weaker periodicity in the winds at about the same frequency. The rescaling of the winds is such that the peaks in the southward currents on 14, 22 January and 1 February approximately coincide with periods of increased northwesterly winds. Because of similar (but not so strong) periodicity in the Shoal site, along-axis currents there also appear to be correlated with the rotated Mana Islands winds, here, increased flow to the southeast is correlated with increased northwesterlies. Spectral coherence computed using a weighed overlapped segment method (Harris, 1978) shows coherence exceeds the 95% confidence levels for periods greater than about three days, but with only one-month-long records, the spectral resolution is low. Cross-axis currents from the two sites are significantly weaker than the respective along-axis components, and there is much less

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Fig. 12. Mana Island wind bin-averaged by drifter location in 2 min (2/601) latitude-longitude bins (see text). Inset shows wind-rose of Mana Islands winds.

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Channel mooring spectral coherence

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2008 Fig. 13. Left-hand panels: Low-pass filtered along-axis currents (blue) superimposed on rotated x-direction winds from Mana Island (green). The Mana Island winds have been scaled to have the same variance as the currents, and for the Channel site have been multiplied by  1. Right-hand panel: Spectral coherence and phase between the filtered currents and Mana Island winds. Coherence between zonal currents and rotated-zonal winds is shown in blue, and coherence between meridional currents and rotated-meridional winds is shown in red. Horizontal lines in the coherence plots indicate the 95% significance levels. Phase is only plotted where coherence exceeds the 95% significance level, and the 95% confidence levels in phase are indicated as vertical lines. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

evidence of an 8-day cycle in the flow, as a result there is little apparent correlation with the Mana Island winds, and computed spectral coherence is less than the 95% confidence limits. 4.4. Dispersion Lagrangian drifters can be used to estimate diffusivity in the ocean by considering the statistics of a patch of drifters. It is commonly assumed (e.g., Davis, 1991; LaCasce and Bower, 2000) that under homogeneous isotropic conditions, the variance of the particle displacement of a patch increases in time following

theory proposed by Taylor (1921). Initially, the patch size grows quadratically in time under what is termed the ‘ballistic regime’. The equations can be generalised to non-isotropic conditions so that during the ballistic regime, the patch displacement variance, sij = /di0 dj0 S, is: sij ðtÞ ¼ /u0i u0j St 2 ;

ð1Þ

where u0i ¼ ui u i is the Lagrangian velocity departure from the mean (in the i-th direction; 1 and 2 are the zonal and meridional directions, respectively).

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Eventually, for times longer than the Lagrangian timescale, the patch grows linearly in time during the ‘random walk’ regime (Rupolo, 2007): sij ðtÞ ¼ 2Kij t

ð2Þ

where Kij is the eddy diffusivity. For each deployment the mean drifter trajectory for all drifters in that deployment was computed, and hence the patch size, sij, from the variance of the drifter displacements about that mean. Fig. 14 shows the three components of sij (which we also denote as sxx = s11, syy = s22, and sxy = s12) plotted as a function of time for all 12 experiments. Since the spacing between drifters at time of deployment varied from one experiment to the next, the timeorigin of each experiment was chosen to be the time when patch variance was 100 m2. On the two occasions when the initial patch size was greater than this, the drifter trajectories were collapsed to have no spread at deployment (i.e., each drifter trajectory was displaced so that all the initial locations coincided), and the timeorigin was calculated when this re-initialised patch had a variance of 100 m2. The figure shows large variations in s as a function of time, reflecting the large differences in the spreading rates of the drifters from experiment to experiment (Figs. 3 and 4). For example, the 25 February 2007 experiment showed little change in s with time, whereas the 2 March 2007 experiment showed large dispersion even though the drifters were deployed in a similar location.

Eqs. (1) and (2) are only expected to hold when averaged over ensembles, and the figures also show the ensemble mean variance plotted against time. (This mean is only computed for the first 13 hours because some deployments only lasted this long after the patch variance was 100 m2.) The ensemble mean variance appears to be nearly quadratic in time, suggesting that dispersion is in the ballistic regime for times approaching one day. One can compute a ‘characteristic’ velocity for each component of s by fitting a quadratic of the form in Eq. (1), and these characteristic velocities are 0.055, 0.065, and 0.045 m s  1, respectively, for each component. The Lagrangian velocity variances /ui0 uj0 S can be directly estimated from the Lagrangian drifters. On timescales of a day or less, the tides are spatially uniform enough so they do not add to particle dispersion, and the tides should be considered as part of the deterministic rather than stochastic/turbulent flow (i.e., ). Thus the Lagrangian velocity anomaly timeu0i ¼ ui u i utide i series for each drifter was computed by removing the local mean (i.e., the field seen in Fig. 11) and the predicted tide at each location. The ensemble-average (i.e., over all 61 drifters) variances, /u10 u10 S, /u20 u20 S, and /u10 u20 S are 0.0632, 0.162, and 0.0572 (m s  1)2, respectively. In other words, according to Eq. (1), the zonal component of the patch size should increase as sxx = (0.063)2t2 during the ballistic regime and such a curve is indicated on the figure, with corresponding curves indicated for the other components. These computed curves are well within the envelope of the observed dispersion, except for the /u1u2S term which is just outside the upper limit to the envelope.

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Fig. 14. Patch size computed as the variance in drifter locations about the mean plotted as a function of time for all 12 experiments (green). Time has been adjusted for each experiment so that patches have variance of 100 m2 at time t= 0 hours (see text). The mean patch size is plotted in blue for times less than 14 hours. Linear least square regression to the mean patch size (solid red line) for times between 7 and 14 hours is used to estimate the local diffusivity. Dashed red lines indicate ‘ballistic regime’ spreading computed with observed ensemble-mean Lagrangian variances, respectively. (a) Zonal variance sxx versus time, (b) Meridional variance syy versus time, (c) Crossvariance sxy versus time, and (d) local eddy diffusivity ellipse tensor plotted in true coordinates (see text). (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

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Fig. 14 shows that even at the end of 13 hours, the dispersion is unlikely to have entered the random walk regime, but it is still instructive to compute local (or instantaneous) eddy diffusivities by fitting a linear slope to the mean curves over the time 8–13 hours (as indicated in the figure). Estimates of the eddy diffusivities Kxx, Kyy, and Kxy derived from linear fits as indicated in Fig. 14 are 150, 118, and 112 m2 s  1, respectively. The diffusion tensor can be rotated into its principal coordinates and plotted as an ellipse (e.g., Davis, 2005) as shown in Fig. 14c. The ellipse has its major axis orientated parallel to the coast, the diffusivity is not isotropic and the alongshore value 247 m2 s  1 is approximately 12 times the cross-shore value of 20 m2 s  1. This strong anisotropy could be a result of cross-shore shear in the long-shore velocity so that patches are stretched in the along-shore direction much faster than in the cross-shore direction. Because of the small number of estimates, and the large variability in the patch spreading rates, uncertainties in these values are large and difficult to estimate. They may well be wrong by a factor of 2 or 3, and the values quoted here should be considered little more than an order of magnitude estimate of the spreading seen in these experiments. 4.5. Mechanistic scaling The influence of Kapiti Island on the flow means that the usual assumptions of homogeneous conditions are highly unlikely to be met in this study—indeed our estimates of diffusivity are highly anisotropic (albeit with large uncertainty, see above). Even so, it is not clear just what the influence of the island is. One might expect the Rauoterangi Channel to be a constraining influence on the flow so that dispersion in the channel would be less than outside, and often this appears to be the case (25 February 2007). On the other hand, on at least one occasion (3 March 2007, 16, 18 January 2008 and 24 February 2008) drifters made tight loops in the lee of Kapiti Island, so that the island appears to be a source of eddies having a scale about half the width of the island. These eddies, which we presume are tidally driven would work to quickly break up a patch, and a simple scaling argument suggests the horizontal diffusivity resulting from this process could be O(uTW), where uT and W are representative velocity and island width scales, respectively. With tidal peak flows reaching 0.5 m s  1 and an island half-width of 1 km, the eddy diffusivity based on this argument would be about 500 m2 s  1. This value is about twice our estimated crossshore value, suggesting that our estimates are consistent with this order of magnitude estimate. Lloyd et al. (2001) experimentally investigated laminar subcritical oscillatory flows around a cylinder to determine the dependence of wake formation on Keulegan–Carpenter and Stability numbers. The Keulegan–Carpenter number is the ratio of the tidal eddy scale to the island scale: KC ¼ ut T=D

ð3Þ

and the Stability number is the ratio of frictional drag to water depth: S ¼ cf D=h

ð4Þ

where ut is the tidal speed, T is the period of the dominant tide (here semi-diurnal), cf is a coefficient of friction, D is a representative island diameter, and h the water depth. Lloyd et al. (2001) summarise previous work (Bearman et al., 1981; Obasaju et al., 1988; Williamson, 1985) by stating ‘‘For KCo7 a pair of attached vortices is generated in each half-cycle. For KC47 vortices are shed: for 7 oKCo15 one vortex is shed per half-cycle, for 15oKC o24 two vortices are shed, and so on.’’

From their own work, they concluded that four modes of wake formation are possible, depending on the value of KC and S, which they denote as: symmetric without pairing, symmetric with pairing, sinuous with pairing and vortex shedding (i.e., essentially going from more-attached to less-attached vortex generation). For our experiment, Kapiti Island is not cylindrical—it is approximately 9.6 by 2.2 km-and it is not immediately clear (even assuming that the scaling for cylinders applies to the island) what one should take as the characteristic diameter of the island. If one takes a representative tidal amplitude speed of 0.5 m s  1 (see Fig. 10) and takes D to be the island width (2.2 km), then KC =10. For this value of KC, Lloyd et al. (2001) obtain vortex shedding when S is less than 0.1 (their Fig. 16), and according to their summary of previous work, one would expect one vortex shed per half-cycle. On the other hand, if one assumes that D is the island length (9.6 km), then KC =2.3. For this value of KC, Lloyd et al. (2001) do not show vortex shedding in their figure, but interpolation of their figure would suggest that shedding would only occur for extremely low values of stability. According to their summary of previous work, one would expect the vortices to be attached to the island. The previous work is for situations with no mean flow. In our case, the mean speed is approximately the same as the tidal amplitude (Fig. 11). It is unlikely that the mean speed can be simply added to the tidal amplitude, but if it could, then KC would be about double the above estimates, so that the higher estimate of KC would put the system well into the vortex-shedding regime. An alternative approach to dealing with the mean flow is to consider an advective or mean flow equivalent to KC where the tidal speed is replaced by the mean speed, ur, so that KCr =urT/D. Coincidentally, because ut/ur is about unity KCr has the same magnitude as KC suggesting that eddy structures are advected away from the island before tidal reversal can bring them back to the island structure. The true value for KC in our case is likely to be somewhere between these various extremes, and while our drifters show some evidence that small-scale tidal vortices are generated in the wake, we cannot determine whether they are shed or not. A more complete description of the island wake processes applicable to Kapiti Island awaits numerical simulations (e.g., Stansby and Lloyd, 2001). It is worth noting that because the mean speed is comparable to the tidal speeds, it is likely that eddy structures are advected away from the island before tidal reversal can bring them back to the island structure. While KC provides a picture of the oscillatory balance (i.e., tides vs. scale), and KCr describes the likelihood of eddy residence near the island, it remains to characterise the mixing. This is especially important when taking a biophysical viewpoint and examining questions relating to productivity and ecological dispersion. Wolanski et al. (1996) introduced an island wake parameter that factors a turbulent Reynolds number with an elevation view aspect ratio (H/L; H is water depth, and L is the island scale) squared:   uL H 2 ð5Þ P¼ Kz L where u is a characteristic velocity (here we use u =ut =ur), and Kz is vertical diffusivity (here we use Kz = 10  4 m2 s  1). According to Wolanski et al. (1996), island wakes are stable when P=O(1), whereas if Pc1 the island wakes are likely to be unstable. Here, assuming H= 50 m, then P= 2.5  103, suggesting a highly variable wake pattern. The combination of KC, KCr, and P provide a picture of the important balances in the wake mechanics. To completely capture island wake variability, we would have needed many

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more observations than those performed here, but certainly the wake varies from deployment to deployment, principally due to tides.

5. Summary and discussion With 13 Lagrangian drifter deployments, two-month-long moored current meter deployments, sporadic vessel-mounted current measurements and CTD profiles, over two summers, this study provides relatively instantaneous (from a seasonal perspective) snapshots of the circulation around Kapiti Island. The nature of the flow variability means it is difficult to separate out temporal and spatial variability, especially when interpreting the Lagrangian drifter data. The current meter data suggest significant vertical structure to the currents, and because of the proximity of the coast and the varying bathymetry, there is likely to be significant vertical velocity. The drifters provide only nearsurface velocities, and this study has been largely a description of the surface circulation. The 3-dimensional structure to the circulation is largely unknown. The drifter measurements were made during periods of settled weather when small-boat operations were safe. Thus the sampling will be biased towards periods of relatively low vertical mixing, low wind shear, and high solar insolation. Nevertheless, the study has provided some information about the mean and variable flows in the region. The water column properties during these surveys are likely to be indicative of mid- to late-summer, with strong thermal stratification. Heterogeneity is marked in both temperature and salinity, indicating significant variability in vertical mixing processes. The near-surface low salinity indicates a local source of fresh water, which we surmise that is obtained from the large local rivers (Rangitikei and Manawatu Rivers). In the mean, the flow around Kapiti Island was to the southwest. Without exception, the net displacement during each of the drifter experiments was towards Cook Strait. Similarly, the dailymean flow in the Channel mooring was to the south-west 90% of the time. Both these observations indicate that the d’Urville Current was persistent during this study, and fit in with our prior knowledge of the current. The mean flow calculated from the drifters (Fig. 11) shows strongest flow in the Rauoterangi Channel, strong flows to the west, and an island wake region in the lee of Kapiti Island where speeds are about half to one-third of those in the channel. This island wake has length and width scales comparable to Kapiti Island. Eddy generation in the lee of islands has been noted elsewhere for some time (Wolanski et al., 1984, and references therein), and it is often presumed that vortex pairs can be generated in the lee of islands. Our data suggest both cyclonic and anticyclonic eddies can be present in the lee of Kapiti Island. The phasing with respect to the tides suggest that these eddies are tidal. We did not see both rotations at the same time, however, because of the sparcity of drifters, we cannot exclude the possibility that vortices are generated as pairs. The scaling arguments and calculation of Keulegan–Carpenter have large uncertainty, but our estimates of KC span the range previous workers have suggested would indicate one or two vortices are shed each tidal cycle. The lifetime of these vortices may well be short, and (at least during these experiments), the mean flow is so strong that they appear to be advected away from their generation region—there were no instances where drifters were maintained in the lee of Kapiti Island for more than one tidal period. An alternative explanation that cannot be entirely discounted is that the loops are due to the superposition of tidal ellipses and low-frequency non-tidal flow. In this case, however, one

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would expect the rotation of the loops to be consistent with tidal rotation, which is cyclonic. Both the drifters and mooring data suggest that the d’Urville Current around Kapiti Island has a significant wind-driven component. Mana Island’s winds are predominantly northwesterlies or south-easterlies. During north-westerlies, the drifters tend to hug the coast, and south-eastwards flows in the Rauoterangi Channel are accelerated. The wind-stress during these events is approximately perpendicular to the coast, so that the stress resolved into along-channel coordinates is essentially zero. The channel acceleration is in the wrong sense relative to the wind stress for it to be Ekman driven, so that one must invoke some other mechanism for the observations. We suggest the observed correlation is a local expression of a South Taranaki basin-scale response to the winds. For example, it may be that during north-westerlies, the short-term response to the stress leads to a piling up of water in the South Taranaki Bight north of Kapiti Island, and a resultant pressure gradient drives the flows to the south-west. It may also be that coastal trapped waves play a role in this observed correlation (Cahill et al., 1991). Finally, while largely beyond the scope of the present work, it is perhaps worth making some comments about the relevance of this work to biophysical interactions, particularly larval retention. The major findings in this work are that the along-shore d’Urville current during our study was consistently strong and to the south-west. The mean flow is comparable to the tidal flows, so that drifters’ along-shore velocity rarely reversed. Certainly away from the island, drifter retention times in the region were virtually negligible. A few drifters (e.g., on 18 January 2007) were caught very close to the island, became entrained in back eddies close to the shore, and spent several hours longer in the region than their counterparts that did not become entrained. Similarly some drifters did one or two (at most) loops in presumed tidal vortices generated in the lee of the island, but these eddies were small, apparently short-lived, and it would appear that they can only play a very limited role in retaining larvae close to the island. Not all larvae are planktonic, however, and many fish larvae are quite mobile. This study suggests that it is only mobile larvae that are likely to be retained close to the island for periods longer than a day or so.

Acknowledgements We thank Brett Grant, Craig Stewart, ‘Snout’, and the skippers of the Ruakawa Challenger, for their help and enthusiasm in data collection. Jeff Shima, principal investigator of the overarching programme is thanked for his support in proposing this work. Funding from a Marsden Grant from the Royal Society of New Zealand is gratefully acknowledged. We thank two anonymous reviewers for their comments which helped improve this article.

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