Dynamic Structure of the Kuroshio South of Kyushu in Relation to the Kuroshio Path Variations

Journal of Oceanography, Vol. 59, pp. 595 to 608, 2003 Dynamic Structure of the Kuroshio South of Kyushu in Relation to the Kuroshio Path Variations EITAROU OKA* and MASAKI KAWABE Ocean Research Institute, The University of Tokyo, Minamidai, Nakano-ku, Tokyo 164-8639, Japan (Received 22 August 2002; in revised form 19 December 2002; accepted 29 January 2003) The variation of velocity and potential vorticity (PV) of the Kuroshio at the PN line in the East China Sea and the TK line across the Tokara Strait were examined in relation to the path variations of the Kuroshio in the southern region of Japan, using quarterly data from a conductivity-temperature-depth profiler and a shipboard acoustic Doppler current profiler during 1987 97. At the PN line the Kuroshio has a single stable current core located over the continental slope and a significant maximum of PV located just onshore of the current axis in the middle part of the main pycnocline. On the other hand, the Kuroshio at the TK line has double current cores over the two gaps in the Tokara Strait; the northern core has a much larger velocity than the southern core on average during periods of the large meander of the Kuroshio, while the difference in strength between the double cores is small during the non-large-meander (NLM) period. At the TK line, PV in the middle pycnocline is variable; it is small and nearly uniform throughout the section for 40% of the total observations, while it has a significant maximum near the northern core for 30% and two maxima corresponding to the double current cores for 23%. The small, nearly uniform PV occurs predominantly during the NLM period, and is closely related to the generation of the small meander of the Kuroshio southeast of Kyushu. Keywords: Kuroshio, potential vorticity, current velocity, Tokara Strait, large and small meanders. 1. Introduction The Kuroshio flows northeastward along the continental slope in the East China Sea with a small variation of the location. The spatial variation of current axis increases after the Kuroshio leaves the continental slope around 29 N, and is significant in the Tokara Strait south of Kyushu (Yamashiro et al., 1993; Yamashiro and Kawabe, 2002). In the further downstream region south of central Japan, the Kuroshio takes a large-meander (LM) path and a non-large-meander (NLM) path alternately, with a primary period of about twenty years (Fig. 1; Yoshida, 1964; Taft, 1972; Kawabe, 1987, 1995). The formation of the large meander, namely the transition process from NLM to LM, takes about four months, during which a small meander of the Kuroshio is generated southeast of Kyushu and propagates downstream to the Kii Peninsula (Yosida, 1961; Shoji, 1972; Kawabe, 1980). * Corresponding author. E-mail: okae@jamstec.go.jp Present address: Frontier Observational Research System for Global Change, Natsushima-cho, Yokosuka, Kanagawa 237-0061, Japan. Copyright The Oceanographic Society of Japan. Previous studies have indicated that the variation between the LM and NLM paths is related to the condition of the Kuroshio south of Kyushu. The Kuroshio takes only an NLM path when its volume transport is small, while it takes either an LM or NLM path when the transport is in the medium and large ranges (Kawabe, 1995). In the latter case, the meridional change of position of the Kuroshio surface axis in the Tokara Strait is closely related to the variation between LM and NLM paths. The Kuroshio surface axis in the Tokara Strait is located farther north during the LM period than the NLM period on average. It shifts northward (southward) about four months before an LM path begins (terminates), corresponding to the formation (decay) process of large meander (Kawabe, 1995; Yamashiro and Kawabe, 1996). A similar relation between the large meander and the northern position of the Kuroshio in the Tokara Strait was reproduced by numerical experiments described in Akitomo et al. (1991, 1997). Kawabe (1996), using a simple dynamical model, concluded that the curvature of the Kuroshio axis south of Kyushu strongly influences the downstream Kuroshio path and must be smaller for the LM path than the NLM path. This relation was shown to hold in the real ocean 595

Fig. 1. Typical paths of the Kuroshio (Kawabe, 1995). nnlm and onlm are the nearshore and offshore non-large-meander paths, respectively. tlm is the typical large-meander path. Thin lines indicate isobaths of 500 m. The lines of PN and TK are CTD lines of the Nagasaki Marine Observatory of the Japan Meteorological Agency. by an analysis of water temperature south of Kyushu (Yamashiro and Kawabe, 2002). Thus, the position and shape (curvature) of the Kuroshio surface axis in the Tokara Strait are associated with the Kuroshio path in the southern region of Japan. What about the vertical structure of the Kuroshio? The current axis of the Kuroshio inclines vertically in general, as it shifts offshore as depth increases (Masuzawa, 1954; Masuzawa and Nakai, 1955). This vertical inclination is larger for the LM path than the NLM path in the whole southern region of Japan including the Tokara Strait (Kawabe, 1985, 1995), although it changes little over the continental slope in the East China Sea (Fujiwara et al., 1987; Yamashiro et al., 1990; Oka and Kawabe, 1998). The vertical structure of the Kuroshio in the Tokara Strait may be related to the Kuroshio path in the southern region of Japan. The structure of potential vorticity (PV) in the Tokara Strait may also be related to the downstream Kuroshio path, since the necessary conditions for instability of a quasi-geostrophic current are derived from a distribution of PV across the current (Pedlosky, 1964). The Gulf Stream has a maximum of PV just on the onshore side of the maximum velocity, and the possibility of instability has been pointed out (Watts, 1983; Bower et al., 1985; Leaman et al., 1989; Hall and Fofonoff, 1993; Hall, 1994). As for the Kuroshio, Chen et al. (1992) showed distributions of PV in two sections in the East China Sea, located between the separation point of the Kuroshio from the continental slope and the Tokara Strait (Fig. 2). PV in the western (upstream) section has a similar maximum to that of the Gulf Stream, while PV in the eastern (downstream) section has two maxima just onshore of two velocity maxima. The double maxima of PV in the eastern section correspond to the double current cores of the Kuroshio in the Tokara Strait shown by Nakano and Kaneko (1990), Bingham and Talley (1991), Nakano et al. (1994), and Feng et al. (2000). The Japan Meteorological Agency (JMA) has conducted observations quarterly since spring 1987 with a conductivity-temperature-depth profiler (CTD) and a shipboard acoustic Doppler current profiler (ADCP) at the PN and TK lines (Fig. 2). Using the CTD and ADCP data, the vertical structure of current velocity and PV of the Kuroshio south of Kyushu is examined in the present paper, particularly in relation to the Kuroshio path in the southern region of Japan. The data and the calculation of PV are explained in Sections 2 and 3, respectively. The characteristics of velocity and PV of the Kuroshio in the East China Sea and the Tokara Strait are described in Section 4. In Section 5, the variation of velocity and PV of the Kuroshio in the Tokara Strait is examined in relation to the variation between the LM and NLM paths as well as a small meander of the Kuroshio generated southeast of Kyushu. A summary and discussion are given in Section 6. 2. Data Quarterly data of CTD and shipboard ADCP during 1987 97, acquired and processed by the Nagasaki Ma- 596 E. Oka and M. Kawabe

Fig. 2. CTD stations at the PN and TK lines (open circles) and the typical path of the Kuroshio (arrow). Dots show tide stations at Naze (Naz), Nakano-shima (Nak), and Nishinoomote (Nis). Solid lines show the two CTD lines of Chen et al. (1992). rine Observatory of the JMA, were used in this paper. Observation months in each season are January February (winter), April May (spring), July August (summer), and October November (fall). The data at the PN line from summer 1989 to spring 1997 and at the TK line from spring 1987 to spring 1997 were used. The data at the PN line from spring 1987 to spring 1989 were not used due to less dense station spacing over the continental slope. No observation was conducted at the TK line in fall 1992. The CTD data at fourteen stations at the PN line were used (Fig. 2). Nine stations with an interval of about 15 nautical miles are named P9 to P17 southeastward. The other five stations in the middle of P9 and P10, P10 and P11,..., P13 and P14 are named P9.5, P10.5,..., and P13.5, respectively. At the TK line there are twelve CTD stations with an interval of about 10 nautical miles, named T1 to T12 southwestward. Salinity data at P12 in summer 1987 are questionable, and were determined in the same way as described in Oka and Kawabe (1998). The CTD Data at P11.5 in winter 1990, P13.5 in summer 1990, and P16 in spring 1991 are lacking, and were interpolated with the data at P11 and P12 (or P12 and P12.5), P13 and P14, and at P15 and P17, respectively. The water density over a steep slope at P10 P12, T1 T3, T6 T8, and T9 T11 was linearly extrapolated along isobars for geostrophic calculation. The average and standard deviation of water properties on isobars and isopycnals were calculated at points where data were available in more than 80% of the total observations. This criterion was decreased to 50% for isopycnals at the TK line as there were fewer data points. The ADCP data of current velocity at a depth of 100 m, averaged into 10-minute bins by the Nagasaki Marine Observatory, were used as the reference velocity in geostrophic calculation, after the normal component to the observation lines were averaged between pairs of CTD stations. The ADCP data at depths of 6 m and 50 m were not used because of included ageostrophic components such as Ekman flow, but the data at 6-m depth were used between T1 and T2 where the water depth is less than 100 m. The ADCP data were used for 28 observations out of 32 for the PN line and 34 observations out of 40 for the TK line. For the other observations with low quality or no measurement of ADCP, a reference level was assumed to be 700 db at P12 P17 following the JMA calculations, 800 db at T8 T9 on the basis of current-meter data (Feng et al., 2000), the shallower bottom between two stations in the shallow regions (P9 P10, T3 T6, T11 T12), and the middle depth of the stations over the slopes (P10 P12, T1 T3, T6 T8, T9 T11). Daily mean sea levels at Naze, Nakano-shima, and Nishino-omote from 1984 through 1997 were used after corrected for daily mean barometric pressure at Naze and Tanega-shima (for Nakano-shima and Nishino-omote). The sea levels were observed by the Hydrographic Department of the Japan Maritime Safety Agency (currently the Japan Coast Guard), and the data were supplied by the Japan Oceanographic Data Center. The barometric pressure data were obtained from the JMA. During 1987 97, the Kuroshio had medium and large amounts of volume transport and took the LM and NLM paths alternately (Kawabe, 1995, 2001). This period is divided into four kinds of period related to the large meander, as in Yamashiro and Kawabe (1996, 2002): the LM period except the LM-decay stage (1 Jan. 1987 6 Mar. 1988, 9 Oct. 1989 25 Jun. 1990), the NLM period except the LM-formation stage (23 Jul. 1988 21 Jul. 1989, 6 Jan. 1991 31 Dec. 1997), the LM-formation stage (22 Jul. 1989 8 Oct. 1989), and the LM-decay stage (7 Mar. 1988 22 Jul. 1988, 26 Jun. 1990 5 Jan. 1991). During these periods, the observations at the TK line were made seven (LM), twenty-eight (NLM), one (LM formation), and four (LM decay) times. 3. Method of Calculating Potential Vorticity Potential vorticity (PV) in continuous density stratification is defined as + Q = ( 2Ω ω ) ρ () θ, 1 ρ Dynamic Structure of the Kuroshio South of Kyushu 597

where Q is PV, Ω the earth rotation vector, ω relative vorticity vector of flow, ρ in-situ water density, ρ θ potential density, and is the gradient operator (e.g., Pedlosky, 1987). According to the scaling analysis (Bower, 1989), Eq. (1) is represented by the dominant terms as f ρ Q = ρ z 1 v ρ v ρ 1 ρ x z z x ρ κν ρ, z θ θ θ θ ( 2) where f is the Coriolis parameter, ν velocity in the main stream direction, κ streamline curvature, x and y the crossand along-stream coordinates (positive offshore and downstream), and z is the vertical coordinate (positive upward). The first term on the right-hand side of Eq. (2) is planetary vorticity, the second and third terms relative vorticity derived from velocity shears, and the fourth term is relative vorticity derived from streamline curvature. Using the hydrostatic approximation and the thermal wind equation, Eq. (2) yields ρ Q= gf p + g v ρ x p g 1 ρ ρ f ρ x x + gκν ρ p θ θ θ θ 2, () 3 where g is the gravity acceleration, and p is water pressure. The last term of Eq. (3), namely relative vorticity due to streamline curvature, is negligible at the PN line, because the Kuroshio flows almost straight along the continental shelf break. On the other hand, it is not negligible at the TK line where the Kuroshio turns counterclockwise (Figs. 1 and 2). Based on the relation between the streamline curvature and the latitude of the Kuroshio axis in Yamashiro and Kawabe (2002), the curvature (km 1 ) of the Kuroshio path at the TK line, κ, was roughly estimated by 1 1 κ = =, r 100 + ( Z 30) 50 ( 4) where r is radius (km) of curvature, and Z is latitude ( N) of the Kuroshio axis estimated with the Kuroshio position index defined by Kawabe (1995) and Yamashiro and Kawabe (1996). The minimum Z during 1987 97 is 29.44 N, and Eq. (4) with this Z yields κ of 0.14 10 6 cm 1. For this value, the ratio of the fourth term to the first term on the right-hand side of Eq. (3), κν/f, is 0.19, if the velocity v is assumed to be 1 m s 1. For the average Z of 29.91 N, κν/f is 0.14. Therefore, relative vorticity due to streamline curvature is 20% of planetary vorticity at most, and is smaller by one order on average. PV was calculated from Eqs. (3) and (4) after potential density was smoothed vertically using a Gaussian filter with a half width of 20 db. The value of ρ θ / p was assumed to be zero if it was negative. Values of ν/ x at a CTD station were calculated using geostrophic velocities between the station and the next one on both sides. The value of ν/ x at the end of the CTD section was assumed to be the same as that at the next station. The values of ν/ x near the sea bottom at T2 and T7 located in the middle of the slopes cannot be estimated, and were assumed to be the same as those at T3 and T8, respectively. 4. Dynamic Characteristics of the Kuroshio at the PN and TK Lines 4.1 PN line Figure 3(a) shows the distribution of average and standard deviation of current velocity at the PN line during 1989 97. The Kuroshio is the remarkable northeastward flow along the continental slope. The strong part of the Kuroshio, faster than 20 cm s 1, is located between P10 and P14, and the maximum velocity is 96 cm s 1 at the sea surface at P11.5 P12. The Kuroshio has one major current core over the continental slope. This feature is common to all the observations at the PN line during 1989 97 (figure 3.5 of Oka, 2000). Countercurrents exist east of P14 and under the Kuroshio over the continental slope at P10 P14. The velocity of the countercurrents is less than 10 cm s 1 west of P15 and reaches the maximum of 16 cm s 1 at the sea surface at P16 P17. The standard deviation of current velocity of the Kuroshio exceeds 20 cm s 1 except at depths greater than 150 db at P12 P13. It is especially large in two areas. One is in a surface layer at depths less than about 60 db between P9.5 and P14. The other is in a subsurface layer at 160 400 db west of P12 on the onshore side of the Kuroshio axis over the shelf break. The average of PV exceeds 6 10 12 cm 1 s 1 in a surface layer at depths less than 100 db, except near the sea surface east of P11, as well as in a subsurface layer at depths less than 300 db west of P13.5 (Fig. 3(b)). It is particularly large at depths less than 300 db west of P12 on the onshore side of the Kuroshio axis. A large onshore gradient of PV exists around the maximum of Kuroshio velocity, namely the Kuroshio axis, at depths less than 400 db. On the other hand, the average PV is small and relatively uniform with values less than 3 10 12 cm 1 s 1 at depths greater than 400 db and 250 db on the onshore and offshore sides of the Kuroshio axis, respectively. In particular, PV is almost uniform at depths of 250 600 db on the offshore side of the Kuroshio axis, corresponding to the main pycnocline. The distribution of the standard deviation of PV is similar to that of the average PV. The standard deviation is large at depths less than 300 db on the onshore side of the Kuroshio axis with 598 E. Oka and M. Kawabe

Fig. 3. Distribution of average and standard deviation of geostrophic velocity (cm s 1 ) (a) and potential vorticity (10 12 cm 1 s 1 ) (b) at the PN line during 1989 97. Positive velocity indicates northeastward current, and shading indicates the countercurrent. Inverted triangles on the top of each panel represent the locations of CTD stations. similar magnitude to the average. The variation of PV in a surface layer has a clear seasonal cycle due to the significant seasonal variation of water density at less than 24.5σ θ (Oka and Kawabe, 1998). In winter, water of less than 24.0σ θ does not exist, and PV at less than 24.5σ θ is mostly less than 10 11 cm 1 s 1 (Fig. 4(a)). In summer, the range of water density expands to below 21.4σ θ (Fig. 4(b)). PV exceeds 10 11 cm 1 s 1 at less than 24.0σ θ in the seasonal pycnocline and west of P12 on the onshore side of the Kuroshio axis with a strong horizontal gradient around the Kuroshio axis. PV reaches the maximum of 4.4 10 11 cm 1 s 1 at 23.8σ θ at P10.5. In a subsurface layer, distribution of current velocity and PV at greater than 25.0σ θ is similar between winter and summer, although the average velocity is a little larger in summer (Figs. 4(a) and (b)). As a result, the an- Fig. 4. Distribution of geostrophic velocity (cm s 1 ) and potential vorticity (10 12 cm 1 s 1 ) at the PN line averaged during 1989 97 with respect to potential density σ θ in winter (a), summer (b), and the annual mean (c). Positive velocity indicates northeastward current, and shading indicates the countercurrent. Inverted triangles on the top of each panel represent the locations of CTD stations. Dynamic Structure of the Kuroshio South of Kyushu 599

Fig. 5. Meridional variations of potential vorticity (10 12 cm 1 s 1 ) averaged in the middle-pycnocline layer between 25.0σ θ and 26.0σ θ at the PN line (P11 P17) during 1989 97. nual mean of PV at greater than 25.0σ θ is similar to each average in winter and summer (Fig. 4(c)). The main pycnocline is located in a range of water density between 24.5σ θ and 26.7σ θ. Variation of temperature and salinity on an isopycnal is small at 25.0 26.0σ θ in a middle part of the main pycnocline (Oka and Kawabe, 1998). In this layer, PV exceeds 10 11 cm 1 s 1 west of P12 on the onshore side of the Kuroshio axis, decreases sharply offshore just west of P12.5 around the Kuroshio axis, and is small and relatively uniform of 2 4 10 12 cm 1 s 1 east of P12.5. This feature is common to all the observations at the PN line during 1989 97 (Fig. 5). The PV averaged at 25.0 26.0σ θ has its maximum at P11 or P11.5, decreases sharply offshore within P11 P12.5, and is small uniformly east of P12.5, except for only a case of the maximum at P12. Thus, PV in the middle part of the main pycnocline is characterized by a strong gradient around the Kuroshio axis, between large PV and small, uniform PV on the onshore and offshore sides, respectively. This is the same feature as in the western section of Chen et al. (1992) and the Gulf Stream described by Watts (1983), Leaman et al. (1989), and Hall and Fofonoff (1993). PV at greater than 26.5σ θ around the bottom of the main pycnocline and in the deeper layer is small and decreases downward. 4.2 TK line The bottom topography at the TK line is quite different from that at the PN line. The topography at the TK line is characterized by two gaps divided by a seamount at T5 with water depth of about 320 m. The northern shallow gap is located at T3 T4 with a water depth of about 460 m, and the southern deep gap is at T7 T10 with a water depth of about 1400 m. Figure 6(a) shows the distribution of average and standard deviation of current velocity at the TK line during 1987 97. Two current cores Fig. 6. Same as Fig. 3 but for the TK line during 1987 97. Positive values in (a) indicate southeastward current. faster than 40 cm s 1 exist separately at T3 T5 and T6 T9 over the two gaps. The maximum velocity in the northern core is 59 cm s 1 at the sea surface at T3 T4, and that in the southern core is 53 cm s 1 at a depth of 200 db at T7 T8. Thus the Kuroshio in the Tokara Strait is divided by the seamount into two current cores with velocity of similar magnitude on average. This is different from the single current core of the Kuroshio at the PN line. According to 40 observations at the TK line during 1987 97 (figure 3.12 of Oka, 2000), the northern core is located at T2 T5, and the southern core is at T6 T11. The current cores do not extend to T5 T6 over the seamount, except in spring 1994. Both the northern and southern current cores have a large velocity greater than 40 cm s 1 in 35 observations out of 40, and only the southern current core has such a large velocity in the remaining five observations. In the 35 observations of double current cores, the northern core has a larger maximum velocity than the southern core in 25 observations (called Type 1 hereafter), and the southern core is stronger in the remaining 10 observations (Type 2). The Kuroshio with 600 E. Oka and M. Kawabe

Fig. 7. Distribution of geostrophic velocity (cm s 1 ) averaged for Types 1, 2, and 3 at the TK line during 1987 97. Types 1 and 2 are for the Kuroshio having double current cores with stronger northern and southern cores, respectively. Type 3 is for the Kuroshio with a single southern core. Positive values indicate southeastward current, and shading indicates the countercurrent. Inverted triangles on the top of each panel represent the locations of CTD stations. Fig. 8. Meridional variations of potential vorticity (10 12 cm 1 s 1 ) averaged in the middle-pycnocline layer between 25.0σ θ and 26.0σ θ at the TK line (T2 T10) during 1987 97. the single southern core is called Type 3. There is no case of a single northern core, because the deep part of the Kuroshio always passes through the southern deep gap and forms the southern core. Figure 7 shows averages of current velocity in the three types. In Type 1, two current cores faster than 40 cm s 1 exist at T3 T5 and T7 T10 at different depths of less than 250 db and 120 550 db, respectively. The maximum velocity in the northern core is 81 cm s 1 at the sea surface at T3 T4, and that in the southern core is 45 cm s 1. In Type 2, the velocity in the southern core reaches the maximum of 72 cm s 1 at 240 db at T7 T8 and a secondary maximum at T9 T10, while that in the northern core is at most 40 cm s 1. In Type 3, the velocity in the southern core reaches 92 cm s 1 at the sea surface at T7 T8, while the northern core almost disappears. A countercurrent exists over the northern gap. The surface current axis of the Kuroshio is associated with the northern core on one occasion and the southern core on another. It is located at T2 T5, T6 T7, and T6 T8 in most cases of Types 1, 2, and 3, respectively. The Kuroshio surface axis changes the position meridionally in a distance of about 90 km. On the other hand, the Kuroshio at depths greater than 500 db is located in the southern gap and has only the southern core. The deep axis of the Kuroshio at a depth of 500 db is located at T8 T9 in Type 1 and T7 T8 in Types 2 and 3, and the meridional variation of the position is much smaller than that at the sea surface. Therefore, the vertical inclination of the Kuroshio axis is large in Type 1 and small in Types 2 and 3. Thus, the vertical structure of the Kuroshio changes greatly in the Tokara Strait. The standard deviation of current velocity is large in the current cores (Fig. 6(a)). It is especially large in the northern core with a maximum of 52 cm s 1 at the sea surface at T3 T4. In the southern core it reaches a maximum of 37 cm s 1 at the sea surface at T7 T8 with large values extending downward to 900 db along the southern flank of the seamount. The larger standard deviation in the northern core than the southern core reflects the fact that the velocity in the northern core is quite different among the three types, being strong in Type 1, moderate in Type 2, and missing in Type 3, while that in the southern core is strong in all the types. The larger variation of velocity in the northern core was shown by Feng et al. (2000) using current-meter data in a section about 20 km downstream of the TK line. The average of PV exceeds 6 10 12 cm 1 s 1 in a middle part of the main pycnocline at depths less than 300 db north of T7, except the near-surface south of T2 and greater than 160 db at T4 (Fig. 6(b)). Around 100 200 db, PV reaches values greater than 8 10 12 cm 1 s 1 north of T7 and 10 11 cm 1 s 1 north of T4. That is, PV in this layer is large on the onshore side of the velocity maximum in the northern current core (northern current axis), secondly large between the northern and southern current axes, and small south of the southern current axis. In Dynamic Structure of the Kuroshio South of Kyushu 601

Fig. 9. Histogram of standard deviation of meridional variations in potential vorticity averaged in the middlepycnocline layer between 25.0σ θ and 26.0σ θ at the TK line (T2 T10). The standard deviation was calculated for each observation during 1987 97. Fig. 10. Eigenfunctions of the first and second EOF modes of potential vorticity averaged in the middle-pycnocline layer between 25.0σ θ and 26.0σ θ at the TK line (T2 T10) during 1987 97. The eigenfunction is normalized by the maximum value. The percentage of variance of each mode to the total variance is shown in parentheses of each panel. a deep layer, a large PV exists at 440 510 db at T7 T8 on the onshore side of the southern current axis, located over the southern flank of the seamount. Therefore, a large northward (onshore) gradient of PV exists at 100 200 db around the northern current axis and 440 510 db around the southern current axis, and a much smaller gradient exists at depths less than 400 db around the southern current axis. Thus, the structure of PV is much more complicated than the PN line, like the current structure, although the large gradient of PV around the current axis is common to both lines. Distribution of standard deviation of PV is similar to that of the average PV but not to that of the standard deviation of current velocity. Therefore, the large variation of PV in a subsurface layer at depths less than 300 db north of T7, in particular north of T4, and around 500 db at T7 T8 is mostly due to variation of water density. Fig. 11. Relation of time coefficients between the first and second EOF modes of potential vorticity averaged between 25.0σ θ and 26.0σ θ at the TK line (T2 T10) during 1987 97. For each mode, the time coefficients are normalized by the standard deviation. Year and season of each observation are shown under each mark. Circles, triangles, rectangles, and crosses indicate Groups 1, 2, 3, and 4, respectively. See the text for the difference between closed and open marks. The variation of PV in a surface layer at depths less than 100 db has a clear seasonal cycle due to significant seasonal variation of water density (figures 3.3 and 3.16 of Oka, 2000), like the PN line. The meridional distribution of PV averaged at 25.0 26.0σ θ in the middle pycnocline changes from time to time (Fig. 8). The spatial variation has a relatively low amplitude throughout the TK line for many observations, while it has a significant maximum or two maxima for some observations. This is different from Fig. 5 for the PN line at which PV always has a single significant maximum just on the onshore side of the Kuroshio axis. The histogram of spatial standard deviation of each curve in Fig. 8 shows two significant peaks at PV of 2.75 3.25 10 12 cm 1 s 1 and 3.75 4.25 10 12 cm 1 s 1 (Fig. 9). A standard deviation of less than 3.25 10 12 cm 1 s 1 defines a group of small spatial variations of PV, named Group 1. Group 1 has small PV, mostly less than 10 11 cm 1 s 1, and a small meridional variation of PV without any significant peak (Fig. 12). The spatial variations of PV were expanded with empirical orthogonal functions (EOF). The first-mode EOF has a negative peak at T3 and a positive peak at T6 602 E. Oka and M. Kawabe

Table 1. Number of observations in Types 1 3 and Groups 1 4 at the TK line during 1987 97. The Kuroshio in Types 1 and 2 has double current cores with stronger northern and southern cores, respectively. Type 3 has a single southern core. Groups 1 4 are defined in terms of meridional distributions of PV, as in Fig. 12 (see the text for the definition). Type Group 1 2 3 4 1 4 1 9 9 5 2 25 2 4 2 3 1 10 3 3 1 1 0 5 1 3 16 12 9 3 40 Fig. 12. Meridional variations of potential vorticity averaged between 25.0σ θ and 26.0σ θ in Groups 1 4 at the TK line (T2 T10) during 1987 97. and changes sign between them, while the second-mode EOF is positive or nearly null and has double positive peaks at T3 and T6 (Fig. 10). The time coefficients of the first and second modes of EOF for each observation are plotted in Fig. 11. The coefficients for Group 1 (closed circles) are near zero between 0.7 and 0.8 for the first mode and mostly negative for the second mode. Besides Group 1, we can define two groups according to coefficients which are negative for the first mode and positive for the second mode (closed triangles, Group 2) and positive coefficients for both the first and second modes (closed rectangles, Group 3). Group 2 has a large peak at T2 or T3 with a large northward (onshore) gradient of PV around T3 T4 located at the northern current axis (Fig. 12). The maximum of PV reaches about 2.4 10 11 cm 1 s 1. Group 3 has two large peaks of PV at T2 (or T3) and T6 with large onshore gradients located at the northern and southern current axes. The southern peak at T6 is more remarkable than the northern peak in many cases, and reaches 2.5 10 11 cm 1 s 1 at the maximum. Eight cases still remain in Fig. 11. By examining their spatial variations of PV, two open triangles and three open rectangles were included in Groups 2 and 3, respectively. The remaining three crosses are different from Groups 1 3 and were named Group 4. Group 4 has a single peak of PV around the southern current axis and small PV outside the peak, although location of the peak is different for each case (Fig. 12). Groups 1, 2, 3, and 4 were observed sixteen, twelve, nine, and three times during 1987 97, respectively. The spatial variation of PV in Group 2 is similar to that at the PN line and in the Gulf Stream. On the other hand, Groups 1 and 3 are unique in the Tokara Strait. Group 1 is more frequent than the other groups, and is most characteristic of PV in the Tokara Strait. Group 3 is similar to PV in the eastern section of Chen et al. (1992). This implies that the PV distribution in Group 3 emerges further upstream than the TK line, at least around 129 E (Fig. 2). The number of occurrences of Groups 1 4 of PV and Types 1 3 of current velocity is shown in Table 1. Group 2 mostly occurs in case of Type 1, and Group 3 mostly in case of Types 1 and 2. This agrees with the relation between velocity and PV at the PN line and the Gulf Stream. However, there is another group, Group 1, at the TK line, which occurs more frequently than the other groups, in case of every type of Types 1 3. Accordingly, one cannot conclude for the TK line that the types of velocity and the groups of PV correspond to each other. This is very different from the PN line and the Gulf Stream. The relation between the average velocity and the average PV shown in Fig. 6 reflects the relation of Groups 2 and 3 with current velocity, since Group 1 does not significantly influence the meridional variation of PV. The PV between 25.0σ θ and 26.0σ θ in every group is almost uniform vertically (Fig. 13). This implies that the characteristics of the meridional variation in Fig. 12 hold for any depth in the 25.0 26.0σ θ layer. Another prominent property found in every group is a PV maximum at 26.0 26.9σ θ at T7 T8 reaching greater than 10 11 cm 1 s 1. This maximum is located in the lower part of the main pycnocline and a little deeper. PV averaged in a layer of 26.4 26.7σ θ, corresponding to the lower Dynamic Structure of the Kuroshio South of Kyushu 603

Fig. 13. Distribution of potential vorticity (10 12 cm 1 s 1 ) averaged for Groups 1 3 at the TK line during 1987 97 with respect to potential density σ θ greater than 25.0σ θ. Inverted triangles on the top of each panel represent the locations of CTD stations. pycnocline, has a significant maximum at T7 and partly at T8 in all the observations, although magnitude of the maximum is variable (Fig. 14(a)). This is different from the PN line at which PV in this layer is small and uniform (Fig. 14(b)). The average PV at the onshoremost station is 1.2 10 11 cm 1 s 1 at the TK line (T7) and 0.3 10 11 cm 1 s 1 at the PN line (P11.5). PV in the lower pycnocline of the Kuroshio increases as it proceeds from the PN line to the TK line. This suggests that the PV is not conserved along the streamline, maybe by a supply of positive PV due to bottom friction at islands and seamounts between the lines. 5. Relation of Dynamic Structure at the TK Line to the Path Variations of the Kuroshio 5.1 Relation to the Kuroshio path in the southern region of Japan Current velocity and PV of the Kuroshio at the TK line are analyzed for four kinds of period related to the large meander (LM) of the Kuroshio, as in Yamashiro and Kawabe (1996, 2002), in terms of Types 1 3 for current velocity and Groups 1 4 for PV. Table 2(a) shows the number of occurrences of Types 1 3 during the periods of non-large-meander (NLM), LM, LM-formation, and LM decay. The number of observations in the LM-formation and LM-decay stages is too few for statistics, and the following discussion of Table 2 concerns the NLM and LM periods. During both periods, Type 1 is most frequent with Type 2 second. During the NLM period, Type 1 occupies 61%, Type 2 is 29%, and Type 3 is 11%. The percentages for the LM period are similar to those for the NLM period, although the number of data may be few for statistics. The average velocity during both the NLM and LM periods shows double current cores (Fig. 15(a)). The northern core is stronger for both periods, but the difference in velocity between the northern and southern cores is small during the NLM period and significant during Fig. 14. Meridional variations of potential vorticity averaged in the lower-pycnocline layer between 26.4σ θ and 26.7σ θ at the TK line (T2 T10) during 1987 97 (a) and at the PN line (P11 P17) during 1989 97 (b). the LM period; the maximum velocities in the northern and southern cores are 54 cm s 1 and 49 cm s 1 (NLM) and 73 cm s 1 and 58 cm s 1 (LM), respectively. This may reflect the fact that the position of the Kuroshio surface axis is farther north during the LM period than the NLM period on average (Kawabe, 1995; Yamashiro and Kawabe, 1996). In contrast to Types 1 3, the occurrence of Groups 1 4 for PV is quite different between the NLM and LM periods (Table 2(b)). During the NLM period, Group 1 is most frequent, occupying 50% of the total, and Group 2 is second with 25%. During the LM period, most observations (86% of the total) are in Groups 2 and 3, occupying 43% each, although the number of observations may be few for a precise conclusion. The average PVs for both the NLM and LM periods show double peaks at 25.0 604 E. Oka and M. Kawabe

Table 2. Number of observations in Types 1 3 (a) and Groups 1 4 (b) at the TK line for periods of NLM, LM, LM formation, and LM decay during 1987 97. (a) Period Type 1 2 3 1 3 NLM 17 8 3 28 LM 4 2 1 7 LM formation 1 0 0 1 LM decay 3 0 1 4 (b) Period Group 1 2 3 4 1 4 NLM 14 7 4 3 28 LM 1 3 3 0 7 LM formation 0 1 0 0 1 LM decay 1 1 2 0 4 26.0σ θ, located just north of the double current cores (Fig. 15(b)). However, the magnitude of the double peaks of PV is clearly different between NLM and LM. The maximum PVs in the northern and southern peaks for NLM (1.5 and 1.2 10 11 cm 1 s 1 ) are smaller than those for LM (1.8 and 1.6 10 11 cm 1 s 1 ). This reflects the much more frequent occurrence of Group 1 during the NLM period (50%) than the LM period (14%). 5.2 Relation to the small meander of the Kuroshio generated southeast of Kyushu The PV of the Kuroshio at the TK line is further examined in association with a small meander of the Kuroshio generated southeast of Kyushu. The transition from NLM to LM is accompanied by a generation of the small meander and its downstream propagation to the Kii Peninsula (Yosida, 1961; Shoji, 1972; Kawabe, 1980), although such a small meander does not always cause the NLM-to-LM transition. During 1987 97, the small meander was generated twelve times, according to the Quick Bulletins of Ocean Conditions issued by the Japan Maritime Safety Agency (currently the Japan Coast Guard). Only one case among the twelve in spring 1989 caused the NLM-to-LM transition. Four kinds of period are defined in relation to the small meander. First, the total period of 1987 97 is divided into two periods with and without small meander. The period with small meander is further divided into two periods, the small-meander period during which a small meander exists southeast of Kyushu (dashed curve in Fig. 16) and the propagation period during which the small Fig. 15. (a) Distribution of geostrophic velocity (cm s 1 ) at the TK line averaged for periods of the NLM and LM paths of the Kuroshio during 1987 97 with respect to water pressure. Inverted triangles on the top of each panel represent the locations of CTD stations. (b) As (a) but for potential vorticity (10 12 cm 1 s 1 ) with respect to potential density σ θ greater than 25.0σ θ. meander has propagated to the downstream region (dotted curve in Fig. 16). The period without small meander (solid curve in Fig. 16) is also divided into two periods, the period for one month preceding the small-meander generation (called the pre-generation period) and the remaining period (non-small-meander period). The number of occurrence of Groups 1 4 during each period is shown in Table 3. Group 1 occupies 100% during the pre-generation period, 80% during the small-meander period, and 86% (12 out of 14) for total of these periods. However, Group 1 is observed much less frequently during the other periods. During the propagation period, Group 1 is never observed, and each of Groups 2, 3, and 4 is observed once. During the non-small-meander period, Group 1 occupies only 17%, and most observations (78% of the total) are in Groups 2 and 3. Accordingly, PV at 25.0 26.0σ θ averaged during the pre-generation and small-meander peri- Dynamic Structure of the Kuroshio South of Kyushu 605

Table 3. Number of observations in Groups 1 4 at the TK line for four categories of period related to the small meander of the Kuroshio generated southeast of Kyushu. The first category is for periods for one month preceding the generation of small meander (pre-generation period). The second is for periods during which a small meander exists between the Tokara Strait and the east of Tanega-shima (small-meander period). The third is for periods during which the small meander has propagated to the downstream region between the east of Tanega-shima and the south of Shikoku (propagation period). The fourth is for periods during which the Kuroshio flows close to the coast between the Tokara Strait and Shikoku, except for the pre-generation period (nonsmall-meander period). Period Group 1 2 3 4 1 4 Fig. 16. Current paths of the Kuroshio in the region between the Tokara Strait and Shikoku in 1992, based on the Quick Bulletins of Ocean Conditions issued by the Japan Maritime Safety Agency (currently the Japan Coast Guard). The solid, dashed, and dotted lines indicate the Kuroshio path in the second half of February, the first half of March, and the second half of May, respectively. Fig. 17. Distribution of potential vorticity (10 12 cm 1 s 1 ) at the TK line averaged for the pre-generation and small-meander periods (a) and the propagation and non-small-meander periods (b) with respect to potential density σ θ greater than 25.0σ θ. Refer to the text and the caption of Table 3 for the definition of the periods. ods is much more uniform than that averaged during the propagation and non-small-meander periods (Fig. 17). Moreover, 92% (22 out of 24) of Groups 2 4 occur during the propagation and non-small-meander periods. Thus, the small meander occurs mostly in case of Group 1 and hardly in case of Groups 2 4. The PV distribution in Pre-generation 4 0 0 0 4 Small meander 8 1 0 1 10 Propagation 0 1 1 1 3 Non-small-meander 4 10 8 1 23 Group 1 may be necessary for the generation of small meander of the Kuroshio. Among the twelve small meanders during 1987 97, eleven were generated during the NLM period (8.0 years in total), and one was in the LM-decay stage. No small meander was generated during the LM period (1.9 years). Thus, the small meander is generated much more frequently during the NLM period than the LM period. This may be because Group 1 occurs much more frequently during the NLM period than the LM period (Table 2). 6. Summary and Discussion The hydrographic data of CTD and surface velocity data of ADCP at the PN line in the East China Sea during 1989 97 and at the TK line across the Tokara Strait during 1987 97 were analyzed to examine the variation of velocity and potential vorticity (PV) of the Kuroshio, in relation to the path variations in the southern region of Japan. The data were taken quarterly in January February (winter), April May (spring), July August (summer), and October November (fall) by the Nagasaki Marine Observatory of the Japan Meteorological Agency. The PN line crosses the continental shelf and slope almost perpendicular to the isobaths and the Kuroshio path, while the TK line is located over complicated bottom topography which is characterized by two gaps in the Tokara Strait, the northern shallow gap with water depth of about 460 m and the southern deep gap with water depth of about 1400 m. The Kuroshio at the PN line is characterized by a single current core, stably located over the continental 606 E. Oka and M. Kawabe

slope, while that at the TK line has double current cores over the two gaps. The maximum velocity in the northern core in the Tokara Strait is much greater than that in the southern core on average during the period of large meander (LM) of the Kuroshio, while the difference in strength between the two cores is small during the nonlarge-meander (NLM) period. This may reflect the tendency of the surface current axis in the Tokara Strait which is located further north during the LM period than the NLM period on average (Kawabe, 1995; Yamashiro and Kawabe, 1996). PV in the surface layer (less than 100 db) shows a large seasonal cycle at both the PN and TK lines, associated with the seasonal variation of water density. On the other hand, PV in the subsurface layer is much less variable than that in the surface layer, and shows different characteristics between the PN and TK lines, as summarized in the following paragraphs. In terms of the deeper layer, PV in the lower pycnocline between 26.4σ θ and 26.7σ θ is small and uniform in the cross-stream direction at the PN line, while it has a significant maximum over the southern flank of the seamount in the Tokara Strait at the TK line. PV in the lower pycnocline therefore increases from the PN line to the TK line. It seems that the PV is not conserved along the streamline, maybe by a supply of positive PV due to bottom friction at islands and seamounts between the lines. PV in the middle pycnocline between 25.0σ θ and 26.0σ θ at the PN line has a significant maximum just onshore of the Kuroshio axis, decreases sharply offshore around the axis, and is small and relatively uniform on the offshore side of the Kuroshio. This is similar to that of the Gulf Stream shown by Watts (1983), Leaman et al. (1989), and Hall and Fofonoff (1993). In contrast, PV in this layer at the TK line is variable, and its horizontal distribution is classified into four groups, named Groups 1 4, with respect to the magnitude of the meridional variation as well as the positions of significant maxima (Fig. 12). Group 1 is defined by small PV with small meridional variation. The other groups have significant variations. Group 2 has a northern maximum of PV located just onshore of the velocity maximum in the northern current core. Group 3 has northern and southern maxima of PV corresponding to the two current cores. Group 4 is a small group characterized by a relatively small southern maximum of PV. Groups 1 4 are observed sixteen, twelve, nine, and three times during 1987 97, respectively. These distributions of PV in the middle pycnocline at the TK line are related to the path variations of the Kuroshio in the southern region of Japan. Group 1 occupies 50% of the observations during the NLM period, being much more frequent than the LM period. On the other hand, most of the observations during the LM period are in Groups 2 and 3. Furthermore, the PV distribution is related to the small meander of the Kuroshio generated southeast of Kyushu. Group 1 occupies 86% of the observations related to the generation of the small meander. That is, the small meander is mostly generated when PV in the middle pycnocline in the Tokara Strait is small and nearly uniform with small meridional variation. Such a PV distribution may be necessary for the generation of the small meander of the Kuroshio. The frequent occurrence of Group 1 during the NLM period may cause the fact that the small meander is generated much more frequently during the NLM period than the LM period. Watts (1983), Hall and Fofonoff (1993), and Hall (1994) discussed the instability of the Gulf Stream using the PV distributions on the basis of instability theory. The instability theory for a quasi-geostrophic current derives two necessary conditions for instability; first, the product of the basic current velocity and the cross-stream gradient of PV is positive somewhere in the current and, second, the cross-stream gradient of PV changes sign somewhere in the current (Pedlosky, 1964). The first condition is almost always satisfied for the strong currents in the ocean. The cross-stream gradient of PV in the Gulf Stream changes sign just offshore of the current axis, and may satisfy the second condition there. PV in the middle pycnocline of the Kuroshio increases sharply onshore around the current axis and has a significant maximum on the onshore side of the current axis at the PN line and in Groups 2 4 at the TK line, like that of the Gulf Stream. Moreover, a PV minimum often occurs on the offshore side of the current axis as well. Therefore, the sign of the cross-stream gradient of PV changes on onshore and offshore sides of the current axis, and the second condition is satisfied there. However, in fact, the current axis of the Kuroshio varies little at the PN line, and the small meander of the Kuroshio is hardly generated in case of Groups 2 4 at the TK line. The small meander is generated frequently in case of Group 1 at the TK line, in which PV is almost uniform. The observations show the opposite result to that expected from the theory. This may imply that the second condition for instability should be examined for PV in the immediate vicinity of the current axis, where PV at the PN line and of Groups 2 4 at the TK line does not change the sign of the cross-stream gradient, while PV of Group 1 can change it due to small-scale meridional variations. Acknowledgements The authors are profoundly grateful to T. Nakano and the Nagasaki Marine Observatory of the Japan Meteorological Agency for kindly supplying the CTD and ADCP data at the PN and TK lines. They also thank the Japan Oceanographic Data Center for providing the sea-level Dynamic Structure of the Kuroshio South of Kyushu 607

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