**Mean structure**

East of Luzon Island (~18°N), the Kuroshio basically flows along the north-south direction (Fig.1a). Therefore, we focus on the meridional velocity of ADCP observed. The observed meridional velocities from three moorings reveal the intensity of the Kuroshio: M1>M2>M3 (Fig. 1b, 1c, and 1d), which indicates that M1 is closer to the axis of the Kuroshio.

In Fig. 2a, the structure of the time-mean meridional velocities shows the maximum of M1, M2, and M3 are 71.9 cm/s (depth: 60 m), 41.8 cm/s (60 m), and 19.9 cm/s (110 m), respectively. This structure indicated that only the eastern part of the Kuroshio current axis was monitored by the array of three moorings, and the Kuroshio near the shore was missing, which is clarified by the HYCOM simulated meridional velocity structure along the 18°N section during the mooring measurements period (Fig. 2b). The simulated result is remarkable consistent with the mooring observations, despite it is a little smaller than the observed value.

**ISV of the meridional velocity**

At first, we compare the mean velocity with the standard deviation of it at the layer of 60 m, 100 m, and 200 m. The mean velocity (the standard deviation) of M1, M2 and M3 are 72 cm/s (23 cm/s), 41 cm/s (17 cm/s), and 18 cm/s (14 cm/s) at 60 m, respectively. The value is 65 cm/s (20 cm/s), 39 cm/s (15 cm/s), 20 cm/s (12 cm/s) at 100 m and 32 cm/s (14 cm/s), 25 cm/s (11 cm/s), 15 cm/s (8 cm/s) at 200 m. The three moorings all show that the standard deviation of velocity accounts for ~ 1/3 to 2/3 of the mean velocity. Noticeable, the standard deviation is nearly equal to the mean velocity, or even larger at 300–350 m. This suggests that the variability of the meridional velocity is very strong and deserves our research. Besides, the observed meridional velocity also shows obvious ISV of about two months in Fig. 1b, 1c and 1d.

In order to remove the interference of low-frequency signals, we extract the ISV of the velocity by using a 20–120 days Lanczos bandpass filter (Fig. S1). The result shows that the intraseasonal velocity changes of the Kuroshio are consistent in the vertical direction at each mooring site, and the intraseasonal velocity is stronger on the surface layer than the lower layer. Power spectrum density (PSD) analysis for observed intraseasonal velocity shows that the intraseasonal period is 40–60 days at M1, 50–60 days at M2 and M3, and vertical consistency (Fig. 3). Notably, the period with a peak of ~100 days is also significant, but the strongest signal of 50–60 days is mainly considered in this study.

Herein, further analysis of the characteristics of the ISV of the meridional velocity in the latitudinal direction. Considering that the ISV of the Kuroshio has vertical consistency, and the intraseasonal signal is more obvious in the surface (Fig. S1), so we choose an average meridional velocity range of 60–100 m to represent the main variability in the intensity of the Kuroshio. The time series of the Kuroshio intensity in three moorings are shown in Fig. S2a, with average values of 68.0 cm/s, 40.1 cm/s, and 19.1 cm/s, respectively. Similarly, Fig. S2b shows the time series of the intraseasonal velocity of average range 60–100 m. Firstly, the latter suggests that there are synchronized ISV at M1, M2, and M3, and there is almost no lag time. Secondly, though the background flow field at M1, M2, and M3 are largely different, the intensity of the ISV is nearly the same (the standard deviations are 12.1 cm/s, 9.7 cm/s, and 10.0 cm/s, respectively), which implies that they are modulated by the same mechanism. In other words, the ISV of the Kuroshio is consistent in the latitudinal direction.

**ISV of the transport**

The above analysis of the observed velocity shows that the ISV is consistent in the temporal and spatial structure at three mooring sites. Next, we will analyze the volume transport of the whole section to explore the characteristics of its ISV. According to observed velocity between 0–350 m depth, the annual average of the Kuroshio transport is calculated to be 6.5 Sv and the standard deviation of 2.6 Sv (Fig. 4). It should be noted that the mooring ADCP miss the Kuroshio above 50 m, thereby we used the constant velocity measured at a depth of 60 m to fill. There are two pieces of evidence to support the above approach. (1). According to the consistent results between the observed velocity of 60m depth by moored ADCPs and the surface velocity from the altimeter, which the correlation coefficient is around 0.8; (2). The HYCOM data during the mooring observed period simulate that the meridional velocity is almost consistent in the vertical direction within 0–50 m, and there is little shear as shown in Fig. 2b.

This result is only responsible for the mooring observation region (123.7°E–123.3°E, 0–350 m), however, the Kuroshio can also be seen near the coast (122.2°E–122.7°E) as shown in Fig. 2b. Previous observations suggested that the Kuroshio has a width of about 100–150 km8,21,33. In this study, the measured width of the mooring array is 64 km, and there are 54 km away from the coast. If the whole transport along 18°N is twice of the observed, the whole transport of the Kuroshio could be roughly estimated to be about twice as large as our observations (13 Sv). By the way, we also use the HYCOM simulated data of the same period to calculate the result to be 11 Sv between the surface and 350m depth (range 122.2°E–122.7°E). These results are almost consistent with the transport (10 Sv and 16.7 Sv) along 18.3°N section20 and close to that 15 Sv along the 18.75°N section21.

In the following, only the actual results observed are discussed. The PSD shows that the observed Kuroshio transport has ISV signal of 50–60 days and 100 days (Fig. 4b), which is consistent with the velocity period of the mooring ADCPs measurements (Fig. 3). Regarding the relationship between intraseasonal transport and intraseasonal velocity at M1, M2, and M3 (Fig. S2b), the coefficient of the two is quite high, with an average value above 0.8 (0.84, 0.87, and 0.72, respectively), which is above the 95% confidence level. The results show that the variability of each mooring is synchronized and consistent with the variability of the whole section.

Moreover, the altimeter data (meridional velocity) during the mooring observation period and over a long period of time (1993–2020) are used to calculate the surface Kuroshio transport ranging from 122.625°E to 123.375°E along the 18.125°N section. The result suggested that the surface Kuroshio also has an ISV period of 50–60 days both the meridional velocity and the transport (not shown), which agrees well with the dominant period of the mooring observed. Thus, the Kuroshio at the observation region has a reliable ISV signal, which is 50–60 days.

**The transport mode and migration mode of the observed Kuroshio **

The empirical orthogonal function (EOF) analysis has been used to investigate the variance associated with the lateral migration of the Kuroshio core from mooring arrays8, 34. Similar to their analysis, we adopt the EOF analysis to decompose the Kuroshio meridional velocity observed into the variation in transport mode (Fig. 5) and migration mode (Fig. 6). The first EOF mode (Fig. 5a) accounts for 74.2% of the total variances and is characterized by the in-phase variation of meridional velocity with the largest amplitude situated at the mean velocity core position (as shown in Fig. 2a). According to the description8, 34, this pattern corresponds to the transport mode, indicating the Kuroshio transport pulses superimposed on the mean structure along the 18°N section. It suggested that the first EOF mode denotes the mean spatial structure of the Kuroshio core along the 18°N section, while its time series represents the magnitude evolution of the Kuroshio transport. As shown in Fig. 5c, the normalized time series of the EOF1 reasonably well tracks the Kuroshio transport time series, with an unbelievable correlation coefficient of 0.99 above the 95% confidence level. Positive values of this mode indicate a pulse of increased meridional flow and larger transport and vice versa.

Relying on the lateral migration of the Kuroshio core appears as a dynamical model of anti-phase cancellation of the flow over the cross-section of meridional velocity8,35. In Fig. 6a, the second EOF mode is characterized by the anti-phase variation of meridional velocity with negative and positive values on the western-lower flank and the eastern-upper flank, respectively. The second EOF mode explains 11.6% of the total variances, where velocity increases on one side and velocity decreases on the other side, probably due to the migration of the Kuroshio core. Meantime, the anti-phase cancellation of the flow indicates less contribution to the Kuroshio transport along the overall section. Similarly, the time series of the EOF2 indicated the lateral migration of the Kuroshio core, where is the positive value corresponds to an offshore position for the Kuroshio core along the 18°N, vice versa (Fig. 6d). A composite analysis of the migration pattern (more than 1 standard deviation) is performed to obtain the in-shore phase (Fig. 6c) and the off-shore phase (Fig. 6e) of the Kuroshio core.

The first two modes of meridional velocity observed by mooring array at 18°N account for 85 % of the total variance in our measurements. Specifically, the result of EOF analysis using velocity observed exhibits a much stronger transport mode (74.2 %) than migration mode (11.6 %). This result has a difference from the Kuroshio east of Taiwan, Zhang et al.8 found the transport and migration modes of the Kuroshio in the PCM1 array explain 34 % and 25 % of the total variances respectively, but Chang et al.34 reported the first two dominant modes for the KTV1 array (the KTV1 array is located about 50 km south of the PCM-1 array) accounting for 29 % (transport mode) and 46 % (migration mode) of the total variance. It seems that the transport mode is dominant for the Kuroshio at 18°N, rather than the migration mode. We perform the same analysis on the meridional velocity simulated by HYCOM, which shows that the first two modes are migration modes (Fig. S3). But it is also found that the pattern in the mooring observation area (dotted frame) is consistent with the analysis result of the mooring array observation (Fig.5a and 6a). Focus on the amplitude of the meridional velocity in the first EOF mode simulated by HYCOM (Fig. S3a), the value near the shore is much smaller than that at the far shore (-20 cm/s vs 70 cm/s), so we believe that it is essentially a transport mode. This result has a great significance in understanding the structural variability of the Kuroshio east of Luzon.

Further research shows that the time series of the transport and migration modes of the Kuroshio at 18°N have a common 50–60 (~56) day periodic signal (Fig. 5b and 6b), which is consistent with the analysis results of the meridional velocity and the transport.