Mooring, CTD, and ADCP observations were made in 2012 in and around the Toyama Trough (TT) cutting across a continental shelf along the Japanese coast of the Japan Sea between Noto Peninsula (NP) and Sado Island (SI) to investigate spatiotemporal characteristics of path transition of the coastal branch of the Tsushima Warm Current (CBTWC). Around SI, downstream of the TT boundary, a wavelike alongshore current perturbation, accompanied by sea level rise, was observed. This perturbation occurred after the seasonal amplification of the CBTWC around the NP on the upstream boundary of the TT. This process was delineated by the results of numerical experiments performed with a two-layer model using idealized topography. The model showed that a current path of the CBTWC shifted from alongshore mode to offshore mode bridged over the TT in association with the lee eddy development behind the NP toward the SI over the TT. This lee eddy is generated by positive vorticity induced over topographic discontinuity between the continental shelf off the northern coast of the NP and deeper region of the TT. The model indicated the period of eddy formation is 60–90 days if the volume transport is 1 Sv (1 Sv ≡ 106 m3 s−1), whereas the observations showed the formation period was only 47 days at 1.2 Sv of volume transport. To explain this discrepancy, temporal variation of the CBTWC, vortex supply from preexisting eddies, or eddies caused by the scattering of coastal-trapped waves were suggested as new processes that accelerate the growth rate of the lee eddy.
Coastal currents are ubiquitous features in coastal oceans worldwide (e.g., Echevin et al. 2003; Kuroda et al. 2006; Kundu et al. 1975). Numerous studies have shown that the interaction between coastal currents and uneven topography contributes to the generation of eddies, and it is well known that mesoscale eddies are generated when baroclinic coastal currents encounter irregular tips of coastlines (Bormans and Garrett 1989; Klinger 1994a,b; Conlon 1982; Pichevin and Nof 1997; Nof and Pichevin 2001). Klinger (1994a,b) suggested that centrifugal force can cause coastal currents to detach when the current rounds a corner, with the detached current subsequently forming the core of a coastal eddy.
The effects of irregular bottom topography on eddy formation are also well investigated. Eddies trapped within submarine canyons are generated when the width of the submarine canyon is narrow, up to the same order of internal radius of deformation (Klinck 1996; Ardhuin et al. 1999). However, eddy formation or separation of coastal currents occurs even when the spatial scale of abrupt bathymetric variations is sufficiently larger than the internal radius of deformation (Yankovsky and Chapman 1997; Echevin et al. 2003). Through numerical experiments, Chapman (2003) showed that the detaching process of advectively trapped buoyancy currents from shelf slopes at a bathymetric bend occurred regardless of the current’s strength and was essentially controlled by the dynamics of the bottom boundary layer.
The possibility of similar processes was reported around the Toyama Trough (TT) by Nakada et al. (2003, hereinafter NK03). The TT has a width of about 100 km and is located off the northern coast of Japan at the southern boundary of the Japan Sea (Fig. 1). The Japanese coast has a wide continental shelf except for around the TT where a trough over a deep submarine canyon cuts across the continental shelf and slope between Noto Peninsula (NP) and Sado Island (SI) toward the Toyama Bay (Fig. 1). Thus, the Toyama Bay is a deep bay and has a narrow continental shelf and steep continental slopes. The coastal branch of the Tsushima Warm Current (hereinafter CBTWC) is known to flow in and around the region of the TT with the shallow-water region on its right (Aiki et al. 2007); the CBTWC originates from the bifurcation of the Tsushima Warm Current in the Tsushima Strait (inset of Fig. 1; e.g., Hase et al. 1999). The volume transport of the CBTWC was reported to be about 1.3 Sv (1 Sv ≡ 106 m3 s−1) at a location off the northern coast of the NP by Watanabe et al. (2006) during the fall season, when the current is at its strongest. By using a two-layer numerical model with simplified bottom topography and a coastline resembling the TT region, NK03 demonstrated that the coastal current flowing over the continental shelf could generate eddies over the submarine canyon that cuts across the continental shelf.
These previous studies suggest that currents trapped by the coast or continental shelf topography are transformed into jets that are not trapped by rigid boundaries; these jets can subsequently develop into topographic eddies embedded between the detached jet and the coastline. This process may result in the transition of the current path in the downstream region from the eddy generation point. Previous studies have mainly discussed steady-state dynamics using numerical experiments or analytical methods. Therefore, there remain many questions regarding the transient stage of the current as it transitions from its coastal to offshore path and the associated eddy formation.
We hypothesize that the rate of the eddy formation can be related to the coastal current volume transport. This hypothesis is based on the analogy between the CBTWC encountering the TT region and the coastal buoyant discharge running off on the continental shelf. In both situations, the current bounded on the right (facing downstream) propagates into deeper water and executes a sharp turn to the right, which gives rise to the formation of anticyclonic bulge. The bulge is an inherently unsteady feature, and its growth rate is proportional to the coastal buoyant discharge (e.g., Nof and Pichevin 2001). The CBTWC volume transport might have a seasonal cycle, although it has not been clarified obviously by previous studies (Kawabe 1982; Nakada et al. 2005). If the CBTWC has seasonality, we anticipate that both the path transition and eddy formation will exhibit similar seasonality.
Coastal-trapped waves (CTWs) are frequently generated in the coastal region where coastal currents exist. Sanay et al. (2008) indicated the possibility of lee eddy formation past a peninsula by wind-induced current. Therefore, interactions between eddies originated from the coastal current and those from the CTWs might occur. To extract each effect of these phenomena from episodic eddy generations, it is needed to observe spatiotemporal variation of eddy development as continuously as possible and to discuss these processes quantitatively. Because such observations have not been previously presented for any coastal ocean, including the TT, it is unclear not only how volume transport and temporal variation of coastal current affect coastal eddy generation but also how probable eddy formation is over the TT.
Several factors make the TT an appropriate region to investigate the time–space characteristics of the coastal current transition process during coastal eddy development. NK03 indicates that topographic eddy generation and accompanied current transition could occur over the TT. In and around the TT, there are many set-nets used so fisheries can deploy current meters. Around the TT, CTWs are frequently generated along the western coast of the NP in association with the northeastern wind (e.g., Igeta et al. 2011; Fukudome et al. 2016). In addition, tidal currents are known to be weak around middle of the Japan Sea (e.g., Mori et al. 2005). The objective of our study is to describe the CBTWC transition from its coastal to offshore path by first presenting observational evidence for this process and second by conducting multiple idealized numerical experiments that systematically study the effects of the coastal current volume transport and other relevant dynamics on the transition process. We construct a schematic diagram of the current path transition over the TT region to summarize both the observational and numerical results.
2. Data and methods
Mooring observations utilizing two types of current meters were performed at seven stations around the TT along the NP and SI (Fig. 1) from April to December 2012. Electromagnetic current meters (Compact-EM, Infinity-EM; Alec Electronics Co., Ltd; accuracy of 1.0 cm s−1) were deployed in the upper layer (10–30 m) of the sea. Locations of the stations and details of the observations are indicated in Table 1.
Hourly sea level data at Nezugaseki (NZ), Sado (SA), Ogi (OG), Kashiwazaki (KS), Toyma (TY), Noto (NT), and Mikuni (MK; Fig. 1), provided by the Geographical Survey Institute and the Japan Meteorological Agency (JMA), were used for analysis. Atmospheric pressure data obtained at 1-h intervals from the tidal gauges provided by the JMA were used to remove the effects of atmospheric pressure from sea level. The sea levels were detided by subtracting predicted tidal oscillation, and these data are referred to as sea level anomalies in this paper.
From May to October 2012, vertical profiles of temperature and salinity were obtained with CTD (SBE19plus; Sea-Bird Electronics, Inc.) observations at stations a–l (Fig. 1) using R/V Koshiji-maru belonging to Niigata prefecture in the same period of the mooring observation used in this study. The salinity data were calibrated by Autosal (Guildline Ltd.), and the temperature and salinity data were 11-m running averaged vertically.
Vertical profiles of currents were obtained along transect line AD (Fig. 1) through four round-trip observations in 24 h by R/V Hakusan-maru belonging to Ishikawa prefecture at 1930 Japan standard time (JST) 5 June 2012 and 0800 JST 11 September 2012. An acoustic Doppler current profiler (ADCP) (Ocean Surveyor 150 kHz; Teledyne RD instruments) was used in this observation. We used only bottom-tracking data calibrated by using the method shown in Joyce (1989). The data were averaged in grids every 1.6 km horizontally × 8 m vertically. The gridded datasets for eight transects were averaged to remove tidal components from the current data (Katoh et al. 1996). If the grid data were incomplete for any of the eight transects, we treated the data as missing.
We used the Grid-Point Value-Mesoscale Model (GPV-MSM) data provided by JMA to estimate wind fluctuation around the TT. The grid dimensions of the model are 0.05° latitude × 0.0625° longitude, and the temporal resolution is 1 h. The northward and eastward wind components were used at the grid point 37°0.39′N, 136°0.52′E, as shown at station W in Fig. 1.
b. Numerical model and experiments
We adopted simple topography and stratification on numerical experiments to facilitate the physical interpretation of the studied dynamics. The computational domain was set 400 km from north to south and 700 km from east to west with 1000-m depth (Fig. 2). In this model domain, a straight coastal line is set along the southern boundary. A rectangular peninsula NPm (50 × 100 km2) and a square island SIm (50 × 50 km2) were placed in the model that represent the NP and SI in the middle of this model domain. In addition, a steplike continental shelf with a depth of 200-m and a 50-km width was set around the NPm. The shelf edge extended eastward from the north off the NPm. A submarine canyon with a width of 100 km was set between the NPm and the SIm to represent the TT. The submarine canyon reaches the coast that is assumed to be the Toyama Bay. Here, there is no shelf along the eastern coast of the NPm, the western coast of the SIm, or the southern boundary of the submarine canyon.
We used the two-layer model described by Kitade and Matsuyama (2000) for the domain mentioned above. This model is based on linearized primitive equations under hydrostatic and Boussinesq approximations. The Arakawa C grid and Euler backward methods are adopted for spatial and temporal integration, respectively. The model has a free surface and does not permit the interface to touch the bottom, meaning that all shelves are in the lower layer. The x axis extends along the coastline (southern boundary) from the western boundary, whereas the y axis is set to coincide with the western open boundary with positive offshore. We used a rectangular grid system, and the horizontal grid size was set to 2 km × 2 km. Clamped open boundary conditions were applied along the eastern and northern open boundaries to create a pressure gradient between western–eastern boundaries. Sponge regions were set along the northern and eastern open boundaries to reduce any disturbances near them. The no-slip condition was applied along rigid boundaries. Smagorinsky-type eddy viscosity was applied in this model (nondimensional parameter: 2.0). The other parameters used in this model were the same as those of Kitade and Matsuyama (2000). Assuming the CBTWC, the barotropic current trapped by the southern coastal line was applied from the western boundary. The barotropic current was driven by increasing sea level and interface displacement along the western open boundary ηw, following these equations:
where ηws and ηwi indicate displacements of sea surface and interface along the western boundary; superscript y means northward distance; a = c/f38 is the internal radius of deformation, where f38 is the Coriolis parameter at 38°N (8.98 × 10−5 s−1); c is the phase speed of internal gravity waves; h is the thickness of the upper layer; D is the depth of the offshore region; ηt is the time variation of the displacements; and η0 is amplitude.
We performed three types of experiments. The first one was the constant inflow case, the second one was the periodical discharging case, and the last one was the wind case; the latter case took into consideration the effect of wind in the system. The first, second, and third are named experiment C, experiment P, and experiment W, respectively.
In experiment C, time variation of the western boundary ηt was set to 1.0 after increasing linearly in 24 h. This method is based on the hypothesis that the Tsushima Warm Current is basically driven by sea level differences between the Tsushima Strait and Tsugaru Strait (Fig. 2) (e.g., Ohshima 1994; Kida et al. 2016). We performed three sets of experiments, using summer (experiment C-S), late summer (experiment C-LS), and fall (experiment C-F) stratification conditions, respectively. The stratification conditions were determined by density profiles obtained by CTD observation at stations a–l (Fig. 1). The stratification conditions are listed in Table 2, with ρ1 and ρ2 representing the densities of the upper and lower layers and h. From the stratification conditions, we can estimate that the internal radius of deformation a is approximately 13, 12, and 11 km in experiments C-S, C-LS, and C-F, respectively.
Eight experiments with differing inflow volume transport were performed for each stratification condition. The volume transports were set to 0.35, 0.5, 0.70, 1.0, 1.5, 2.0, 2.8, and 3.0 Sv through line A shown in Fig. 2, and they were controlled by the η0 in Eq. (1). We performed 24 experiments in total in experiment C. We named each experiment according to the stratification condition and the volume transport. For example, in experiment C-F-1.0 in the constant inflow case, fall stratification conditions were used and the volume transport of the inflow was 1.0 Sv.
In case of periodic discharge, experiment P, we use
where Tp, the period of inflow, was set to 180 days. The stratification conditions and maximum volume transport were set to fall conditions and 1.0 Sv (η0 = 3 cm).
For the third case, experiment W, wind stresses were applied to the model domain. We use the set of experiment C-F-1.0, and the northward winds blowing for 4 days with wind speed of 10 m s−1 was given five times with 6-day interval during the period of 0–50 days only within the region of the western off the NPm as shown in Fig. 2. This condition was based on the method used by Fukudome et al. (2016) in order to avoid inertial oscillations in the interior region that would obscure the signals of analyzed processes. In addition, experiment with only the wind stress mentioned above (no inflow condition) was performed, which was named experiment Wo.
a. Observation results
Alongshore currents around the TT (at stations 1–7) are shown in Fig. 3a. These time series were 15-day running averaged to remove the effects of atmospheric disturbances (about 7–10-day fluctuations; e.g., Igeta et al. 2011; Fukudome et al. 2016). Wavelike alongshore current perturbation was found at station 3 located at the western side of the SI from August to October. Such current fluctuations were not found on the eastern side of the SI (stations 1 and 2). Before the wavelike perturbation occurred, the alongshore current at station 5 on northern part of the NP had strengthened and kept its strength during the wavelike perturbation at station 3. The alongshore current at stations 7 and 6 strengthened before it was amplified at station 5. At station 4, located at the tip of the NP, the alongshore current strengthened after mid-September. This amplification seems to propagate downstream (from station 7 to 4). The series of fluctuations have time scales of about 2 months (from early August to early October).
Figure 3b shows the 15-day running averaged sea level anomaly at each tidal gauge station. Sea level difference from OG were calculated and superposed on the time series at KS, TY, and NT. Increasing sea level differences that indicate coastal sea level rise were found at tidal gauges surrounding the SI (at KS, TY, and NT) from the end of August to mid-September. After the sea level difference maximum, sea level anomaly rapidly rose only around the SI (at OG and SA). As a result, sea level difference decreased after the period indicated by broken line d in Fig. 3. The increasing of sea level difference seems to be correlated with the alongshore current strengthening at station 5. This indicates the CBTWC strengthens during this period (from broken lines b to d in Fig. 3). During the former half of this period, currents with the coast on the right were strengthened at station 3, whereas the current reversed in the latter half of this period.
Cross sections of the potential density (kg m−3) along the CTD transect shown in Fig. 1 are indicated in Fig. 4 to infer density fields over the TT. At the end of May, although no obvious horizontal structure was found, weak downwelling was identified (contour lines of 25.5 and 26) in the coastal region stations a–c (Fig. 4a). After about 1.5 months, the coastal downwelling strengthened, and seasonal stratification developed (Fig. 4b). This signal suggests strengthening of the CBTWC. At the beginning of September, the coastal downwelling retained its structure despite the development of a mixed layer (Fig. 4c). Isopycnals were inclined toward the coastal region around stations g–i, which played a role in the formation of an anticyclonic eddy centered at around stations g–h. About 1 month later, although the density frontlike structure was still identified in almost the same area, the anticyclonic eddy structure was hardly found; this is most likely due to horizontally distributing isopycnals from stations a to g (Fig. 4d). Thus, by this point, coastal downwelling had completely disappeared in this region.
Contour lines of geostrophic currents are overlaid on these figures. The calculations were made by using potential density data, and we chose the shallower bottom depth between the two stations as the reference layers. The results support the speculation from density structures explained in the previous paragraph regarding the strengthening of the CBTWC during summer and the existence eddy structure over the TT, despite inaccurateness caused by the uncertain reference layer.
Vertical sections of detided current vectors along line AD (Fig. 1) in Fig. 5 show the characteristics of the CBTWC flowing into the TT. The currents have two cores in the coastal and offshore region, with seamounts between them. They were almost alongshore or along shelf and perpendicular to the line AD. Angles of their main axes of currents were 82 and 59 degrees in June and September, respectively. To prevent underestimation of volume transport, these angles were determined to be the angles at which maximum volume transport occurred. The volume transport was calculated using current data of the entire section. Any incomplete data for depths shallower than 20 m were substituted with the value found at 20 m for each respective location, and incomplete data at the very bottom of the model area were replaced with the valid data point from the next deepest location. This extrapolation method is justified by the following: 1) the current had almost barotropic structure in June (Fig. 5a), and 2) the vertical structure of density was almost homogenous in the region shallower than 20 m in September (Fig. 4c). Volume transports caused by the CBTWC within these transects were approximately 0.64 and 1.2 Sv in June and September, respectively.
Vertical transects of main axes’ components of detided velocities are also shown in Fig. 5. The CBTWCs trapped near the NP coast were found in June and September. Before the strengthening, the CBTWC had current barotropic structure in this region; after strengthening, the CBTWC had strong baroclinicity. Increased transport in late summer agrees with the results of mooring and sea level data analysis at tidal gauges.
Several-day period fluctuations relating to wind-induced CTWs are checked during this observation period. The main generation area of the CTWs is known to be the western coast of the NP, identified by signals of sea level fluctuations accompanied by the northeastward wind (Igeta et al. 2011; Fukudome et al. 2016). Figure 3c shows the tide-killer filtered (Hanawa and Mitsudera 1985) sea level anomaly at MK and NT (Fig. 1). The time variation of the northeastward wind is also shown in Fig. 3d. Sea level elevations with periods on the scale of several days are found at both stations, as indicated by 1–6 during the current path transition period. These sea level events were identified just after the strong northeastern wind had blown, with the exception of the event indicated by broken line 3. Based on previous studies of this region, we deduced that these signals indicate large-amplitude CTWs accompanied by currents with the coast on their right in the upper layer of the ocean. Such wave events subsequently propagated into the TT and Toyama Bay at least five times during the study period.
According to the observational result, the following processes were identified: 1) after the CBTWC had strengthened around the NP, an anticyclonic eddy appeared over the TT; 2) the northward current changed its direction toward the south at the western coast of the SI while the eddy was present, which was accompanied by sea level elevation; 3) the CBTWC and the anticyclonic eddy over the TT disappeared, whereas the jet flowing toward the northeast remained off the western coast of the SI; and 4) at least five CTW events were generated in this study region during observation period.
From the observation and previous studies, we can guess eddy generation and propagation toward the SI occurs after the CBTWC strengthens. Next, we focus on this process by using a numerical experiment. One of the important points of inquiry is whether or not the speculated eddy-generation processes can generate the observed wavelike current perturbation and sea level rising at the western side of the SI.
b. Experimental results
Figure 6 shows the sequential pattern of the horizontal distribution of the current in the upper layer as well as surface displacement of the experiment C-F-1.0 results. In this case, maximum sea level displacement [η0 in Eq. (1)] is 3 cm. At the beginning of the calculation, currents are developed along the coast (5 days). After 20 days from calculation, currents are basically trapped by the coast, but the current reversed near the coast at the northeastern tip of the NPm. This region developed toward the east off the NPm in a period of 20–70 days and developed anticyclonic eddy–like forms. This anticyclonic eddy, or lee eddy of the NPm, continued to develop and reached the SI in about 92 days. After that, the eddy developed toward the north (92–300 days). The anticyclonic eddy seems to be trapped by the submarine canyon.
In the current path of view, the current axis coincides with the northern part of this eddy. Thus, the current axes seem to move from the alongshore path to the offshore path as the eddy develops. After 200 days, the current bifurcates into northward and southward components west of SIm. Such bifurcations are recognized obviously from 70 days, and the separation points move from south to north with time (92–300 days). The bifurcation becomes more obvious with the eastward development of the lee eddy. Here, the northward current is recognized along the western coast of the SIm before the bifurcation signals were elicited at 20 and 50 days. This indicates that the alongshore current bifurcated northward at the shelf edge along the mouth of the strait.
c. Comparison between the observation and the experiment
We check experimental results of current and sea level fluctuations. Figure 7 shows the alongshore currents and surface displacements at monitoring points of stations 3m, 5m, OGm, NTm, TYm, and KSm (Fig. 2) that coincide with currents and tidal observation sites in the model domain. The wavelike alongshore current fluctuations found at station 3m (Fig. 7a) around 0–150 days are similar to that observed at station 3 (Fig. 3a). These fluctuations are generated by the lee eddy development toward SIm, shown by the current direction changing from northward to southward when the bifurcation point of the current passed from south to north through station 3m in the model. Increasing surface displacement is recognized only at OGm in the model in association with the wavelike current fluctuation at station 3m (Figs. 7b,c). This increasing of the surface displacement results in decreasing of the difference of the surface displacement between OGm and surrounding stations (Fig. 7c). These features result from the lee eddy development over the submarine canyon as well. These results resemble the observed data (Fig. 3b).
Figure 8 indicates the eastward current in the upper and lower layers along the transect line B (Fig. 2). The sea surface and interface displacement are added in these figures. The coastal-trapped current and density structure has baroclinic characteristics, like internal Kelvin waves, at 5 days. After the transition, at 200 days, even though the coastal-trapped current disappears, the jet structure is identified just off the SIm. Weak baroclinicity is found in the jet structure where the current in the lower layer is weaker than the current in the upper layer. The jet is characterized by corresponding upward/downward displacements of free surface/interface at 80–100 km offshore (Fig. 8c). The surface/interface was almost uniformly piled up/depressed in the southern region from the jet that coincides with Toyama Bay. In the coastal region, since the surface displacement slightly decreased, a current forms with the coast on its left in the upper and lower layer. As a result, an anticyclonic eddy can be identified over the submarine canyon. In the middle of transition, at 92 days, moderate feature can be found between Figs. 8a and 8c, that is, both the coastal-trapped current and anticyclonic eddy are found over the submarine canyon.
Features of the coastal-trapped baroclinic current and density structure shown in Fig. 8a coincide with the observations obtained in August when the CBTWC started to strengthen (Fig. 4b). Likewise, characteristics of the jetlike density and current structures off the SIm shown in Fig. 8c agree with the observed conditions in October (Fig. 4d). The density structure arising from the lee eddy in Fig. 8b agrees well with that observed in September (Fig. 4c). Thus, we can conclude that the CTD observations captured the density structure variations in association with the CBTWC path transition.
4. Observed transition process of coastal branch of the Tsushima Warm Current
We try to explain the transition process by relating the observational results to the numerical results. We separate Fig. 3 into four periods delineated by broken lines b, c, and d to explain the sequential current fluctuation. Figures 9a and 9b show the schematic view of the current path transition of the CBTWC.
Before CBTWC strengthens around the period indicated by broken line b, it is thought to flow along the coast of the NP (arrow 1 in Fig. 9a). The flow is controlled by bottom topography (along f/H contour lines, where f is the Coriolis parameter and H is the depth), and the CBTWC has a gentle current. This assumption is supported by the vertical homogenous current along the line AD shown in Fig. 5a. At a shelf edge lying along a mouth on the western side of Sado Strait, the CBTWC was considered to be separated into a northward component and alongshore component because the CBTWC follows f/H contour lines (e.g., Echevin et al. 2003; Igeta et al. 2005). The northward current shown at station 3 around line b in Fig. 3 is considered to be a signal of this northward current.
During the former half of the period from line b to line c in Fig. 3, the CBTWC strengthened gradually, as shown by strengthening of the alongshore current at station 5 and increases in coastal sea levels (Figs. 3a,b). In this period, the northward current west of the SI also strengthened (Fig. 3a of station 3). The core of the eddy over the TT was thought to have generated at a tip of the NP based on the numerical experiment (20 and 50 days in Fig. 6). Thus, the current path was considered to take arrow 2 as in Fig. 9a.
After that, development of the anticyclonic eddy continued during the strengthening of the CBTWC (arrow 3 in Fig. 9b) in the latter half of period indicated from line b to line c in Fig. 3 based on numerical experiments (70 days of Fig. 6). In this stage, the separation point between the northward component and alongshore component of the CBTWC approached station 3. This resulted in weakening of the northward current at the SI (around dotted line c in Fig. 3a).
The separation point of current mentioned above moved northward and passed around station 3 based on the numerical experiment (after 70 days of Fig. 6). The current path shown by arrow 4 resulted from the development of the anticyclonic eddy at the time indicated by broken line d in Fig. 3. These signals were recognized as changing of current direction from northward to southward at station 3 at the time indicated by broken line c in Fig. 3.
The CBTWC might take the current path indicated by arrow 5 in Fig. 9b after the time indicated by broken line d in Fig. 3. This is based on the cross section of the geostrophic current shown in October of Fig. 4. This figure also indicates that alongshore current disappeared at the mouth of Sado Strait. This interpretation is supported by the decreasing of the sea level difference between KS and OG caused by the sea level rising only around the SI found in Fig. 3b. Thus, this sea level rising can be used as a signal of the transition of the current path from coastal mode to offshore mode.
The curvatures of arrows 3 and 4 are stronger than the current path obtained by numerical experiments. The schematic views are based on the cross sections of geostrophic current shown in Fig. 4. The curvature of the current path of the CBTWC is more exaggerated in the real ocean than it is in this numerical experiment because of the existence of complicated coastal line and bottom topography.
Some uncertainty remains regarding a temporal delay of current amplification at station 4 relative to the wavelike perturbation onset at station 3 and strong current development at stations 6 and 7. This might be related to the distance between moorings and current path rather than local bottom depth. The arrow 4 in Fig. 9b indicates such features around station 4. The current path might be affected by the local coastline and development of boundary layer of horizontal viscosity.
The results of the numerical experiment strongly suggest that the observed current path transition processes are caused by development of the anticyclonic lee eddy embedded in the submarine canyon. In this subsection, the process dynamics of lee eddy generation are discussed.
a. Dynamics of the current path transition
After 2 days, the coastal current had broad structure over the continental shelf of the northern coast of the NPm in the upper layer (Fig. 10a). Interface displacement was depressed around the eastern edge of the shelf. This depressed area propagated southward and was accompanied by southward flow. While the depression continued to generate, the core of the lee eddy formed at the northeastern tip of the NPm after 5 days. After that, this anticyclonic eddy develops and moves southeastward.
In the lower layer, the coastal current also had a broad structure over the continental shelf off the northern coast of the NPm. The current had a barotropic structure over the shelf as given by the boundary condition along the western boundary. However, no obvious current is identified along the eastern coast of the NPm in the lower layer. As a result, the coastal current propagating southward had strong baroclinicity, as shown in Fig. 8a. Since the submarine canyon has no shelf, this phenomenon is interpreted to be the front of the coastal current propagating with characteristics of an internal Kelvin wave. The transition from barotropic mode to baroclinic mode occurred around the eastern edge of the continental shelf, where the amplitude of the interface displacement became large.
Around this area, the current flowed southward along the eastern shelf edge in the lower layer. This feature results from the coastal current tendency to follow f/H contours in the lower layer. As a result, the current converges at the northeastern tip of the NPm, and the current within this region gets large toward the southeast where the submarine canyon is deeper. Because of these enhanced currents, the water columns in the lower layer are forced to move toward the deeper region of the submarine canyon. The water columns are stretched and get positive vorticity to conserve the potential vorticity PV = (f + ζ)/H (where ζ indicates relative vorticity). As a result, a positive vorticity region is generated in the deeper-water region just off the northeastern tip of the NPm after 5 days (Fig. 10b). After that, since this positive vorticity is consistently supplied by enhanced southeastward flow toward the submarine canyon, the cyclonic eddy continues to develop southeastward.
Conversely, generation of the negative vorticity region is found on the other side of the cyclonic eddy (5 days). This negative vorticity region is considered to be a secondary result of the existence of a southeastward jet in the otherwise calm region. The positive and negative vorticity regions continue to develop in the lower layer (20–50 days). Here, the positive/negative vorticity in the lower layer makes its interface deepen/rise through geostrophic adjustment. Because this results in stretching/shrinking of the water column in the upper layer, the same sense of vorticities is generated in both layers. This tendency is clearly identified as distortion in the contour lines toward the northeast of the interface (deepening of the interface) at crossover points of dashed lines at 20 and 50 days after calculation.
The generation of this lee eddy in the upper layer is quite similar to those reported by Klinger (1994b), which was considered to be generated by detaching of the baroclinic coastal current rounding around the northeastern corner by centrifugal force. However, additional experiments similar to C-F-1.0 with baroclinic flow as in Fig. 8a, but without a continental shelf topography, show no lee eddy generation (not shown). This interpretation indicates that the sequential current path transition processes, including the lee eddy generation, are bottom controlled in this set of the experiments, a result that corresponds more to NK03 than to Klinger (1994b).
b. Transition time scale and volume transport of the coastal branch of the Tsushima Warm Current
We now discuss the time scale of the current path transition in order to investigate its determining factor. A transition time scale (TTS) is defined as the maximum value of time derivative of the time series of surface displacement at the OGm. In the case of experiment C-F-1.0, the TTS is 92 days (Fig. 7b), and its flow pattern is shown in Fig. 6. Taking into account the relation of time and the wavelike current perturbation at station 3m, the 92 days is considered to be relatively consistent with broken line d in Fig. 3, when the fishing set-net near station 3 was destroyed by the strong current on 16–17 September.
Figure 11 indicates the relation between the transition time and eastward volume transport through the transect line A (Fig. 2). The TTS decreases proportionally as transport volume increases. The TTS becomes short when thickness of the upper layer decreases; however, no significant differences from the strength of stratifications can be found. When the volumetric transport increases, the TTS seems to approach a limit of approximately 50/40 days for fall/summer stratification, respectively.
The current path transition was estimated to last about 47 days from the observational result. The period was from 1 August to 16 September (Figs. 3a–d). Here, the start date was determined by using the time variation of the current at stations 3 and 5 because the currents started getting strong. This is based on a hypothesis that the core of the lee eddy formed after the CBTWC developed around the NP. The end date was provided from current perturbation at station 3 consistent with the numerical experiment and the fact that the set-net for fisheries at station 3 was destroyed by the strong currents. To explain this observed transition time scale, the CBTWC needed to have more than 2 Sv around the NP during the current path transition based on experimental results. Such volume transport is significantly larger than those speculated in the previous studies (1.0 Sv in NK03; 1.3 Sv in Watanabe et al. 2006) and the estimation of this study (1.2 Sv; Fig. 5b).
To clarify the details of the current path transition processes, we need to judge whether the CBTWC could realistically have carried more than 2 Sv of volume transport during our observation. The throughflow of the Tsushima Strait, where the Tsushima Warm Current originates, is known to have 1.2–3.4 Sv of volume transport (Takikawa et al. 2005; Fukudome et al. 2010). The volume transport through the eastern channel of the Tsushima Strait that is directly related to the CBTWC is generally estimated to be about 1–1.5 Sv (Fukudome et al. 2010). Thus, recirculation in the Japan Sea or local enhancement of the CBTWC is required to maintain >2 Sv under such case. In addition to this, since >2 Sv was estimated by using summertime stratification condition experiments (experiment C-S, C-LS), such effective situation would need to last throughout the whole period of the transition process. Thus, it seems that these facts deny the possibility of >2 Sv flow in the CBTWC.
Unusual enhancement of the CBTWC caused by increasing of the throughflow of Tsushima Strait could have occurred at the time of observation. This problem may relate to the current system, including the whole of the Tsushima Warm Current and adjacent ones, for example, Kuroshio. It is required to understand interannual variation of the CBTWC, Tsushima Strait throughflow, and so on. While this is an important question to be addressed, it is beyond the scope of this study.
Therefore, we will proceed with discussions based on the fact that the CBTWC had at most 1.2 Sv of volume transport in this study, an estimate based on data from the ADCP observation (Fig. 5b) that was collected during a time when alongshore current velocity at station 5 was strengthened (line c in Fig. 3a). From these experimental results, we judge that the transition process takes about 60–90 days (Fig. 11). This suggests the existence of additional mechanisms that can accelerate the current path transition speed, that is, generation speed of the lee eddies.
6. Possible factors of accelerating of coastal current transition
Experiment C did not have temporal variations of inflow, any preconditions, or other forcing. The first and second are considered to be related to periodicity, that is, seasonality of the CBTWC. The third might include the mechanism of interaction between wind-induced, CTWs and the CBTWC.
a. Effect of the seasonality of the CBTWC and preexisting eddies over the Toyama Trough
The transition processes were identified after the amplification of the CBTWC had propagated down from the upstream region to around the NP (Fig. 3a). This amplification was summertime development of the CBTWC. This observational result indicates the possibility that the development of the lee eddy was linked to the seasonal variation of the CBTWC. The relation between the periodicity of the CBTWC and lee eddy generations was investigated using results of the numerical experiment P. Here, 180 days were chosen as the period of the coastal current fluctuation because the CBTWC generally develops and weakens within 6 months at most (from May to November).
Figure 12 shows the sequential pattern of horizontal distribution of current vectors in the upper layer, as well as surface displacements, in experiment P. The first and second cycles are shown. The lee eddy generation behind the NPm can be identified associated with the development of the coastal current between 83.5 and 130 days. After the coastal current weakened, the anticyclonic eddy remained over the submarine canyon until 180 days. After the second cycle began, the coastal current strengthened and core of the lee eddy was generated again around the northeastern tip of the NPm (263.5 days). This lee eddy developed eastward under the existence of an anticyclonic eddy (263.5–310 days). In other words, the current path transition occurred with the existence of a weak current that bridged the submarine canyon.
The time scale of the current path transition in the second cycle seemed to be almost identical to that of the first cycle, but the location of the anticyclonic eddy over the submarine canyon in the second cycle was closer to the SIm than the location of the first cycle (310 and 130 days). The cyclonic eddy over the northern part of the submarine canyon, which formed the dipole eddy structure with anticyclonic eddy over the southern part of the submarine canyon in the experiment C (Fig. 6), seemed to grow relative to that of the first cycle.
We focus on two points: 1) effects of the temporal variation of the inflow condition and 2) influence of the preconditions. In both, the estimation of the transition time scale is quite important. The simplest way to estimate this is to adopt the same method as in section 5b by using the rise of the surface displacement at OGm. Initially, we checked the northward current fluctuations at 3m and surface displacement at OGm (Figs. 13a,b). Wavelike current perturbations, shifting from the northward current to the southward, were identified in association with surface displacement rising at station 3m in the first cycle. The peaks of the southward currents after the second cycle seem to emerge earlier than that of the first cycle. These characteristics coincided well with that of the experiment C-F-1.0 (Fig. 7a) and the observations (Fig. 3a). After the second cycle, the wavelike current perturbation basically repeated and was accompanied by the rising of surface displacements. The surface displacements were not reset to zero at beginning of each cycle after the second cycle. As a result, the maximum time value derivative of the surface displacement could not be used as the current path transition index because the signal is weak and is further masked by the periodic inflow from the upstream. Thus, we cannot compare the results of experiment P to those of experiment C using the same indices.
First, the effects of time variations in current strength on eddy formation will be discussed. We used net vorticity flux through line C (Fig. 2) as an index for current path transition in order to compare the transition speed estimated in experiment C-F-1.0 with that of experiment P. This is based on our interpretation that the lee eddy was driven by positive vorticity generated around the northeastern tip of the NPm.
Zero contour lines of upper-layer vorticity at 83.5 and 130 days of experiment P are indicated as the representative of lee eddy generation at early and developing stages, respectively (Fig. 14). At 83.5 days, vorticity flux through line C has a maximum value (1.71 × 10−5 m3 s−2). We overlaid the same zero contour lines obtained from experiment C-F-1.0 (Fig. 14); from this case, 35.5 and 76 days were selected for the early and developing stages, respectively. In each stage, the same amount of net vorticity flux passed through line C in both experiments (early stage is 5.0 m3s−1; developing stage is 111.0 m3s−1), which means the same forcing was injected to the lee eddies of both experiments. Although the lee eddies are almost the same size in both stages, the result of experiment P is slightly smaller/larger than that of experiment C-F-1.0 in the early/developing stage. This means that the time variation of the current strength can accelerate the lateral spreading speed of the lee eddy.
Next, the effects of the preconditions are investigated. We compared the lateral scales of the lee eddies at 83.5 days and at 263.5 days, as representatives of the early stages’ lee eddy generation in the first and the second cycle by using the same method shown in Fig. 14. This clearly shows the lee eddy of the second cycle was larger than in the first cycle at the same stage (not shown), which indicates the possibility that the current path transition is promoted after the first cycle.
The southward current fluctuation at station 3m links to the location of the bifurcation point of the current in this model. Thus, the maximum time value of the southward current is adopted to estimate the current path transition time scale TTSsm in experiment P. Figure 15 indicates the relation between the TTSsm in association with the cycle. The TTSsm develops earlier after the first cycle, with the earliest one about 15 days earlier than in the first cycle. This indicates the growth rate of the lee eddy can be accelerated by preexisting eddy fields.
b. Effect of the wind-induced, coastal-trapped waves
We discussed the effect of wind-induced CTWs on the generation of the lee eddy. To demonstrate the effect of the CTWs on the current path transition, experiment W was performed. First, propagation processes of the CTWs were investigated by using the result of experiment Wo. The CTWs were generated along the western coast of the NP with characteristics of continental shelf waves. As they propagated, the CTWs changed their characteristics to those of internal Kelvin waves at discontinuity of the continental shelf off the northeastern tip of the NP. After that, the CTWs propagated into the submarine canyon with characteristics of internal Kelvin waves following every wind forcing event (not shown). This process was similar to the coastal current adjustment in previous model runs on day 2 (Figs. 10a,b). The result of experiment W showed that such a CTW propagation process (experiment Wo) is simply superposed on the current path transition process shown in Fig. 6 (experiment C-F-1.0).
Figures 16a and 16b show the alongshore current and surface displacement obtained by experiment W, with the results of experiment C-F-1.0 superimposed. The signals of the CTWs were superposed on the signals of the current path transition of the alongshore current and surface displacement fluctuation of experiment C-F-1.0. However, the peak of the southward current at station 3m was accelerated by approximately 7 days compared to the windless experiment. This indicates that the current path transition was accelerated by CTWs, and its acceleration rate was 1.6 days for every CTW generated by alongshore winds with amplitudes of 10 m s−1.
In this set of the experiments, adjustments for bottom-controlled vorticity balance occurred as a result of CTWs’ propagation around the northeastern tip of the NPm. Actually, positive vorticity was supplied through scattering of the CTWs at the shelf edge northeast of the NPm during mode conversion from the barotropic mode to baroclinic mode in experiment Wo (Fig. 17). Such positive vorticity was considered to help growth of the lee eddy. Sanay et al. (2008) indicated the lee eddy formation behind the peninsula by wind-induced current. We have concluded that similar phenomena occurred in this experiment and that energy conversion from the CTWs can translate into eddy formation.
We investigated current path transition processes of the coastal branch of the Tsushima Warm Current (CBTWC) caused by topographic eddy development over the Toyama Trough (TT). The TT is a region that cuts across a continental shelf on the Japanese coast between Noto Peninsula (NP) and Sado Island (SI). The NP and the SI play a role in the eastern (upstream) boundary and the western (downstream) boundary of the TT, respectively. We verified coastal eddy generation by conducting the mooring observations and shipboard ADCP observations and quantitatively discussed the spatiotemporal scale of the current path transition and the controlling factors of these processes.
From mooring observations, a wavelike current perturbation, accompanied by sea level rises, was identified along the SI downstream-side boundary of the TT in September. This current and sea level perturbation occurred during the CBTWC amplification (1.2 Sv: from the ADCP observation). The processes had an observed time scale of 47 days. Anticyclonic eddy structure was revealed over the TT by CTD observation during this period.
The observed features were well reproduced by numerical experiments performed using a two-layer model with idealized topography through a lee eddy formation process over a submarine canyon between a peninsula and island. The core of the lee eddy was formed by positive vorticity from the stretching of a water column forced to move into the submarine canyon by constant barotropic coastal flow over the continental shelf.
The model showed that the development time scale of the lee eddy, that is, the coastal current path transition, was inversely proportional the transport volume. The speculated transition time is 60–90 days for 1.0 Sv of volume transport. This estimation is considerably longer than the observed transition time of 47 days for approximately 1.2 Sv of volume transport, which suggests the existence of additional mechanisms that can accelerate the current path transition speed.
In numerical experiments with constant inflow and inflows fluctuating sinusoidally up to a 180-day period, two types of processes were shown related to the seasonality of the CBTWC: 1) temporal variation of the CBTWC, and 2) interaction with preexisting topographic eddy. We showed that the lee eddy formed by gradually increasing the inflow grew faster than that by constant discharge, even when the same amount of net vorticity was supplied. For the latter process, the numerical result indicated that a preexisting topographic eddy formed by the precycle coastal current shortened the current path transition time by 10–20 days in the case of the topographic scale of this study.
We also showed that the coastal-trapped waves (CTWs) can accelerate the lee eddy development. The CTWs supplied vorticity to the topographic eddies through their scattering at the shelf edge in the entrance of the submarine canyon. This indicates the possibility that the CTWs frequently interact with topographic eddies.
In this study, the developing time scale of the topographic eddies was discussed quantitatively, and new coastal processes that accelerate the eddy formation were suggested. This study did not, however, discuss other possible contributing factors like unusual increasing of the CBTWC or local enhancement caused by recirculation, such as a cold eddy berthing originating from the offshore jet. In the future, we will need to analyze long-term observational data and numerical experiments with realistic topography to clarify these conversion processes.
The authors thank Dr. Y. Kitade, Dr. N. Hirose, and Dr. T. Senjyu for useful discussions. We thank the anonymous reviewers for their valuable comments and suggestions to improve the paper. We are indebted to Casey Brayton for editing the manuscript. This research was supported by the Research Project for Utilizing Advanced Technologies in Agriculture, Forestry, and Fisheries in Japan. AY was supported by the U.S. NSF Grant OCE-1537449. This work was supported by JSPS KAKENHI Grant 16K07831. The tidal data, meteorological data, and GPV-MSM data were provided by the Japan Meteorological Agency. The figures were produced by the GFD-DENNOU software library.