Typhoon Effect on Kuroshio and Green Island Wakes: a Modelling Study

atmosphere

Article Typhoon Effect on Kuroshio and Green Island Wakes: A Modelling Study

Tai-Wen Hsu 1, Meng-Hsien Chou 2, Wei-Ting Chao 3 and Shin-Jye Liang 3,*

1 Department of Harbor and River Engineering, National Taiwan Ocean University, Keelung 202, Taiwan; [email protected] 2 Department of Hydraulic and Ocean Engineering, National Cheng-Kung University, Tainan 701, Taiwan; [email protected] 3 Department of Marine Environmental Informatics, National Taiwan Ocean University, Keelung 202, Taiwan; [email protected] * Correspondence: [email protected]; Tel.: +886-2-2462-2192 (ext. 6317)

Received: 5 January 2018; Accepted: 20 January 2018; Published: 23 January 2018

Abstract: Green Island, located in the typhoon-active eastern Taiwan coastal water, is the potential Kuroshio power plant site. In this study, a high resolution (250–2250 m) shallow-water equations model is used to investigate the effect of typhoon on the hydro-dynamics of Kuroshio and Green Island wakes. Two typhoon–Kuroshio interactions—typhoon Soulik and Holland’s typhoon model—are studied. Simulation results of typhoon Soulik indicate salient characteristics of Kuroshio, and downstream island wakes seems less affected by the typhoon Soulik, because the shortest distance of typhoon Soulik is 250 km away from Green Island and wind speed near Green Island is small. Moreover, Kuroshio currents increase when flow is in the same direction as the counterclockwise rotation of typhoon, and vice versa. This finding is in favorable agreement with the TOROS (Taiwan Ocean Radar Observing System) observed data. Simulations of Kuroshio and Holland’s typhoon model successfully reproduces the downstream recirculation and vortex street. Numerical results reveal that the slow moving typhoon has a more significant impact on the Kuroshio and downstream Green Island wakes than the fast moving typhoon does. The rightward bias phenomenon is evident—Kuroshio currents increase (decrease) in the right (left) of the moving typhoon’s track, due to the counterclockwise rotation of typhoon.

Keywords: Green Island wakes; Kuroshio; shallow water equations; typhoon

1. Introduction According to Zdravkovich [1], during flow past a bluff obstacle with the Reynolds number Re = u∞ L/vt in the range of 50 and 800, a well-organized downstream wake occurs, where u∞ is the characteristic flow velocity, L the characteristic length, and vt the eddy viscosity of fluid. Flow becomes periodic with the detachment of the free shear layers and consequent alternate shedding of vortices. The periodic phenomenon is referred to as the vortex shedding, where the anti-symmetric clockwise and counterclockwise wakes pattern is called the von Karman vortex streets [1]. Vortex streets occur frequently in the atmosphere and oceans [2,3]. The phenomenon of vortex shedding behind bluff bodies has long been of interest to the fluid dynamics community and has been intensively studied by many researchers [1,4–6]. The downstream island wakes produce the upwelling and enhance the nitrate concentration in the upper ocean. This kind of phenomenon is often captured by satellite imagery [7–11], field measurement [12], and numerical modeling [13–16]. The Kuroshio, a western boundary current of the sub-tropic North Pacific Ocean, originates from the North Equatorial Current and flows northward to the eastern coast of Taiwan. The passage of the Kuroshio mainstream is parallel to the eastern shoreline of Taiwan. Green Island is located at

Atmosphere 2018, 9, 36; doi:10.3390/atmos9020036 www.mdpi.com/journal/atmosphere Atmosphere 2018, 9, 36 2 of 22

(121◦280 E, 22◦350 N) and is 40 km off the southeastern coast of Taiwan. The climatology of the Kuroshio velocity as revealed from in-situ measurements shows that Green Island is approximately located in the mainstream of the energetic Kuroshio passage and acts as an obstacle to the stream. Hence, downstream island wakes are prone to occur. Characteristics of the vortex streets in downstream Green Island can be found from the moderate resolution imaging spectroradiometer (MODIS) satellite images and in-situ measurements [17]. The seasonal variation of mainstream current patterns, and the transport of the Kuroshio in the east of Taiwan, has been numerically investigated [18]. Spatial and temporal scales of downstream Green Island wakes due to passing of the Kuroshio have been numerically studied [19]. The seasonal wind-, heat flux-, and buoyancy-driven circulation and thermohaline structure of the Caspian Sea is numerically investigated [20]. Salient features of the mesoscale dynamics, mixing and transport of the Caspian Sea are well reproduced, and compared well with the observation. Typhoons, also known as tropical low-pressure cyclones, occur in the tropical and subtropical seas, and are a frequent cause of serious disasters in coastal countries and regions. Taiwan is located in the Northwest Pacific—one of the most typhoon-active areas of the world. An annual average of four to five typhoons hit the island according to the records of the Central Weather Bureau (CWB) of Taiwan (http://www.cwb.gov.tw/) over the past century (1958–2009). Typhoons typically occur in the period from late April to December, but with most storms concentrated in July through September. In recent years, the number of typhoons and the maximum wind speed have increased and the central pressure of typhoons have decreased due to the climate change. Typhoons have a significant impact on the physical and chemical characteristics of the water of the Kuroshio. The storms disturb the Kuroshio’s path and reduce its flow rate, while strengthening upwelling and lowering the surface temperature. The impact of typhoons on the upper water layers is quite dramatic in the Kuroshio. Suda [21] suggested that typhoons are the main cause for the Kuroshio meandering near Japan. Sun et al. [22] conducted a numerical analysis for the impact of typhoons on the Kuroshio’s path south of Japan, and found that violent disturbances on the sea surface caused by a typhoon produces a strong upwelling, further strengthening the counterclockwise eddy and causing the Kuroshio to deviate southward from its original path by about 2◦ of latitude. Chen et al. [23] suggested that, in the sea of eastern Taiwan, typhoons with a diameter exceeding 200 km (a large counterclockwise eddy) can reduce significantly the Kuroshio’s flow volume and cause a 180◦ change of the Kuroshio flow direction. Taiwan has an excellent marine current energy resource as it is an island country and experiences abundant marine current flows. However, this resource has yet to be explored. The Kuroshio is known for its strong and steady flow. It could be a potential source of renewable energy as it flows steadily all year round, and Green Island is the potential plant site for Kuroshio current energy in Taiwan. Chen [24] proposed a conceptual design for the Kuroshio power plant. The assessment of the potential Kuroshio power test site has been performed using the in-situ measurements and modeling by Hsu et al. [25]. Safety, maintenance and operations of the Kuroshio power plant may be subjected to impacts from earthquakes, typhoons, climate change, and other natural factors. To prevent the potential damages caused by typhoon-driven waves, meandering vortex shedding, and the cavitation occurring on the surface of turbine blades, turbines and platforms should be submerged several tens of meters below the water surface. The effect of monsoon on the Green Island wakes has been previously studied [25,26]. The effect of typhoon on the Kuroshio and Green Island wakes is presented using a high resolution (250–2250 m) shallow water equations (SWEs) model in this study.

2. Theory and Numerical Method Shallow-water equations (SWEs) for describing shallow water flows and the space–time least-squares finite-element method (STLSFEM) used to solve SWEs are briefly introduced in this section. Atmosphere 2018, 9, 36 3 of 22

2.1. Shallow-Water Equations The two-dimensional vertical-averaged SWEs are a simple form for describing the horizontal structure of the ocean dynamics [27–30]. SWEs can be expressed in the conservative or non-conservative form. Comparison of the conservative and non-conservative form of SWEs can be found in Toro [31,32]. The two-dimensional viscous SWEs in a non-conservative form read

∂η ∂u ∂(H+η) ∂v ∂(H+η) ∂t + (H + η) ∂x + u ∂x + (H + η) ∂y + v ∂y = 0 " ∂(hu) ∂(hv) ∂(hu) # ∂ 2ρvt ∂ ρvt + ∂u + u ∂u + v ∂u + g ∂H − f v = −g ∂zb + 1 τs − τb + ∂x + ∂x ∂y ∂t ∂x ∂y ∂x ∂x h x x ∂x ∂y (1) " ∂(hu) ∂(hv) ∂(hv) # ∂ ρvt + ∂ 2ρvt ∂v ∂v ∂v ∂H ∂zb 1 s b ∂y ∂x ∂y ∂t + u ∂x + v ∂y + g ∂y + f u = −g ∂y + h τy − τy + ∂x + ∂y where η is the water surface elevation, t is time, H is the still water depth, h = η + H is the total water depth, u is the x-component velocity, v is the y-component velocity, Zb is the bottom height, and vt is the eddy viscosity which is an important parameter for modeling the Reynolds stresses for b b the ﬂuid [33]. τx and τy representing the x- and y-component bottom frictional shear stresses are expressed as b p 2 2 τx = ρCDb u + v u (2)

b p 2 2 τy = ρCDb u + v v (3) where CDb is the coefficient of bottom friction ranging between 0.0025 to 0.0040 for ocean modeling [34]. Holland’s wind field model [35] is employed to compute the typhoon wind field. The equation of the gradient of wind speed is

1 " B # 2 100B(pn − pc)(Rmw/r) Wg = (4) (R /r)B ρaire mw where B is a scaling number, Pn is the ambient pressure, Pc is the pressure of typhoon center, Rmw is 3 the radius of maximum wind speed, r is the radius to typhoon center, and ρair = 1.2 kg/m is the air density. The wind shear stresses on the water surface are usually expressed in terms of the wind speed at 10 m above the water surface W10. Powell [36] suggested that the relationship between the gradient of s s wind speed Wg and W10 can be expressed as W10 = 0.8Wg. Therefore, τx and τy representing the x- and y-component wind shear stresses are given as q s 2 2 τx = ρairCDs W10x + W10y W10x (5)

q s 2 2 τx = ρairCDs W10x + W10y W10y (6) where W10x and W10y are the x- and y-component of W10, CDs is the coefﬁcient of surface stresses [37].

2.2. Space-Time Least-Squares Finite-Element Method We use the two-dimensional SWEs to illustrate the space–time least-squares ﬁnite-element method (STLSFEM). The two-dimension SWEs read

∂η ∂u ∂(H+η) ∂v ∂(H+η) ∂t + (H + η) ∂x + u ∂x + (H + η) ∂y + v ∂y = 0 ∂u ∂u ∂u ∂t + u ∂x + v ∂y − f v = Sx (7) ∂v ∂v ∂v ∂t + u ∂x + v ∂y + f u = Sy Atmosphere 2018, 9, 36 4 of 22 where the source terms of the momentum equations are

 ∂(hu) ∂(hv) ∂(hu)  ∂ 2ρvt ∂ ρvt + 1 s b ∂x ∂x ∂y Sx = τ − τ + +  h x x ∂x ∂y

 ∂(hu) ∂(hv) ∂(hv)  ∂ ρvt + ∂ 2ρvt 1 s b ∂y ∂x ∂y Sy = τ − τ + +  h y y ∂x ∂y

The Newton method is applied to linearize the nonlinear terms in Equation (7), and the resulting equations are

∂η ∂u ∂H ∂(ηeu+ηue−ηeue) ∂v ∂H ∂(ηev+ηve−ηeve) ∂t + H ∂x + u ∂x + ∂x + H ∂y + v ∂y + ∂y = 0 ∂u ∂u ∂ue ∂ue ∂u ∂ue ∂ue ∂t + ue∂x + u ∂x − ue∂x + ve∂y + v ∂y − ve∂y − f v = Sx (8) ∂v ∂v ∂ve ∂ve ∂v ∂ve ∂ve ∂t + ue∂x + u ∂x − ue∂x + ve∂y + v ∂y − ve∂y + f u = Sy where the symbol “~” denotes the value from the previous iteration or time step. In the STLSFEM, the unknowns u = {η, u, v}T are approximated by the polynomial interpolations

     η(x, y, t) M(x, y)N(t) η       u(x, y, t) =  M(x, y)N(t)  u (9)  v(x, y, t)  M(x, y)N(t)  t  where M(x) and N(t) are the space and time interpolation functions, respectively. Substituting the approximations Equation (9) into Equation (10), the residuals can be written as

    n+1 Re MN + u + v MN (HM + H M + ηM)N HM + H M + ηMN η  η  2 ex ey 2 x x e 2 y y e 2   e   Rx =  0 MN2 + uMe x + uex M + vMe y N2 uey M − f M N2  u  e     Ry  0 (vex M + f M)N2 MN2 + uMe x + vMe y + vey M N2  v    n   (10) MN + u + v MN (HM + H M + ηM)N HM + H M + ηMN η S 1 ex ey 1 x x e 1 y y e 1    eη    + 0 MN2 + uMe x + uex M + vMe y N1 uey M − f M N1  u + Seu     0 (vex M + f M)N1 MN2 + uMe x + vMe y + vey M N1  v   Sev 

Note that a piecewise continuous linear interpolation function for time is used, where the subscripts 1 and 2 denote the number of temporal local nodes, and superscripts n and n + 1 denote the values of the space-time element at t = tn and t = tn+1, respectively. Upon applying the least square method, we thus have Z min R2dΩ (11)

Ωxt

T n e e e o where R = Rη, Ru, Rv are the residuals, Ωxt is the element of the space–time. Equation (11) can be rewritten in the form ( ) Z ∂R RdΩ = 0 (12) ∂u Ωxt Details of the STLSFEM can be found in Gunzburger [38], Hughes and Hulbert [39], Jiang [40], Laible and Pinder [41], Liang and Hsu [42].

3. Computed Results and Discussion In this section, the effect of typhoon Soulik and wind ﬁeld of Holland’s model [35] on the Kuroshio and Green Island wakes is presented. Atmosphere 2018, 9, x FOR PEER REVIEW 5 of 22

Note that a piecewise continuous linear interpolation function for time is used, where the subscripts 1 and 2 denote the number of temporal local nodes, and superscripts n and n + 1 denote n n1 the values of the space-time element at t t and t t , respectively. Upon applying the least square method, we thus have

2 min  R d (11) xt

e e e T where R  R , R u , R v are the residuals, xt is the element of the space–time. Equation (11) can be rewritten in the form   R 0   Rd  (12) xt u  ~  Details of the STLSFEM can be found in Gunzburger [38], Hughes and Hulbert [39], Jiang [40], Laible and Pinder [41], Liang and Hsu [42].

3. Computed Results and Discussion In this section, the effect of typhoon Soulik and wind field of Holland’s model [35] on the Kuroshio and Green Island wakes is presented. Atmosphere 2018, 9, 36 5 of 22 3.1. Typhoon Soulik A3.1. high Typhoon resolution Soulik (250–2250 m) SWEs model is used to investigate the hydrodynamic characteristicsA high of resolutionthe Kuroshio (250–2250 and downstream m) SWEs model Green is Island used to wakes. investigate Green the Island hydrodynamic is located at (121°28characteristics′ E, 22°350′ N), of the 40 Kuroshiokm off the and southeastern downstream coast Green of Island Taiwan. wakes. Figure Green 1a depicts Island isthe located study at area, ◦ 0 ◦ 0 the location(121 28 ofE, 22Lanyu350 N),Island 40 kmand off Green the southeastern Island, and coast the ofbathymetry Taiwan. Figure of the1a depictsadjacent the sea study waters. The bathymetryarea, the location of the of study Lanyu area Island varies and Greenfrom 400 Island, to 5000 and them, with bathymetry an average of the value adjacent of about sea waters. 2000 m. The bathymetryThe bathymetry around of the the study Green area Island varies fromis within 400 to the 5000 range m, with from an average500 to 4000 value m, of aboutwith an 2000 average m. The bathymetry around the Green Island is within the range from 500 to 4000 m, with an average value value of 2000 m. There are sea-mountains in the northwest of the Green Island where water depth of 2000 m. There are sea-mountains in the northwest of the Green Island where water depth varies varies from 200 to 400 m. from 200 to 400 m.

(a) (b)

FigureFigure 1. (a) 1. Schematic(a) Schematic illustration illustration of ofthe the study study area area and the bathymetrybathymetry derived derived from from the the ETOPO1 ETOPO1 and (andb) computational (b) computational meshes meshes with with fine ﬁne meshes meshes used used in the coastalcoastal waters waters around around Lanyu Lanyu Island Island and and GreenGreen Island. Island.

However, Kuroshio is a sub-surface flow where flow mainly occurs at the top 400 m layer of water with an average current speed around 1.0 m/s; water below 800 m is essentially motionless [17]. Therefore, we limit the bathymetry ranging from 10 to 360 m as the redefined bathymetry from the ETOPO1 (1 Arc-Minute Global Relief Model) in the simulations. Figure1b depicts the computational meshes. It contains 50,842 nodes and 101,125 triangles. Spatial resolution varies from 250 to 2250 m. Fine meshes are employed near Lanyu Island and Green Island since flow field is expected to change dramatically in these areas. The increment of time step ∆t = 45 s is used in the computations. The eight-day simulation of typhoon Soulik takes about 40 h on a personal computer equipped with an Intel(R) CoreTM i7-4700HQ [email protected]. The flow field data of HYCOM (hybrid coordinate ocean model) on 7 November 2014 after interpolation to the model grids, shown in Figure1b, is utilized to initiate the flows. The choice of this particular flow field as the initial condition is based on the hypothesis proposed by Zheng and Zheng [43] in which the downstream Green Island wakes are prone to occur when Kuroshio mainstream heads on the island. Figure2 shows the boundaries of the study domain. AB is the land boundary where no flux and free-slip boundary condition is applied, BC is the open boundary where the radiation boundary conditions are specified, and CD, DO, and OA are the velocity boundaries using the flow field data from HYCOM on 7 November 2014. Atmosphere 2018, 9, x FOR PEER REVIEW 6 of 22

However, Kuroshio is a sub-surface flow where flow mainly occurs at the top 400 m layer of water with an average current speed around 1.0 m/s; water below 800 m is essentially motionless [17]. Therefore, we limit the bathymetry ranging from 10 to 360 m as the redefined bathymetry from the ETOPO1 (1 Arc-Minute Global Relief Model) in the simulations. Figure 1b depicts the computational meshes. It contains 50,842 nodes and 101,125 triangles. Spatial resolution varies from 250 to 2250 m. Fine meshes are employed near Lanyu Island and Green Island since flow field is expected to change dramatically in these areas. The increment of time step Δt = 45 s is used in the computations. The eight-day simulation of typhoon Soulik takes about 40 h on a personal computer equipped with an Intel(R) CoreTM i7-4700HQ [email protected]. The flow field data of HYCOM (hybrid coordinate ocean model) on 7 November 2014 after interpolation to the model grids, shown in Figure 1b, is utilized to initiate the flows. The choice of this particular flow field as the initial condition is based on the hypothesis proposed by Zheng and Zheng [43] in which the downstream Green Island wakes are prone to occur when Kuroshio mainstream heads on the island. Figure 2 shows the boundaries of the study domain. AB is the land boundary where no flux and free-slip boundary condition is applied, BC is the open boundary where the radiation boundary conditions are specified, and CD, DO , and OA are the velocity Atmosphere 2018, 9, 36 6 of 22 boundaries using the flow field data from HYCOM on 7 November 2014.

FigureFigure 2.2. StudyStudy domaindomain andand boundaries,boundaries, as wellwell asas streamlinesstreamlines fromfrom thethe hybridhybrid coordinatecoordinate oceanocean model)model) (HYCOM).(HYCOM).

FigureFigure3 3 shows shows a a composite composite ERS-1 ERS-1 SAR SAR (European (European Remote Remote Sensing Sensing satellite1, satellite1, Synthetic Synthetic Aperture Aperture Radar)Radar) imageimage ofof downstreamdownstream islandisland vortexvortex trainstrains ofof LanyuLanyu IslandIsland andand GreenGreen IslandIsland takentaken withwith oneone weekweek intervalinterval sequentially sequentially between between 17:01 17:01 UT UT 25 25 September September (lower) (lower) and and 19:02 19:02 UT 2UT October 2 October (top), (top), 1996. Two1996. downstream Two downstream island island vortex vortex trains aretrains clearly are cl seen.early Oneseen. a smallOne a distancesmall distance from the from coast, the calledcoast, thecalled Lanyu the Lanyu Island (alsoIsland called (also thecalled Orchid the Orchid Island) Island) vortex train,vortex occurs train, downstreamoccurs downstream of Lanyu of IslandLanyu (aIsland little (a beyond little beyond the southern the southern boundary boundary of the image), of the andimage), consists and ofconsists three vortexes,of three vortexes, two cyclonic two appearingcyclonic appearing as bright shadingas bright and shading one anticyclonic and one an appearingticyclonic as appearing dark shading as dark vortexes. shading Another vortexes. near theAnother eastern near coast the of eastern Taiwan, coast called of Taiwan, the Green called Island the vortex Green train,Island occurs vortex downstream train, occurs of downstream Green Island, of andGreen consists Island, of and three consists pairs ofof cyclonicthree pairs vortexes of cyclonic (bright vortexes center) (bright and anticyclonic center) and vortexes anticyclonic (dark vortexes center). Spatial(dark center). and temporal Spatial scalesand temporal of downstream scales of Green down Islandstream wakesGreen dueIsland to passingwakes due of the to passing Kuroshio of hasthe beenKuroshio numerically has been studied numerically [19]. The studied main difference[19]. The betweenmain difference Liang et between al. [19] and Liang the et present al. [19] study and liesthe inpresent a constant study inﬂow lies in useda constant in Liang inflow et al. used is replaced in Liang byet al. a spatial is replaced varying by a inﬂow spatial from varying HYCOM inflow in from the presentHYCOM study. in the present study. The SWEs model is applied to simulation the typhoon Soulik event. Typhoon Soulik hit the Taiwan area during 7 to 14 July 2013. Figure4 depicts the track of typhoon Soulik. Typhoon Soulik, developed from a tropical depression on 7 July 2013 through a tropical storm, moderate typhoon, severe typhoon, and then decreased its strength and made landfall on Taiwan on 7 December 2013. The typhoon Soulik data with temporal intervals of every 6 h are from the CWB of Taiwan, which are computed by the NFS (non-hydrostatic forecast system). NFS uses the structured orthogonal meshes; however, the SWEs model uses the unstructured triangular meshes. Therefore, wind data needs to be interpolated into the computational nodes of the SWEs model. The IDW (inverse distance weighted interpolation [44]) is employed to interpolate the data from NFS into nodal points of the SWEs model. In this study, the 5-km resolution typhoon Soulik data is used. The maximum wind speed of typhoon Soulik is 51 m/s, categorized as a severe typhoon. The closest distance of typhoon to Green Island is about 250 km. The maximum wind speed of the model area is 17 m/s and the average value is smaller than 10 m/s. Atmosphere 2018, 9, 36 7 of 22 Atmosphere 2018, 9, x FOR PEER REVIEW 7 of 22

(a) (b)

Figure 3. (a) A composite ERS-1 SAR image of island-induced ocean vortex trains of Lanyu Island Figure 3. (a) A composite ERS-1 SAR image of island-induced ocean vortex trains of Lanyu Island and Green Island taken at 17:01 UT 25 September (lower) and 19:02 UT 2 October (top), 1996. (b) and Green Island taken at 17:01 UT 25 September (lower) and 19:02 UT 2 October (top), 1996. Zoomed(b) Zoomed Green Green Island Island and and head head of ofvortex vortex train train (m (modiﬁedodified from from Figure Figure 22 of of Zheng Zheng and and Zheng [43]). [ 43]). Blue circle represents for cyclonic (bright shading) vortexes and red circle re representspresents for anticyclonic (dark shading) vortexes.

The SWEs model is applied to simulation the typhoon Soulik event. Typhoon Soulik hit the Figure5a depicts the global view of the study area, where the enclosed region near the Green Taiwan area during 7 to 14 July 2013. Figure 4 depicts the track of typhoon Soulik. Typhoon Soulik, Island indicates the sub-domain that will be presented in the succeeding plots of the downstream developed from a tropical depression on 7 July 2013 through a tropical storm, moderate typhoon, recirculation and island wakes. Figure5b depicts the local view of the sub-domain as well as the severe typhoon, and then decreased its strength and made landfall on Taiwan on 7 December 2013. location of the cross section Q Q and monitor point P at downstream Green Island, where time series The typhoon Soulik data with0 temporal1 intervals of every 6 h are from the CWB of Taiwan, which of flow quantities are presented and analyzed. Length of Q Q is 20 km. It is located about 22 km are computed by the NFS (non-hydrostatic forecast system).0 NFS1 uses the structured orthogonal downstream the Green Island. meshes; however, the SWEs model uses the unstructured triangular meshes. Therefore, wind data Figure6 depicts the typhoon wind field and flow streamlines as well as vectors of wind (red) needs to be interpolated into the computational nodes of the SWEs model. The IDW (inverse distance and flow (blue) along cross section Q Q at S –S five time instances with a 12 h of increment, shown weighted interpolation [44]) is employed0 1 to 0interpol4 ate the data from NFS into nodal points of the in Figure5, where S represents 00:00 of 12 July, S 12:00 of 12 July, S 00:00 of 13 July, S 12:00 of SWEs model. In this 0study, the 5-km resolution typhoon1 Soulik data is2 used. The maximum3 wind 13 July, and S 00:00 of 14 July 2013, respectively. As can be seen, the downstream island wakes speed of typhoon4 Soulik is 51 m/s, categorized as a severe typhoon. The closest distance of typhoon are well reproduced. The flow field is affected by the typhoon, especially in the shallow water area to Green Island is about 250 km. The maximum wind speed of the model area is 17 m/s and the and the lee of the islands. Interactions of Kuroshio and downstream island wakes with typhoon are average value is smaller than 10 m/s. obvious. When typhoon approaches the study area, because of the cyclonic rotation and southward Figure 5a depicts the global view of the study area, where the enclosed region near the Green winding of typhoon, Kuroshio current decreases. At S , we can see the moment when the center of the Island indicates the sub-domain that will be presented3 in the succeeding plots of the downstream typhoon is closest to the Green Island. The wind starts to change its direction and to blow northward. recirculation and island wakes. Figure 5b depicts the local view of the sub-domain as well as the Comparing flow vectors along cross section Q0Q1 at S2 with that at S1 and S3 of Figure6, it is noticed location of the cross section Q0Q1 and monitor point P at downstream Green Island, where time that downstream island wakes are significantly affected. Kuroshio currents increase after S2 due to the seriesnorthward of flow winding quantities and are resumes presented its normal and analyzed. flow condition Length after of typhoonQ0Q1 is passes 20 km. far It away.is located about 22 km downstream the Green Island.

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Figure 4. Track of typhoon Soulik from 7 to 14 June 2013, where symbol denotes the tropical

FigureFigureFigure Figure4. 4. Track Track 4.4.Figure ofTrack Trackof typhoon typhoon 4. of ofTrack typhoon typhoon Soulik Soulik of typhoon Soulikfrom from Soulik Soulik7 from 7to to 14 14from from7 June toJune 714 7 to2013, 2013,Juneto 14 June 14where 2013,where June 2013, wheresymbol symbol where2013, symbol symbol where denotes denotes symbol denotesdenotes the the tropical tropicalthe the tropical tropicaldepression denotes depression thewith tropical maximum wind speed Vmax < 17.2 m/s; the tropical storm, 17.2 m/s < Vmax < depressiondepressiondepressiondepression with withwithFigure maximum maximumwith maximum 4. maximum maximumTrack wind wind windof speed typhoon windspeed speed wind Vmaxspeed Vmax VmaxSoulik speed

(a) (b) (a(a) ) (b(b)) (a) (b) Figure 5. (a) Global view of the study area, where the enclosed region near the Green Island indicates (a) (b) FigureFigure Figure5. 5. ( a()a )Global Global5. (a) Globalview view of ofview the the study ofstudy the area, study area, where wherearea, thewhere the encl encl theosedosed encl region regionosed regionnear near the the near Green Green the IslandGreen Island indicatesIsland indicates indicatesthe sub-domain that will be presented in the succeeding plots of the downstream recirculation and thethe sub-domain sub-domainFigure that that will 5.will ( abe )be Global presented presented view in ofin the thethe succestudy succeeding edingarea, plotswhere plots of ofthe the the encl downstream downstreamosed region recirculation recirculationnear the Green and and Islandisland wakes,indicates and (b) local view of the sub-domain as well as location of the cross section Q Q and the sub-domainFigure 5. that(a) Globalwill be viewpresented of the in study the succe area, whereeding plots the enclosed of the downstream region near therecirculation Green Island and indicates 0 1 islandisland wakes, wakes, and theand (sub-domain b(b) )local local view view that of of the thewill sub-domain sub-domain be presented as as wellin well the as as succelocation locationeding of of theplots the cross cross of thesection section downstream QQQQ and andrecirculation and island wakes,the sub-domain and (b) local that view will of be the presented sub-domain in the as well succeeding as location plots of of the the cross downstream section00 1 1 Q recirculation0Qmonitor1 and point and P at downstream Green Island. Length of Q0Q1 is 20 km. It locates about 22 km island wakes, and (b) local view of the sub-domain as well as location of the cross section Q0Q1 and monitormonitormonitor point point islandP pointP at at downstream downstream wakes,P at downstream and (Greena (Greenb) ) local GreenIsland. Island. view Island.Length ofLength the Length sub-domainof of QQ0 Q0ofQ1 1 Qis is 0 asQ20 201 wellkm. iskm. 20 Itas It km.locates locationlocates It( b locatesabout )about of the 22about 22 cross km kmdownstream 22 section km Q0 Qthe1 Green Island. downstreamdownstream the themonitorand Green Green monitor Island.point Island. point P atP downstreamat downstream Green Green Island. Island. Length Length of ofQ0QQ01Q 1isis 20 20 km. km. It It locates locates about about 22 22 km Figuredownstream 5. (a) Globalthe Green view Island. of the study area, where the enclosed region near the Green Island indicates downstream the Green Island. Figure 6 depicts the typhoon wind field and flow streamlines as well as vectors of wind (red) the sub-domain that will be presented in the succeeding plots of the downstream recirculation and FigureFigureFigure 6 6 depicts depicts 6 depicts the the typhoon typhoon the typhoon wind wind fieldwind field and fieldand flow flowand streamlines flowstreamlines streamlines as as well well as as aswell vectors vectors as vectors of of wind andwind of flow (red)wind (red) (blue) (red) along cross section Q0Q1 at S0–S4 five time instances with a 12 h of increment, shown andand flow flowand island(blue) (blue)flow (blue) alongwakes, alongFigure crossalong cross and 6 sectiondepicts cross section(b) local section the QQ0 Qview0 Qtyphoon1 1 Qat at0 ofQS S01 –0the –S atSwind4 4five Ssub-domainfive0–S timefield 4time five instances and instancestime flowas instances well with streamlineswith as a awith location12 12 h h aof of 12as increment, increment, hofwell of the increment, asin cross vectorsFigure shown shown section shown5,of where wind Q 0 (red)QS01 represents and 00:00 of 12 July, S1 12:00 of 12 July, S2 00:00 of 13 July, S3 12:00 of 13 inin Figure Figurein Figure 5, 5, where whereand 5, flowwhere S S0 0represents represents(blue) S0 represents along 00:00 00:00 cross of00:00 of section12 12 July, ofJuly, 12 SQ July,S10 1Q12:00 12:001 Sat1 ofS12:00 of0 –12 S124 July,five ofJuly, 12 timeS July,S2 200:00 00:00 instances S2 of00:00 of 13 13 July,with ofJuly, 13 Sa July,S 312 312:00 July,12:00 h Sof3 and of12:00 increment,of 13 13 S 4 of00:00 13 shown of 14 July, 2013, respectively. As can be seen, the downstream island wakes are well monitor point P at downstream Green Island. Length of Q0Q1 is 20 km. It locates about 22 km July,July, and July,and S S4 and 400:00 00:00in SFigure4 of 00:00 of 14 14 July, 5, ofJuly, where 14 2013, 2013,July, S respectively. 0 2013, respectively.represents respectively. 00:00 As As can can of As be 12be can seen, July,seen, be the S seen,the1 12:00 downstream downstream the of downstream 12 July, island island S2 00:00 islandwakes wakes ofreproduced. wakes are13 are July, well well are S 3well The12:00 flow of 13 field is affected by the typhoon, especially in the shallow water area and the downstream the Green Island. reproduced.reproduced.reproduced. The July,The flow flowandThe field Sflowfield4 00:00 is fieldis affected ofaffected 14is July,affected by by 2013, the the by typh typhrespectively. theoon, oon,typh especially especiallyoon, As especially can in inbe the theseen, inshallow shallow the the shallowdownstream water water waterarea arealee islandand ofandarea the the the andwakes islands. the are Interactions well of Kuroshio and downstream island wakes with typhoon are obvious. leelee of of thelee the ofislands. islands. thereproduced. islands. Interactions Interactions Interactions The of flowof Kuroshio Kuroshio fieldof Kuroshio is and andaffected downstream downstream and by downstream the typh island islandoon, islandwakes wakes especially wakes with with typhoon inwithtyphoon the typhoon shallow are are obvious. obvious. arewater obvious. area and the Figurelee of6 thedepicts islands. the Interactions typhoon of wind Kuroshio field and and downstream flow streamlines island wakes as with well typhoon as vectors are obvious. of wind (red) and flow (blue) along cross section Q0Q1 at S0–S4 five time instances with a 12 h of increment, shown in Figure 5, where S0 represents 00:00 of 12 July, S1 12:00 of 12 July, S2 00:00 of 13 July, S3 12:00 of 13 July, and S4 00:00 of 14 July, 2013, respectively. As can be seen, the downstream island wakes are well reproduced. The flow field is affected by the typhoon, especially in the shallow water area and the lee of the islands. Interactions of Kuroshio and downstream island wakes with typhoon are obvious.

Atmosphere 2018, 9, x FOR PEER REVIEW 9 of 22

When typhoon approaches the study area, because of the cyclonic rotation and southward winding of typhoon, Kuroshio current decreases. At S3, we can see the moment when the center of the typhoon is closest to the Green Island. The wind starts to change its direction and to blow northward.

Comparing flow vectors along cross section Q0Q1 at S2 with that at S1 and S3 of Figure 6, it is noticed that downstream island wakes are significantly affected. Kuroshio currents increase after S2 due to Atmosphere 2018, 9, 36 9 of 22 the northward winding and resumes its normal flow condition after typhoon passes far away.

Figure 6. Cont.

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(unit: m/s) (unit: m/s)(a) (b)(c) (a) (b)(c) Figure 6. (a) W10 vectors and contours (unit: m/s), (b) flow streamlines, and (c) wind vectors (red) and flow

Figurevectors 6. (a (blue)) W10 vectors of cross andsection contours Q0Q1 (unit: at S0 –m/s),S4 five (b time) flow instances streamlines, of the andtyphoon (c) wind Soulik, vectors see Figure (red) 5. and flow Figure 6. (a) W10 vectors and contours (unit: m/s), (b) flow streamlines, and (c) wind vectors (red) and vectorsflow (blue) vectors of (blue) cross ofsection cross sectionQ0Q1 Q at0Q S10–atS4S five0–S4 timefive timeinstances instances of the of typhoon the typhoon Soulik, Soulik, see see Figure Figure 5.5 . Figure 7a illustrates the location of 22.84° N (y = 150 km) cross section, where black dots denote the position of TOROS data, and Figure7b,c depicts the comparison of the TOROS-observed surface FigureFigure 7a7 illustratesa illustrates the the location location of 22.84 °◦ NN( (y = 150 km)km) crosscross section, section, where where black black dots dots denote denote currents with the computed flow vectors along the 22.84° N cross section at S0–S4: five time instances. the theposition position of ofTOROS TOROS data, data, and and Figure7b,c Figure7b,c depi depictscts thethe comparisoncomparison of of the the TOROS-observed TOROS-observed surface surface Since TOROS data are the surface flow quantities, they◦ are larger than the depth-averaged model currentscurrents with with the the computed computed flow flow vectors vectors along along the 22.8422.84°N N cross cross section section at atS0 S–0S–4S:4 five: five time time instances. instances. predictions, in general. Moreover, the left one-third of the cross section (0–20 km) is right in the lee SinceSince TOROS TOROS data data are are the the surface surface flow flow quantities, quantities, theythey areare largerlarger than than the the depth-averaged depth-averaged model model of Green Island. The meandering downstream island wakes are observed in the modelling, but not predictions, in general. Moreover, the left one-third of the cross section (0–20 km) is right in the lee predictions,present in in the general. TOROS Moreover, data, because the leftof its one-third coarse spatial of the resolution cross section (~10 (0–20km). However,km) is right computed in the lee of Green Island. The meandering downstream island wakes are observed in the modelling, but not of Greenresults Island. show Kuroshio The meandering currents increasedownstream when islandflow is wakesin the sameare observed direction inas the counterclockwisemodelling, but not present in the TOROS data, because of its coarse spatial resolution (~10 km). However, computed presentrotation in the of TOROStyphoon, data, and because vice versa. of its This coarse fin dingspatial is resolutionconsistent (~10with km).the However,TOROS measured computed results show Kuroshio currents increase when flow is in the same direction as the counterclockwise resultsdatasets show [45]. Kuroshio currents increase when flow is in the same direction as the counterclockwise rotation of typhoon, and vice versa. This finding is consistent with the TOROS measured datasets [45]. rotation of typhoon, and vice versa. This finding is consistent with the TOROS measured datasets [45].

(a)

Figure 7. Cont. (a)

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(b) (c)

Figure 7. (a) LocationLocation ofof thethe 22.8422.84°◦ N(N (yy= = 150150 km)km) crosscrosssection, section, where where black black dots dots denote denote the the position position of TOROS data.data. (b)) andand ((cc)) depictdepict comparisoncomparison of of ﬂow flow vectors vectors of of TOROS TOROS data data and and model model predictions predictions along 22.84°◦ N cross section at S0–S4: five time instances, see Figure 5. along 22.84 N cross section at S0–S4: ﬁve time instances, see Figure5.

Atmosphere 2018, 9, x FOR PEER REVIEW 12 of 22 Atmosphere 2018, 9, 36 12 of 22

3.2. Effect of Model Typhoon on Green Island Wakes 3.2. Effect of Model Typhoon on Green Island Wakes Figure 8 depicts flow streamlines around the Green Island of no wind forcing in a period of vortex shedding.Figure8 depicts There flow are streamlinessmall recirculations around the in Green the Islandlee of ofGreen no wind Island. forcing Its insize a period is about of vortex the size of shedding. There are small recirculations in the lee of Green Island. Its size is about the size of the the island (~8 km). A well-organized coherent and alternating asymmetric meandering eddies in the island (~8 km). A well-organized coherent and alternating asymmetric meandering eddies in the lee lee of the Green Island is reproduced, which has been observed in field measurement [17] and satellite of the Green Island is reproduced, which has been observed in field measurement [17] and satellite imagesimages [19,43]. [19,43 In]. this In this study, study, simulation simulation using using thethe boundaryboundary conditions conditions from from HYCOM HYCOM produces produces a a moremore realistic realistic Kuroshio Kuroshio flow flow and and downstream downstream GreenGreen Island Island wakes. wakes.

t = 1/4 T t = 3/4 T

t = 1/2 T t = T

FigureFigure 8. Flow 8. Flow streamlines streamlines of of the the Green Green IslandIsland wakes wakes in in the the no no wind wind forcing forcing case. case.

AccordingAccording to the to thestatistical statistical analysis analysis of typhoons of typhoons from from 1911 1911 to to2010 2010 by by the the CWB CWB of ofTaiwan, Taiwan, 83.6% of typhoons83.6% of typhoonspass the pass eastern the eastern Taiwan Taiwan coastal coastal waters waters and and 13.5% 13.5% pass thethe western western Taiwan Taiwan coastal coastal waters.waters. Therefore, Therefore, two two typical typical tr tracksacks of of typhoons, typhoons, namelynamely the theSN SNtyphoon typhoon (17% (17% of total) of total) moving moving from from southwestsouthwest to tonortheast northeast and and thetheEW EWtyphoon typhoon (67% (67% of total) of movingtotal) moving from east from to west, east shown to west, in Figure shown9, in Figureare 9, chosen are chosen to investigate to investigate the effect the of typhoon effect of on typhoon the Kuroshio on the and Kuroshio Green Island and wakes. Green Two Island typical wakes. Twovalues typical of thevalues typhoon of movingthe typhoon speed, 2.5moving m/s (9 speed, km/h) and2.5 5.0m/s m/s (9 (18km/h) km/h), and are 5.0 considered. m/s (18 Value km/h), of are the radius of maximum wind speed R = 50 km and pressure of typhoon center P = 950 hPa are considered. Value of the radius of maximummw wind speed Rmw = 50 km and pressurec of typhoon center used in the Holland’s wind ﬁeld model. The resulting maximum of W10 is about 47 m/s. Pc = 950 hPa are used in the Holland’s wind field model. The resulting maximum of W10 is about 47 m/s.

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FigureFigure 9. Schematic 9. Schematic diagram diagram of of the the study study domaindomain and and track track of of SNSN andand EWEW typhoon.typhoon. Figure 9. Schematic diagram of the study domain and track of SN and EW typhoon. In order to better quantify the net influence of typhoon on Green Island wakes, we subtract the In order to better quantify the net influence of typhoon on Green Island wakes, we subtract the flow field of SN typhoon case and EW typhoon case with no wind forcing case. The net influence of In order to better quantify the net influence of typhoon on Green Island wakes, we subtract the flow fieldtyphoon of SN on thetyphoon flow field case is anddefinedEW bytyphoon case with no wind forcing case. The net influence of typhoonflow field on of theSN flowtyphoon field case is defined and EW by typhoon case with no wind forcing case. The net influence of typhoon on the flow field is defined by unet  uwind  uno wind (13) unet = uwind − uno wind (13) u u u netvnet windvwind novno wind wind (14)(13) vnet = vwind − vno wind (14) Figures 10 and 11 show the “net”vnet u- andvwind v-contours vno wind of SN typhoon at T0–T2 three time instances(14) Figuresas indicated 10 and in Figure 11 show 16. It the is not “net”ed thatu- and the veffect-contours of typhoon of SN ontyphoon the y-component at T0–T2 velocitythree time are more instances as indicatedFigurespronounced in10 Figureand than 11 on 16.show the It x isthe-component noted “net” that u- andvelocity, the v effect-contours because of typhoon of the SN direction typhoon on the of aty moving-component T0–T2 threeSN typhoon time velocity instances and are the more pronouncedas indicatedmainstream in than Figure of on Kuroshio the 16. xIt-component is is not theed same, that velocity, thein general. effect because of Due typhoon to the the directionon counterclockwi the y-component of movingse rotation velocitySN typhoon of typhoon,are more and the mainstreampronouncedflow accelerates than of Kuroshio on (decelerates) the x-component is the when same, velocity,itin flows general. in because the favorable Due the to direction the (adverse) counterclockwise of directio movingn of SN wind. rotationtyphoon For example, and of typhoon, the mainstreamFigures 14of andKuroshio 15 show is thethat same, y-component in general. velocity Due increases to the counterclockwi in the right of seSN rotation typhoon’s of tracktyphoon, and flow accelerates (decelerates) when it flows in the favorable (adverse) direction of wind. For example, flow decreasesaccelerates in (decelerates) the left of SN whentyphoon’s it flows track, in the sofavorable called rightward (adverse) bias directio phenomenon.n of wind. The For rightward example, Figures 14 and 15 show that y-component velocity increases in the right of SN typhoon’s track and Figuresbias 14 phenomenon and 15 show of uthat contours y-component is not as evidentvelocity as increases v contours, in sincethe right the northeastward of SN typhoon’s Kuroshio track andand decreases in the left of SN typhoon’s track, the so called rightward bias phenomenon. The rightward decreasesx-component in the left wind of SN forcing typhoon’s are not track, in the the same so orcalled opposite rightward direction. bias phenomenon. The rightward bias phenomenon of u contours is not as evident as v contours, since the northeastward Kuroshio and bias phenomenonComparing of uFigure contours 10 with is not Figure as evident 11, we noticeas v contours, that the impactsince the of thenortheastward slow-moving Kuroshio typhoon (andWT x x-component-component= 2.5 m/s) wind is more forcing forcing significant are are not not thanin in the the the same same fast-moving or or opposite opposite typhoon direction. direction. (WT = 5.0 m/s), especially in the y- Comparingcomponent velocity, Figure when10 with the Figuretyphoon 11 moves, we in notice favor thatof the the Kuroshio impact mainstream of the slow-moving direction. When typhoon Comparing Figure 10 with Figure 11, we notice that the impact of the slow-moving typhoon (WT W the typhoon moves slowly, it takes a longer time to travel the sameW distance. Therefore, more (= 2.5T = m/s) 2.5 m/s) is moreis more significant significant than thanthe fast-moving the fast-moving typhoon typhoon (WT = (5.0T m/s),= 5.0 especially m/s), especially in the y in- the momentum and energy are input to water, and water takes more time to respond to the wind forcing. ycomponent-component velocity, velocity, when when the typhoon the typhoon moves moves in favo inr of favor the Kuroshio of the Kuroshio mainstream mainstream direction. When direction. Whenthe typhoon the typhoon moves moves slowly, slowly, it takes it takesa longer a longer time timeto travel to travel the same the same distance. distance. Therefore, Therefore, more more momentummomentum and energy energy are are input input to to water, water, and and water water takes takes more more time time to respond to respond to the to wind the wind forcing. forcing.

Figure 10. Cont.

AtmosphereAtmosphere 20182018, 9,, x9 ,FOR 36 PEER REVIEW 14 14of of22 22 Atmosphere 2018, 9, x FOR PEER REVIEW 14 of 22

(a)( a) (b(b)()(cc))

(unit: m/s) (unit: m/s) (unit: m/s) (unit: m/s) Figure 10. Contours of (a) W10, “net” (b) u-, and (c) v-contours of (unit: m/s) SN typhoon with moving FigureFigure 10. 10. ContoursContours of of(a) (a W) W10,10 “net”, “net” (b) ( bu)-,u and-, and (c) ( cv)-contoursv-contours of of (unit: (unit: m/s) m/s) SNSN typhoontyphoon with with moving moving speed WT = 2.5 m/s at T0–T2 three time instances indicated by the three vertical lines of Figure 16a. speedspeed WWT =T 2.5=2.5 m/s m/s at T at0–T20 –threeT2 three time time instances instances indicated indicated by th bye three the three vertical vertical lines lines of Figure of Figure 16a. 16a.

Figure 11. Cont.

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(a) (b)(c) (a) (b)(c)

(unit: m/s) (unit: m/s) (unit: m/s) (unit: m/s) Figure 11. Contours of (a) W10, “net” (b) u-, and (c) v-contours of (unit: m/s) SN typhoon with moving Figure 11. Contours of (a) W10, “net” (b) u-, and (c) v-contours of (unit: m/s) SN typhoon with moving Figure 11. Contours of (a) W , “net” (b) u-, and (c) v-contours of (unit: m/s) SN typhoon with moving T 0 2 10 speedspeed W = W 5.0T = m/s5.0 m/s at T at– TT0– Tthree2 three time time instances instances indicatedindicated byby th the ethree three vertical vertical lines lines of Figureof Figure 16b. 16b. speed WT = 5.0 m/s at T0–T2 three time instances indicated by the three vertical lines of Figure 16b.

FigureFigure 12 plots 12 plots the the wind wind field field as as well well as as wind wind vectors (red) (red) and and flow flow (blue) (blue) vectors vectors along along Q0Q 1Q 0Q1 Figure 12 plots the wind field as well as wind vectors (red) and flow (blue) vectors along Q0Q1 at at T0–atT T2 0three–T2 three time time instances. instances. The The flow flow field field and and downstreamdownstream island island wakes wakes are are significantly significantly affected affected T0–T2 three time instances. The flow field and downstream island wakes are significantly affected by by thebythe northeastward the northeastward northeastward typhoon. typhoon. KuroshioKuroshio Kuroshio currents currents currents increase increase as theasas the typhoonthe typhoon typhoon approaches approaches approaches and and decrease and decrease decrease as as theasthe typhoon the typhoon typhoon passes passes passes away. away. away.

Figure 12. Cont.

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Atmosphere 2018, 9, x FOR PEER REVIEW 16 of 22

(a) (b) (a) (b) Figure 12. (a) W10-contours and (b) wind vectors (red) and flow vectors (blue) of SN typhoon along FigureFigure 12. 12.(a) (Wa) 10W-contours10-contours andand ((b) wind vectors vectors (red) (red) and and flow ﬂow vectors vectors (blue) (blue) of SN of typhoonSN typhoon along along crosscross section section Q QQ Q withwith moving moving speed speed W T = 2.52.5 m/sm/s atatT T0––TT2three three time time instances instances indicated indicated by the by the cross section0 1 0 Q01Q1 with moving speed WTT = 2.5 m/s at T0–T0 2 three2 time instances indicated by the threethree verticalthree vertical vertical lines lines of lines Figure of of Figure Figure 16a. 16a. 16a.

Figures 13 and 14 plot the “net” u- and v-contours of EW typhoon at T0–T2 three time instances FiguresFigures 13 and13 and 14 14plot plot the the “net” “net” u-u- andand v-v-contourscontours ofofEW EWtyphoon typhoon at atT0 –TT0–2Tthree2 three time time instances instances indicatedindicated in Figurein Figure 16. 16. The The rightward rightward bias bias feature feature du duee to tothe the counterclockwise counterclockwise rotation rotation of typhoon of typhoon is is indicatedevident, in Figure especially 16. The for thrightwarde slow moving bias typhoon feature and du ye-component to the counterclockwise velocities. Comparing rotation Figures of 10 typhoon is evident, especially for the slow moving typhoon and y-component velocities. Comparing Figures 10 and 11 evident, andespecially 11 with Figuresfor the 13 slow and 14,moving the impact typhoon of SN andtyphoon y-component on the Kuroshio velocities. and downstream Comparing Green Figures 10 with Figures 13 and 14, the impact of SN typhoon on the Kuroshio and downstream Green Island and 11 withIsland Figures wakes is 13apparently and 14, more the significantimpact of than SN EW typhoon typhoon. on The the effect Kuroshio of the typhoon and strengthensdownstream Green wakes is apparently more signiﬁcant than EW typhoon. The effect of the typhoon strengthens when the Island wakeswhen theis apparently typhoon moves more in favor significant of the Kuroshio than andEW weakens typhoon. when The the effect typhoon of movesthe typhoon against the strengthens typhoonKuroshio. moves in favor of the Kuroshio and weakens when the typhoon moves against the Kuroshio. when the typhoon moves in favor of the Kuroshio and weakens when the typhoon moves against the Kuroshio.

Figure 13. Cont.

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Atmosphere 2018, 9, x FOR PEER REVIEW 17 of 22

(a) (b)( c) (a) (b)(c)

(unit: m/s) (unit: m/s)

(unit: m/s) (unit: m/s) Figure 13. Contours of (a) W10, “net” (b) u-, and (c) v-contours (unit: m/s) of EW typhoon with moving Figure 13. Contours of (a) W10, “net” (b) u-, and (c) v-contours (unit: m/s) of EW typhoon with moving speedFigure W T13. = 2.5Contours m/s at ofthree (a) Wtime10, “net” instances (b) u-, T and0–T2 (c)indicated v-contours by the(unit: three m/s) vert of EWical typhoon lines of Figurewith moving 16a. speed WT = 2.5 m/s at three time instances T0–T2 indicated by the three vertical lines of Figure 16a. speed WT = 2.5 m/s at three time instances T0–T2 indicated by the three vertical lines of Figure 16a.

(a(a)) (b)()(cc) )

(unit: m/s) (unit: m/s) (unit:(unit: m/s) m/s)

Figure 14. Contours of (a) W10, “net”(b) u-, and (c) v-contours of (unit: m/s) EW typhoon with moving speed WT = 5.0 m/s at T0–T2 three time instances indicated by the three vertical lines of Figure 16b. Atmosphere 2018, 9, x FOR PEER REVIEW 18 of 22

AtmosphereFigure2018 14., 9Contours, 36 of (a) W10, “net”(b) u-, and (c) v-contours of (unit: m/s) EW typhoon with moving18 of 22 speed WT = 5.0 m/s at T0–T2 three time instances indicated by the three vertical lines of Figure 16b.

FigureFigure 15 plots the wind fieldfield as well asas windwind vectorsvectors (red)(red) andand flowflow vectorsvectors (blue) (blue) along alongQ 0QQ0Q1 at1 atT0 –TT0–2Tthree2 three time time instances instances of of the theEW EWtyphoon typhoon case. case. The The flow flow field field and and downstream downstream island island wakes wakes are arealso also significantly significantly affected affected by the byEW thetyphoon. EW typhoon. Kuroshio Kuroshio currents decreasecurrents asdecrease the typhoon as the approaches typhoon approachesand increase and in aincrease short period in a short as the period typhoon as the passes typhoon away. passes away.

(a) (b)

Figure 15. (a) W10-contours and (b) wind vectors (red) and flow vectors (blue) of EW typhoon along Figure 15. (a) W10-contours and (b) wind vectors (red) and ﬂow vectors (blue) of EW typhoon along cross section Q Q with moving speed WT = 2.5 m/s at T0–T2 three time instances indicated by the cross section Q00Q1 with moving speed WT = 2.5 m/s at T0–T2 three time instances indicated by the threethree vertical vertical lines lines of of Figure Figure 16a.

FigureFigure 16 showsshows a comparison comparison of time series of u andand vv ofof the the monitor monitor point point PP ofof no no wind wind forcing forcing case and SN typhoon case with (a) WT = 2.5 m/s and (b) WT = 5.0 m/s, respectively. Three vertical lines case and SN typhoon case with (a) WT = 2.5 m/s and (b) WT = 5.0 m/s, respectively. Three vertical are drawn and represent the three time instances. The first time instance (T0), represented by the red lines are drawn and represent the three time instances. The ﬁrst time instance (T0), represented by the vertical dashed line, indicates the time instance when the typhoon is located 50 km southwest of red vertical dashed line, indicates the time instance when the typhoon is located 50 km southwest of Green Island. The second time instance (T1), represented by the green vertical dashed line, indicates Atmosphere 2018, 9, x FOR PEER REVIEW 19 of 22 Atmosphere 2018, 9, 36 19 of 22

Green Island. The second time instance (T1), represented by the green vertical dashed line, indicates thethe moment moment when when the the typhoon typhoon passes passes the the Green Green Island. Island. The thirdthird timetime instance instance ( T(T2),2), represented represented by by thethe blue blue vertical vertical dashed dashed line, line, indicates indicates the the time time instance instance when when the typhoontyphoon is is located located 50 50 km km northeast northeast of Greenof Green Island. Island. This This shows shows that that the the typhoon typhoon has has little little influence influence on thethe flowflow fieldfield near nearP Pwhen when it it approachesapproaches P andP and is isfar far away away from from PP. .However, However, the the influence influence ofof thethe typhoontyphoon increases increases as as the the typhoon typhoon approachesapproaches P, Pand, and remains remains significant significant in in a ashort short period period after after the the typhoon typhoon has passed farfar awayaway fromfromP P. .

(a) (b)

FigureFigure 16. 16. ComparisonComparison of of u andandv vof of monitor monitor point pointP of P no of wind, no wind,SN, and SNEW, andtyphoon EW typhoon with the movingwith the moving speed WT = (a) 2.5 m/s (upper row) and (b) 5.0 m/s (lower row), respectively. speed WT = (a) 2.5 m/s (upper row) and (b) 5.0 m/s (lower row), respectively.

4. Conclusions4. Conclusions Safety,Safety, maintenance, maintenance, and and operations operations of of Kuroshio Kuroshio power plant maymay bebe subjectedsubjected to to impacts impacts from from earthquakes,earthquakes, typhoons, typhoons, climate climate change, change, and and other other na naturaltural factors. Typhoons have have a a significant significant impact impact on onthe the physical physical and and chemical chemical characteristics characteristics of of the the water of thethe Kuroshio.Kuroshio. AA shallow shallow water water model model basedbased on onthe the shallow shallow water water equations equations and and the the space–time space–time least-squaresleast-squares finite-elementfinite-element method method has has beenbeen developed. developed. The The model model has has been been applied applied to to study study the hydrodynamics ofof Kuroshio Kuroshio and and Green Green × IslandIsland wakes wakes with with a small a small computational computational domain domain (72 kmkm × 156156 km) and coarsecoarse meshmesh resolution resolution [19 [19,25],25] (500–3500(500–3500 m). m). The The spatial spatial and and temporal temporal scales scales of of meandering meandering downstream Green Green Island Island wakes wakes have have been quantified and compared with the in-situ measurements and satellite images. Special efforts of been quantified and compared with the in-situ measurements and satellite images. Special efforts of the present study are made to refine the model, including to integrate Holland’s wind field model [35], the present study are made to refine the model, including to integrate Holland’s wind field model [35], to use a larger computational domain (124 km× 220 km) with a finer mesh resolution (250–2250 m), and to use flow field from HYCOM as the initial and boundary conditions to drive the flows.

Atmosphere 2018, 9, 36 20 of 22 to use a larger computational domain (124 km× 220 km) with a finer mesh resolution (250–2250 m), and to use flow field from HYCOM as the initial and boundary conditions to drive the flows. A high resolution (250–2250 m) shallow-water model is used to investigate effect of typhoon on the hydrodynamics of the Kuroshio and Green Island wakes. In the first case, we simulate the typhoon Soulik event to validate the applicability of the SWEs model. Computed results indicate that salient characteristics of Kuroshio and meandering downstream island wakes seem less affected by the typhoon because typhoon Soulik is 250 km away Green Island and wind speed is smaller than 10 m/s near the region of Green Island. However, Kuroshio currents increase when flow is in the same direction as the counterclockwise rotation of typhoon, and vice versa. This finding is consistent with the TOROS observed dataset [45]. In the second case, the SWEs model, forced by the Kuroshio and Holland’s wind field model, successfully reproduces the downstream recirculation and meandering vortex streets. Kuroshio and the downstream Green Island wakes are found to be significantly affected by the moving typhoon that passes the Green Island directly, especially for the shallow waters and the lee of the islands. Computed results clearly reveal the rightward bias phenomenon—due to the counterclockwise rotation of the typhoon, Kuroshio currents increase in the right of the moving typhoon’s track and decrease in the left of the moving typhoon’s track. Computed results also show that the slower the moving typhoon, the more significant is the impact of the typhoon on the Kuroshio and downstream Green Island wakes.

Acknowledgments: This study is supported by the MOST project under the grants of MOST 105-2221-E-019-022-MY2 and MOST 105-2221-E-019-043-MY2. Author Contributions: Tai-Wen Hsu and Shin-Jye Liang proposed the method and wrote this paper. Meng-Hsien Chou and Shin-Jye Liang surveyed literatures, implemented the algorithms, performed the simulations, and analyzed the modeling results. Wei-Ting Chao helped with paper formatting and revising. All authors contributed to the discussion of the results and the writing of the manuscript. Conﬂicts of Interest: The authors declare no conﬂict of interest.

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