Energetics and temporal variability of internal tides in Luzon Strait: a nonhydrostatic numerical simulation

Chinese Journal of Oceanology and LimnologyVol. 30 No. 5, P. 852-867, 2012http://dx.doi.org/10.1007/s00343-012-1289-2

Energetics and temporal variability of internal tides in Luzon Strait: a nonhydrostatic numerical simulation*

LI Mingjie (李明杰) 1, 2, 3 , HOU Yijun (侯一筠) 1, 2 , * * , LI Yuanlong (李元龙) 1, 2, 3 , HU Po (胡珀) 1, 2 1 Key Laboratory of Ocean Circulation and Waves ( KLOCAW ) , Chinese Academy of Sciences , Qingdao 266071 , China 2 Institute of Oceanology , Chinese Academy of Sciences , Qingdao 266071 , China 3 Graduate University of Chinese Academy of Sciences , Beijing 100049 , China

Received Dec. 24, 2011; accepted in principle Jan. 29, 2012; accepted for publication Mar. 7, 2012 © Chinese Society for Oceanology and Limnology, Science Press, and Springer-Verlag Berlin Heidelberg 2012

Abstract A fully nonlinear, three-dimensional nonhydrostatic model driven by four principal tidal constituents (M 2 , S 2 , K 1 , and O 1 ) is used to investigate the spatial-temporal characteristics and energetics of internal tides in Luzon Strait (LS). The model results show that, during spring (neap) tides, about 64 (47) GW (1 GW=10 9 W) of barotropic tidal energy is consumed in LS, of which 59.0% (50.5%) is converted to baroclinic tides. About 22 (11) GW of the derived baroclinic energy fl ux subsequently passes from LS, among which 50.9% (54.3%) fl ows westward into the South China Sea (SCS) and 45.0% (39.7%) eastward into the Pacifi c Ocean, and the remaining 16 (13) GW is lost locally owing to dissipation and convection. It is revealed that generation areas of internal tides vary with the spring and neap tide, indicating different source areas for internal solitary waves in the northern SCS. The region around the Batan Islands is the most important generation region of internal tides during both spring and neap tides. In addition, the baroclinic tidal energy has pronounced seasonal variability. Both the total energy transferred from barotropic tides to baroclinic tides and the baroclinic energy fl ux fl owing out of LS are the highest in summer and lowest in winter.

Keyword : internal tide; energetics; temporal variability; Luzon Strait (LS); MITgcm

1 INTRODUCTION

Internal tides, as a ubiquitous phenomenon in the ocean, play an important role in regulating energy dissipation, abyssal mixing, and meridional overturning circulation. Munk and Wunsch (1998) estimated that the magnitude of diapycnal mixing necessary to maintain abyssal stratifi cation is 10 - 4 m 2 /s. However, direct microstructure/fi nestructure measurements (Gregg, 1989; Polzin et al., 1995) and tracer release experiments (Ledwell et al., 1998) suggest that diapycnal diffusivities in most of the abyssal ocean are only of order O (10 - 5 m 2 /s). Hence, there is a demand for the elevated mixing level in marginal seas, e.g., the South China Sea (SCS). Intensive tidal mixing in the SCS, reaching 10 - 3 m 2 /s, was reported in recent studies (Lien et al., 2005; Qu et al., 2006; Tian et al., 2009). Understanding and parameterizing such a high mixing level requires a better interpretation of baroclinic tides in this region.

The generation of internal tides is primarily associated with oceanic topography. With a steep continental shelf, submarine ridges/trenches, and numerous seamounts, the topography of the northern SCS is extremely complicated (Fig.1), which makes this domain a preferred region for the generation of internal tides and an ideal region for the study of internal tides and solitary waves. Vigorous internal tides and solitary waves are frequently caught in remotely sensed images (Hsu et al., 2000; Zhao et al., 2004; Du et al., 2008) and in-situ observations (Ramp et al., 2004; Lien et al., 2005; Duda et al., 2008; Alford et al., 2010) of this region.

Luzon Strait (LS), which is the only deepwater

* Supported by the Key Program of National Natural Science Foundation of China (No. 41030855) and the National High Technology Research and Development Program of China (863 Program) (No. 2008AA09A402) ** Corresponding author: [email protected]

853No.5 LI et al.: Internal-tide energetics and variability in Luzon Strait

passage connecting the western Pacifi c Ocean and the northern SCS, is blocked by two submarine ridges: the Heng-Chun Ridge and Orchid Ridge (also referred to as the Luzon island arc). As tidal currents fl ow to and fro over these rough and prominent topographic features, LS acts as an internal tide generator. Subsequently, the generated internal tides can either propagate eastward to the western Pacifi c Ocean or westward into the northern SCS (Niwa and Hibiya, 2004; Buijsman et al., 2010a). While propagating shoreward from the shelf break, the tides may transform into internal solitary waves (ISWs) with strikingly large amplitudes (Hsu et al., 2000; Ramp et al., 2004; Lien et al., 2005). Therefore, LS is believed to be an important source area of the nonlinear internal waves observed in the northern SCS, and there have been many works on the generation and evolution of ISWs (Cai et al., 2002; Du et al., 2008; Shaw et al., 2009; Buijsman et al., 2010b; Warn-Varnas et al., 2010; Guo et al., 2011; Li and Farmer, 2011). Unfortunately, the exact locations of ISW generation are still unclear, because both remotely sensed images and numerical simulations suggest a separation of the actual locations where ISWs are generated and the locations where the strongest fl ow occurs (Du et al., 2008). On the other hand, the Kuroshio infl ow brings Pacifi c water masses into the SCS (Qu et al., 2000; Centurioni et al., 2004). These water masses are

warmed and then fl ow back to the northwestern Pacifi c, which is an important component in the Pacifi c overturning circulation (Qu et al., 2006). In this process, enhanced diapycnal mixing due to tidal dissipation in the LS and SCS plays an important role in driving the vertical convection (Tian et al., 2009). Therefore, a better description of barotropic/baroclinic tides in LS is necessary not only for explaining the generation and evolution of the observed ISWs in the SCS, but also for understanding large-scale water mass conversion and oceanic circulation in the Pacifi c Ocean.

Numerical models have been frequently used to investigate the general features of internal tides in recent studies (Niwa and Hibiya, 2004; Chao et al., 2007; Jan et al., 2007, 2008). Niwa and Hibiya (2004) investigated the energetics of the M 2 internal tide throughout the East China Sea (including LS) with a fully three-dimensional (3D) primitive equation model. According to their evaluation, the M 2 net baroclinic energy fl ux away from LS amounts to 7.4 GW (1 GW=10 9 W), 43% of which is directed toward the Pacifi c Ocean with the remaining 57% directed to the SCS. Using an analogous 3D model, the generation of the K 1 internal tide in LS and its effect on the surface tide have also been investigated by Jan et al. (2007). They confi rmed that the generation of vigorous internal tides in LS considerably modifi es

Fig.1 Bathymetry of our model domain, which covers the northern South China Sea (SCS), Luzon Strait (LS), and part of the northwestern Pacifi c

854 CHIN. J. OCEANOL. LIMNOL., 30(5), 2012 Vol.30

the characteristics of the K 1 barotropic tide. Using a 3D hydrostatic model and a two-dimensional (2D) nonhydrostatic model, Chao et al. (2007) evaluated the role of the western ridge in modifying the westward propagation of the M 2 internal tide. They found that the western ridge in the middle reaches of the LS was a damper of the incoming M 2 baroclinic tide from the eastern ridge, while in the northern portion of the LS, the western ridge was a secondary generation site for the M 2 baroclinic tide. Following the previous works, Jan et al. (2008) further probed the energetics of four principal constituents and the mechanism of the western ridge in modulating both the M 2 and K 1 baroclinic tides. However, most of these research works are based on hydrostatic simulations with relatively low resolutions, and they cannot primarily resolve the processes of nonlinear internal waves. An artifi cial linear dissipation term is usually introduced into their models instead. More recent studies (Vlasenko et al., 2010; Guo et al., 2011) investigated the vertical structure of internal waves in the vicinity of LS using a 3D nonhydrostatic fi ne-resolution model. They indicated that the eastern ridge was responsible for the generation of progressive fi rst-mode tidal waves that disintegrated into packets of fi rst-mode internal solitary waves, whereas the western ridge produced a strong higher-mode signal. However, because of the limited domain (covering only the middle part of LS) in their model, their study could not present a panoramic picture of the internal tidal energetics in LS.

The purpose of this paper is to explore the generation, evolution, and dissipation processes of internal tides in LS with better numerical accuracy and physical reasonability. Our investigation is based on a fully nonlinear 3D nonhydrostatic model with high spatial resolution and realistic topography, stratifi cation, and barotropic tide forcing. Compared with previous works, the advanced model setting enables us to detect the specifi c generation and dissipation sites of internal tides in LS and locate the potential source regions of ISWs in the SCS. In addition to spatial variations, spring-neap and seasonal variability of tidal energetics are also addressed. With these efforts, we aim to provide a more comprehensive and realistic description of internal tides in LS. Note that the Kuroshio, having a strong density front and multiple intrusion styles in LS, is not represented in our model so as to more clearly understand the tidal dynamics in LS.

2 NUMERICAL MODEL

The model used in this study is the MIT general circulation model (MITgcm) (Marshall et al., 1997; Adcroft et al., 2002), which is fully nonlinear and nonhydrostatic. Figure 1 shows the topography of our model domain, which covers the northern SCS, LS, and part of the West Pacifi c (110°–126°E, 16°–26°N), taken from ETOPO-1 digital topography (Amante and Eakins, 2008; http://www.ngdc.noaa.gov/mgg/global/global.html). Our model has horizontal resolution of 1/30°×1/30° over the entire domain. There are 66 uneven levels in the vertical direction, with a thickness of 10 m near the surface, gradually increasing to 500 m at the bottom (Fig.2e). Along the four open boundaries, 1-degree-wide sponge layers are added to avoid artifi cial refl ection.

The tidal forcing is obtained from the latest version of the global inverse barotropic tidal model (TPXO 7.2) (Egbert et al., 1994; Egbert and Erofeeva, 2002), providing tidal parameters for eight primary (M 2 , S 2 , N 2 , K 2 , K 1 , O 1 , P 1 , and Q 1 ), two long-period (Mf and Mm) and three non-linear (M 4 , MS 4 , and MN 4 ) harmonic constituents, with spatial resolution of 1/4° in global tidal solution and 1/30° in the regional tidal solution of the China Seas. The model is driven from a quiescent state by the tidal current velocities of four principal tidal constituents (M 2 , S 2 , K 1 and O 1 ) in combination extracting from the latter (available at http://volkov.oce.orst.edu/tides/YS.html). We did not include all nine tidal constituents because the four-constituent runs capture most features of the internal tides in LS, and the nine-constituent runs would be computationally expensive.

The initial condition of the model is taken from data assimilative runs of HYCOM Consortium (available at http://hycom.org/dataserver). The temperature and salinity profi les near (120°E, 20°N) in October are adopted as the initial stratifi cation in this model (hereafter also refer to as the reference model); i.e., the initial fi eld is horizontally homogenous and vertically stratifi ed so that the currents generated by the thermal wind relation are excluded. The profi les in April (spring), July (summer), October (autumn), and January (winter) for the upper 1 500 m shown in Fig.2a–d is used to explore the seasonal variability of internal tides in LS. It takes about 5–6 d for the fi rst vertical mode of the internal tide to propagate from the eastern boundary to the western boundary. The model run is therefore set to 15 d, starting from 00:00 UTC on September


30, 2008, and hourly model results of days 7–8 (spring tide) and days 14–15 (neap tide) are analyzed. We use a time step of Δ t =90 s, which gives 14 400 time steps. The horizontal and vertical diffusion coeffi cients are constant and given by K h =50 m 2 /s and K z =10 - 5 m 2 /s, respectively. The horizontal and vertical Laplacian dissipation coeffi cients are also constant and are given by A h =400 m 2 /s and A z =10 - 5 m 2 /s, respectively.

Along with the prognostic model, another model is run in diagnostic mode to obtain the barotropic surface elevation (see column 2 in Fig.3). The characteristics of barotropic tides in the northern SCS have been elaborated in many previous studies (Fang et al., 1999; Niwa and Hibiya, 2004; Zu et al., 2008). As seen in Fig.3, the barotropic model visually shows a high level of agreement with TPXO throughout the entire model region except in nearshore areas, which is due to the imprecision of the nearshore topography and the lack of nonlinear shallow water constituents. In relation to TPXO, the root-mean-square (RMS) errors (depths less than 200 m are neglected) for the principal constituents M 2 , S 2 , K 1 , and O 1 are 7.4, 2.4,

2.7, and 2.2 cm, respectively. The last column in Fig.3 shows the discrepancy between baroclinic and barotropic models, from which we see the surface features of semidiurnal and diurnal internal tides clearly. The incident internal tides in LS propagate eastward and westward, with wavelength of ~370 km for diurnal internal tides and ~150 km for semidiurnal internal tides, suggesting that LS is the main source region of internal tides and its derivative ISWs in the northern SCS and one of the most important source areas for the West Pacifi c. According to Niwa and Hibiya (2004), there is 3.2 GW of M 2 baroclinic energy fl ux from LS fl ow into the Pacifi c Ocean, while in the East China Sea, the net baroclinic energy fl ux amounts to 3.1 GW. Note that the Ryukyu island chain is about three times as long as LS. Table 1 compares the depth-integrated baroclinic energy fl ux between the observation of the Dongsha Plateau by Chang et al. (2006) and our model results. Although their observation was made in spring and ours in autumn, the energy fl uxes agree well, especially for the directions.

Fig.2 a–d. Temperature T (in °C, dashed with dots), salinity S (black dashed), and squared buoyancy frequency N 2 (in s - 2 , black solid) profi les for the four seasons at 120°E, 20°N as the initial stratifi cation of the model runs; e. Model layer thickness Δ Z (in m, dashed) and depth Z (in km, solid) as functions of the model level


The temperature and vertical velocity discrepancies between the nonhydrostatic and hydrostatic models are displayed in Fig.4. Compared with the case for deeper water, the nonhydrostatic effects are stronger near the thermocline. There is no doubt that the nonlinear internal waves especially for high frequency waves are better illustrated. However, the difference in the depth-integrated baroclinic energy fl ux is small (less than 0.1 kW/m). Although the grid resolution is not yet fi ne enough to exhibit the outstanding advantage of the nonhydrostatic model, the processes of nonlinear waves can be resolved well without an artifi cial linear dissipation term. Furthermore, boundary conditions that are more accurate could be obtained for our further study at fi ner resolution.

To better understand the barotropic tidal properties for LS, semidiurnal and diurnal barotropic currents of some representative sites, which are derived from TPXO 7.2, are analyzed. Because of their similarity, only the currents at the site of (122°30′E, 19°30′N) are shown in Fig.5. Diurnal tidal currents are stronger (weaker) than the semidiurnal currents during spring (neap) tides. That is to say, the barotropic tidal currents exhibit the characteristics of diurnal (semidiurnal) tidal currents in the spring (neap) tide (see Fig.5e–f), which is important in understanding the spring-neap variability of internal tides in LS.

3 RESULT AND DISCUSSION

3.1 Calculation

To calculate the internal tidal energy fl ux, the formulae for the perturbation density, pressure, and baroclinic velocity described in the work of Nash et al. (2005) are employed. Firstly, the perturbation density is:

z z z (1) where ρ is the instantaneous density and < ρ > is the tidal period mean of the vertical density profi le. The perturbation pressure is:

(2)

Although the baroclinically induced surface pressure p s ( t ) is not measured, it can be inferred from the baroclinicity condition that the depth-averaged pressure perturbation must vanish:

z z′ (3)

The baroclinic velocity is:

zzz′u�

u�

u� �

(4)

where u is the instantaneous velocity vector, u

the

tidal period mean of u, and U

the depth average of

u.

The formulation of the depth-integrated barotropic ( F bt ) and baroclinic ( F bc ) energy fl uxes and the barotropic-to-baroclinic energy conversion rate ( E bt2bc ) averaged over days 7–8 (spring tide) or days 14–15 (neap tide) is (Niwa and Hibiya, 2004; Jan et al., 2008):

z�

′ (5)

z′ ′u�

(6)

z′ (7)

where the angle brackets represent the tidal-period mean, ρ 0 is the initial background density stratifi cation, H and ƞ denote the mean water depth and sea level displacement respectively, the factor α is the loading effect due to ocean tides and assumed to be 0.9 following Ray et al. (2001), the factor β is the effective Earth elasticity, and ξ is the equilibrium tidal potential expressed as (Foreman et al., 1993):

(8)

for semidiurnal tides and

(9)

for diurnal tides. Here ϕ is latitude, χ is longitude east, ω n is the tidal frequency, and V n is the astronomical argument phase angle. The tidal potential amplitude h n and β values for the four tidal components are chosen according to Foreman et al. (1993).

The Cartesian vertical velocity w bt relevant to the

Table 1 Comparison of the depth-integrated baroclinic energy fl ux between the observation made by Chang et al. (2006) and our model results

Location Water depth (m)

F bc (kW/m) Direction (deg)

Observation Model Observation Model

117°13.17′E, 21°02.77′N 545.5 8.5 8.9 173 167

117°46.31′E, 21°44.53′N 476.8 1.0 2.8 140 141

115°11.43′E, 21°26.77′N 116.7 0.25 0.02 149 142

The direction of the energy fl ux in degrees is counterclockwise from east.


Fig.4 Snapshot of the discrepancy between the nonhydrostatic and hydrostatic models along 21°10′Na. temperature (in °C); b. vertical velocity (in mm/s) .

Fig.3 Co-tidal charts of four principal constituents from TPXO 7.2 (column 1), the barotropic (BT) model (column 2), and the baroclinic (BC) model (column 3) The last column shows the discrepancy between baroclinic and barotropic models (BC-BT) (unit: cm)


barotropic fl ow is given by (Mellor, 2004):

∂ ∂∂∂

∂∂ ∂

∂ ∂∂

(10)

where U x and U y are the barotropic velocities in the x and y directions respectively, D is the total water depth ( D=H + ƞ ), and σ is defi ned by σ =( z – ƞ )/ D .

3.2 Energetics of internal tides

In this section, we delineate the characteristics and investigate the mechanism of the generation and propagation of the baroclinic tidal energy during spring tide in LS. The spatial distribution of the divergence of the depth-integrated baroclinic energy fl ux, conversion rate, and dissipation rate averaged over the spring tide are shown in Fig.6. The two ridges (divided by a dashed line) are the main sites of internal-tide generation, with the Orchid Ridge being

much more effi cient (71.2%) than the Heng-Chun Ridge (28.2%), which is consistent with the results of Jan et al. (2008). Notably, there are several hot spots in LS (outlined in red in Fig.6a), with a maximum value of 11.7 W/m 2 , and most of them are on the eastern slopes of the two ridges at a depth of 80–3 000 m. The spots found on the western slopes of the ridges are mainly located to the southwest of Sabtang Island (around 121.7°E, 20°N), the northwest of Calayan Island (around 121.4°E, 19.6°N), and the west of Barit Island (around 121.2°E, 18.7°N), which are areas that have been speculated to be the generation sites of ISWs in the northeastern SCS, according to the propagating direction of the ISWs in Synthetic Aperture Radar (SAR) images (Zhao et al., 2004; Du et al. 2008; Guo et al., 2011). The distribution of dissipation sites of internal tide energy, namely the difference between Fig.6a and b regardless of advection of baroclinic energy (Niwa and Hibiya, 2004), is very close to the generation sites (Fig.6c), implying strong dissipation of the newly born internal

Fig.5 a, b. Semidiurnal barotropic tidal currents; c, d. Diurnal barotropic tidal currents; e, f. The mixed barotropic tidal currents including four principal tidal constituents (TCs) at 122°30′E, 19°30′N over a period of one month derived from TPXO 7.2 (unit: cm/s)


tides. It is also discernible that that the fi eld of the conversion rate ( E bt2bc ) greatly resembles that of the divergence of baroclinic energy fl ux (•Fbc). Along the two ridges, the barotropic tidal energy converts to internal tides and a small quotient of the derived internal tidal energy transforms back to barotropic tides not far from generation sites. Note that the negative conversion in Fig.6b does not correspond to turbulent energy dissipation but to the backward transform of energy from the baroclinic tide to the barotropic tide due to pressure work (Zilberman et al., 2009).

The depth-integrated baroclinic tidal fl ux in the spring tide in LS is shown in Fig.7a. One can see that the westward-propagating baroclinic energy fl ux, which is probably responsible for the ISWs found in the northern SCS, is much larger than the eastward-propagating energy fl ux. Strong energy fl ux emerges to the southwest of the Batan Islands as expected, not far from the detected hot spots. The maximum

westward energy fl ux into the northern SCS reaches 74.4 kW/m. The westward energy fl ux slightly weakens when crossing the Heng-Chun Ridge. A considerable portion turns north and propagates along the Luzon trough. This portion can further split at the Bashi Channel, with some of the fl ux propagating eastward into the Pacifi c and the remnant westward into the SCS before reaching Taiwan Island (Fig.7c). The ongoing westward-propagating energy fl ux can strengthen when striding over the western ridge. It should be emphasized that, although the strong energy fl ux greatly increases to the west of Heng-Chun Ridge, it does not mean that the western ridge is effi cient in generating internal tides. As a matter of fact, the ridge contributes equally to the generation (50.8%) and dissipation (49.2%) of internal tides, while the ratio for the Orchid Ridge is 59.6% to 40.4% (Fig.10a). In Fig.7b, the boundary between the westward and eastward energy fl uxes is easily recognized. Along the transverse between Taiwan

Fig.6 a. Divergence of the depth-integrated baroclinic energy fl ux; b. Depth-integrated conversion rate from the barotropic to baroclinic tidal energy; c. Depth-integrated dissipation rate of the baroclinic energy (i.e., a–b) during spring tide in LS (in W/m 2 )

The positive (warm colors) and negative (cool colors) values denote the generation and dissipation of the internal tide in (a), and barotropic-to-baroclinic and baroclinic-to-barotropic energy transformation in (b) (Zilberman et al., 2009). The energetics in the rectangular boxes are displayed in Fig.10 .


Island and Luzon in LS, most energy fl ux propagates westward, and there is fl ux transmission from the Heng-Chun Ridge to the Orchid Ridge only in a small segment.

3.3 Spring-neap variability of internal tides

Compared with the results for the spring tide, both the westward and eastward baroclinic energy fl uxes during neap tide are weaker and smoother (Fig.8b). Especially, the eastward fl ux from the Heng-Chun Ridge is refl ected back at the Orchid Ridge and yields the internal tide resonance between the two ridges. In addition to having a generally lower value, the spatial distribution differs signifi cantly from that during spring tide (Figs.6 and 7). Figure 8a shows that, although there is still intense generation along the two ridges, there are more hot spots located along the Heng-Chun Ridge during neap tide. Such spring-neap difference is probably due to the semidiurnal (diurnal) barotropic tides dominating during neap (spring) tides in LS. According to Jan et al. (2008), the Heng-Chun Ridge is more effi cient in generating the westward-

propagating M 2 tide than generating the K 1 baroclinic tide. For this reason, the Heng-Chun Ridge becomes more important during neap tide. To verify this speculation, runs driven by solely the K 1 or M 2 tide are conducted. We also fi nd that the spring-tide distribution (Fig.7a) is similar to that of the K 1 baroclinic tide (Fig.9a), whereas the neap-tide pattern (Fig.8b) is more like that of the M 2 baroclinic tide (Fig.9b). The results shown in Fig.9 also suggest that the diurnal baroclinic tides are responsible for the southwest energy fl ux into the SCS, and the semidiurnal baroclinic tides contribute to the northwestward energy fl ux.

For a better interpretation of the spring-neap tidal energy variability, four typical regions (A1, A2, A3, and A4 in Fig.6a) covering most of the hot spots are further analyzed. Energy budgets in these regions during spring and neap tides are summarized schematically in Figs.10 and 11, respectively. During spring tide, the barotropic tidal energy fl ux rushes into LS (the rectangle) from the east (~124 GW) and north (~35 GW), fl owing over ridges and trenches,

Fig.7 a. Depth-integrated baroclinic energy fl ux (kW/m) and its (b) zonal and (c) meridional components in the spring tide in LS

In (a), color shading denotes the magnitude. In (b) and (c), positive (negative) values stand for eastward (westward) and northward (southward) fl uxes, respectively. The background contours show selected model isobaths (200, 500, 1 000, 2 000, 3 000, 4 000, and 5 000 m) .


and fi nally propagates out of LS through the western (~95 GW) and southern (~0.3 GW) boundaries. That is to say, about 64 GW (40.0%) of barotropic tidal energy is lost in LS. About 59.0% (~38 GW) of the lost barotropic energy is converted to baroclinic energy, only 56.8% (~21 GW) of which passes out of LS through the four boundaries, indicating strong local dissipation compared with the dissipation estimated at the Hawaiian ridge (8%–25%; Klymak et al., 2006). About 11.17 GW (50.9%) of the net baroclinic energy fl ux away from LS propagates

westward into the northern SCS. The eastward energy fl ux into the Pacifi c Ocean amounts to 9.87 GW, corresponding to about 45.0% of the net baroclinic energy fl ux. The westward (eastward) baroclinic energy fl ux out of LS estimated by Jan et al. (2008) is 10.73 (9.28) GW, which is slightly less than that determined with our model. Such discrepancy may be due to the difference in model settings; e.g., the spatial resolution. We can also roughly evaluate the contributions of the two ridges from the results in Fig.10a. Note that the contributions of the western

Fig.9 Depth-integrated baroclinic tidal energy fl ux (kW/m) of K 1 (a) and M 2 (b) constituents

Fig.8 a. Divergence of the depth-integrated baroclinic energy fl ux (W/m 2 ); b. depth-integrated baroclinic energy fl ux (kW/m) in the neap tide in LS


ridge to the generation and dissipation of the baroclinic tides in LS are 28.8% and 36.7% respectively, implying that the Heng-Chun Ridge is more effi cient in dissipating than in generating baroclinic tidal energy, although the area-integrated divergence of baroclinic energy fl ux is a little larger than the corresponding dissipation. We can also deduce that the net baroclinic tidal energy “given” by the Orchid Ridge to the western ridge is about 5 GW.

The area-integrated divergence of baroclinic energy fl ux (Div.), baroclinic energy dissipation (Dis.), and barotropic-to-baroclinic conversion energy (Con.) in the four main generation regions during spring tide are shown in Fig.10b. The total sum of Con. in the four regions accounts for 94% of the total for the whole LS, while the percentage for Dis. is 57.6%. Obviously, A3 and A4 have prominent performance in generating internal tides during the spring tide (meantime the dissipation in A4 is strong because of the presence of several islands in this region). We believe that during the spring tide, the hot spots to the southwest of Sabtang Island, the west of the Balintang Islands, and the north of Calayan Island (Fig.6a) are primarily responsible for the ISWs in the northeastern SCS.

Figure 10c shows the meridional-section or zonal-section integrated baroclinic energy fl ux at the

boundaries of the four regions, from which we see the baroclinic energy exchanges between them. The net baroclinic energy fl uxes of A1 and A2 both propagate eastward into the Pacifi c Ocean, while the net energy fl uxes of A3 and A4 fl ow into the SCS.

During neap tide, about 47 GW of the barotropic tidal energy is lost in LS, 50.5% (~24 GW) of which is converted to baroclinic energy. In addition, eventually about 11 GW (47.0%) of the baroclinic energy fl ows out of LS (Fig.11). Moreover, the net baroclinic tidal energy that the eastern ridge “gives” to the western ridge deceases from 5 GW to about 2 GW. It seems that the dissipation of the barotropic and baroclinic tides in LS is stronger than that during spring tide. Moreover, the western ridge plays a more important role in generating baroclinic energy, which is also refl ected in Fig.11b. The main generation areas of baroclinic tides also change to A1 and A3 at neap tide, suggesting that the hot spots in these two regions may become the source area of the ISWs in the SCS accordingly, although the ISWs may not be as pronounced as those during spring tide. The net baroclinic energy fl uxes of the four regions all propagate westward into the SCS except in the case of A2, which is why the westward energy fl ux accounts for 54.3% of the total net energy fl ux passing out of LS (the percentage is 50.9% during spring tide). The

Fig.10 Diagram of the energetics in the spring tide in LS (2-day average, in GW) W(E)R: the west (east) ridge; BT(C)E E(W) : meridional-section integrated barotropic (baroclinic) energy in the eastern (western) sections of the pane in (a); BT(C)E S(N) : zonal-section integrated barotropic (baroclinic) energy in the south (north) sections; Div: the divergence of area-integrated baroclinic energy fl ux; Con: the area-integrated conversion rate from barotropic to baroclinic tidal energy; Dis: the area-integrated dissipation rate of the baroclinic energy. The percentages in parentheses indicate the corresponding ratio of the energetics calculated for local regions to the energetics calculated for LS (the pane in (a)).


baroclinic tidal energy generation, energy fl uxes, and energy dissipation rates during spring tide are about twice those during neap tide.

Unlike the case for the Hawaiian ridge (Holloway

and Merrifi eld, 2003), the tidal beams do not maintain their overall structure over the spring-neap cycle. We see from the snapshot of the cross-sectional baroclinic velocity along 20°10′N and 21°N presented in Fig.12

Fig.11 Same as Fig.10 but during neap tide

Fig.12 Snapshot of the cross-sectional baroclinic velocity along 20°10′N (left panels) and 21°N (right panels) for the fl ood and ebb tides during the spring (a–d) and neap tides (e–h)


that the length of the tidal beams at neap tide deceases to about half that at spring tide. Meanwhile, the interval between fl ood and ebb tides deceases from 12–13 h to 6–7 h.

3.4 Seasonal variability of internal tides

The generation and dissipation of internal tides are sensitive to environmental conditions, especially changes in background density stratifi cation. Small oscillation in stratifi cation may provoke a large phase shift (Baines, 1973; Gerkema, 2002; Katsumata et al., 2010). Holloway (2001) found that the seasonal variability in baroclinic energy fl ux reaches about 20% of the mean value on the Australian North West Shelf. In LS, the most prominent seasonal variability is the seasonal intrusion of Kuroshio water. During boreal winter, when the northeast monsoon is fully developed and the Kuroshio is relatively weak, the

intrusion is strongest (Sheremet, 2001; Qu et al., 2004). Salty Pacifi c water occupies the upper layer (0–200 dbar) of LS in winter, which acts to weaken the surface/subsurface density difference (Fig.2). Moreover, wintertime atmospheric cooling erodes the vertical thermal gradient in the seasonal thermocline. The combined effects of temperature and salinity signifi cantly decrease N 2 during winter (Fig.2). Such evident seasonal variability in upper-ocean stratifi cation is expected to substantially affect the energetics of internal tides in LS. For example, the occurrence frequency of SAR-observed ISWs has evident seasonal variability in the northern SCS (Zheng et al., 2007). However, the simulations of internal tides in LS by Jan et al. (2008) showed only a weak seasonal cycle of baroclinic energetics. In this study, with a nonhydrostatic model and higher spatial resolution, this process is re-examined.

Fig.13 Comparison of the depth-integrated baroclinic energy fl ux (kW/m) in the four seasons a. Spring; b. Summer; c. Autumn; d. Winter


Table 2 compares the results of simulations initialized with the stratifi cation for the four seasons shown in Fig.2. Note that the results and analysis presented in earlier subsections are based on results of the autumn-stratifi ed simulation. Table 2 and Fig.13 show that both the barotropic-to-baroclinic tidal energy transformation and the baroclinic energy fl ux through LS are greatest in summer and least in winter. Correspondingly, barotropic tidal loss reaches a maximum in winter and minimum in summer. That is to say, the energy transfer from barotropic tides to internal tides is the most (least) effi cient in summer (winter). Stronger stratifi cation in the summertime thermocline (Fig.2) is preferable for the growth of fi rst-order baroclinic instabilities and the energy cascade from barotropic to baroclinic tides. Note that, in Fig.2, the tidal energetics in autumn are at a similar level to those in summer (Con.: 37.59 GW vs. 38.18 GW; Div.: 21.35 GW vs. 22.17 GW; Dis.: 16.24 GW vs. 16.01 GW). This is clearly due to similar stratifi cation in the two seasons (Fig.2b and c). In spring, by comparison, baroclinic energy is slightly higher than the winter minimum owing to the shoaling mixed-layer depth and formation of the seasonal thermocline in April (Fig.2a).

Compared with the winter run, about 12.4% more barotropic tidal energy is converted to baroclinic energy in summer; 21.5% more baroclinic energy passes out of LS; and the westward baroclinic energy fl ux, which is of the most interest because of its close connection with the generation of ISWs in the northern SCS, increases by about 15.8% in summer. This could explain why ISWs are more frequently captured by satellite in summer (Zheng et al., 2007).

4 CONCLUSION

In this paper, we presented the spatial-temporal characteristics and energetics of internal tides in LS using a fully nonlinear nonhydrostatic 3D model driven by four principal tidal constituents (M 2 , S 2 , K 1 , and O 1 ). It was found that, during spring (neap) tides, about 64 (47) GW of barotropic tide is lost in LS, 59.0% (50.5%) of which is converted to baroclinic tide. About 22 (11) GW of the incident baroclinic energy fl ux passes out LS, among which 50.9% (54.3%) passes westward into the SCS and 45.0% (39.7%) eastward into the Pacifi c Ocean, and the remaining 16 (13) GW is lost locally through dissipation and convection. The ratio of the contribution of the western and eastern ridges in generating baroclinic energy is about 3 to 7, which is consistent with the result of Jan et al. (2008).

The model results show that the region around the Batan Islands is one of the most important generation sites of internal tides during both spring and neap tides. The region round the Babuyan Islands and Heng-Chun Ridge are secondary important generation sites during spring and neap tides, respectively. The difference in the main generation sites for baroclinic tides between the spring and neap tides implies different source areas for the corresponding ISWs in the northern SCS. We also found that the spatial pattern of energy fl ux at neap tide is similar to that of the M 2 baroclinic tide, whereas during spring tide, the distribution is more like the K 1 baroclinic pattern. Compared with the spring-tide case, the western ridge (Heng-Chun Ridge) plays a more important role in both generating and dissipating baroclinic energy during neap tide.

The results of four numerical simulations reveal that the energetics of LS internal tides has a well-defi ned and pronounced seasonal cycle. Both the barotropic-to-baroclinic tidal energy transformation and the baroclinic energy fl ux through LS are greatest in summer and least in winter, which mainly refl ects the variations in density stratifi cation in LS. Scenarios of saline water intrusion and sea-surface heat fl ux changes give rise to prominent variability of density stratifi cation in the upper ocean of LS, which in turn modulates the seasonal fl uctuation of baroclinic tidal energy. Compared with the winter run, about 12.4% more barotropic tidal energy is converted to baroclinic energy, and westward baroclinic energy fl ux passing from LS into the northern SCS increases by about 15.8%, providing an explanation for the elevated ISW

Table 2 Results of model experiments testing the sensitivity of internal tidal energetics (GW) to the seasonal variations in stratifi cations

Case Autumn (Oct.) Winter (Jan.) Spring (Apr.) Summer (Jul.)

BTLOS 63.68 76.29(+19.8%) 78.16(+22.7%) 51.97(-18.4%)

Con. 37.59 33.97(-9.6%) 35.03(-6.8%) 38.18(+1.6%)

Div. 21.35 18.24(-14.6%) 18.75(-12.2%) 22.17(+3.8%)

Dis. 16.24 15.73(-3.1%) 16.28(+0.3%) 16.01(-1.4%)

WEF 11.17 10.15(-9.1%) 10.13(-9.3%) 11.75(+5.2%)

EEF 9.87 7.48(-24.2%) 8.02(-18.7%) 10.06(+2.0%)

BTLOS: barotropic energy loss in LS. W(E)R: the western (eastern) ridge; W(E)EF: westward (eastward) baroclinic energy fl ux in the western (eastern) section of the rectangle in Fig.10a. The percentages in parentheses are the relative increases from the reference (autumn) run.


occurrence in remote sensing observations. In addition, our results on temporal variability

encourage further investigations. The Kuroshio-related LS transport also has pronounced interannual variations that have been demonstrated to be related to El Niño/La Niña-Southern Oscillation (ENSO) events (Qu et al., 2004; Chang et al., 2008). By affecting water mass properties and eddy (turbulent) fl uxes, interannual variability of internal tides and the relevant mixing fi eld may also play a role in transmitting ENSO signals into the SCS. On the other hand, the frequent summer/autumn tropical cyclones in LS (Lin et al., 2008), which produce signifi cant perturbations in oceanic stratifi cation, may also affect the energetics of internal tides. The generation and evolution of internal tides and associated ISW formation in the SCS under typhoon conditions are another interesting theme for future research.

5 ACKNOWLEDGMENT

We thank two anonymous reviewers whose comments and suggestions were helpful in improving this work. Simulations were carried out at the High Performance Computational Center, Institute of Oceanology, Chinese Academy of Sciences (IOCAS).

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Energetics and temporal variability of internal tides in Luzon Strait: a nonhydrostatic numerical simulation