Multimodal structure of the internal tides on the continental shelf of the northwestern South China Sea

Multimodal structure of the internal tides on the continental shelf of the northwestern South China Sea

Estuarine, Coastal and Shelf Science 95 (2011) 178e185 Contents lists available at SciVerse ScienceDirect Estuarine, Coastal and Shelf Science journ...

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Estuarine, Coastal and Shelf Science 95 (2011) 178e185

Contents lists available at SciVerse ScienceDirect

Estuarine, Coastal and Shelf Science journal homepage: www.elsevier.com/locate/ecss

Multimodal structure of the internal tides on the continental shelf of the northwestern South China Sea Zhenhua Xua, b, *, Baoshu Yina, b, Yijun Houa, b a b

Institute of Oceanology, Chinese Academy of Sciences, Qingdao, China Key Laboratory of Ocean Circulation and Waves (KLOCAW), Chinese Academy of Sciences, Qingdao, China

a r t i c l e i n f o

a b s t r a c t

Article history: Received 6 July 2011 Accepted 22 August 2011 Available online 26 August 2011

Based on the moored current and temperature observations during the summer of 2005, the vertical structure of the internal tides on the continental shelf of the northwestern South China Sea (SCS) is studied. The vertical structure of the internal tides was found to differ greatly between semidiurnal and diurnal constituents. Generally, the diurnal constituents are dominated by the first-mode motions, which are consistent with the overwhelming first-mode signals in the northeastern SCS. In contrast, the semidiurnal internal tides, unlike the predomination of the first-mode variations in the northeastern area, exhibit a higher modal structure with dominate second-mode signals in the observational region. Moreover, although the diurnal internal tides are much stronger than the semidiurnal component, the shear caused by the latter over various scales was found to be significant compared to that induced by the diurnal tides, probably due to the superposition of the first-mode and higher-mode (smaller scale) semidiurnal variations. Further analysis demonstrates that the shear induced by the diurnal internal tides is larger than that induced by the semidiurnal variations around 45 m depth, where the first-mode current reversal in the vertical happens, while below 45 m depth higher-mode semidiurnal internal tides generally produce larger shear than that by the diurnal component. The northwest-propagating semidiurnal internal tides of higher-mode with small vertical scale, probably do not originate from a distant source like Luzon Strait, but were likely generated near the experiment site. Ó 2011 Elsevier Ltd. All rights reserved.

Keywords: internal waves internal tides South China Sea shear

1. Introduction Internal tides are internal gravity waves generated in stratified waters by the interaction of barotropic tidal currents with variable topography features (Helfrich and Melville, 2006; Garrett and Kunze, 2007). They are usually associated with large pycnocline fluctuations and strong currents, which play a significant role in affecting the offshore drilling operations and biology system in the ocean (Wolanski et al., 2004; Liu et al., 2008). Internal tides are also known to stimulate strong benthic dissipation and mixing, having an important influence on the decay of internal tidal energy and meridional circulation (Alford, 2003; Nash et al., 2004). Low-mode internal tides may propagate for thousands of kilometers before dissipating (St. Laurent and Garrett, 2002; Alford et al., 2007), whereas high-mode (short vertical wavelength) internal tides usually break and dissipate near their source region, and thus lead to local ocean mixing (Moum et al., 2002). As a result, * Corresponding author. Institute of Oceanology, Chinese Academy of Sciences, 7, Nanhai Road, Qingdao 266071, China. E-mail address: [email protected] (Z. Xu). 0272-7714/$ e see front matter Ó 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.ecss.2011.08.026

many studies suggested that small-scale baroclinic M2-motions generally did not exist in the ocean except near their topography source (Rainville and Pinkel, 2006; van Haren, 2007). Furthermore, more recent studies have also revealed the evidence of rich multimodal internal tide field in many regions of the world seas (Park et al., 2006; Zhao et al., 2010). The northern South China Sea (SCS) has been proposed to be an area with strong internal tides among the world seas. The internal tides mostly originate near the Luzon Strait (Jan et al., 2007; Shaw et al., 2009), propagate westward across the SCS basin (Duda et al., 2004; Liu and Hsu, 2004; Zhao et al., 2004; Farmer et al., 2009), and disintegrate into nonlinear waves (Liu et al., 1998; Lien et al., 2005). Most previous studies of the internal tides in the northern SCS were restricted to its east side (between Dongsha Plateau and Luzon Strait), and focused on the first-mode motions in this area (Duda et al., 2004; Yang et al., 2004). More recently, both in-situ measurements and numerical simulations also revealed the presence of higher-mode internal tides in the northeast region of the SCS (Vlasenko et al., 2010; Klymak et al., 2011). Nevertheless, all existing researches found that the first-mode motions predominated in the baroclinic wave field, though higher-mode signals may

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be significant during some specific cases within a short period (Wang et al., 2008). Until recently, little attention has been devoted to the study of internal tides in the northwestern SCS, due to the shortage of highresolution in-situ observations. Measurements by Liu et al. (2010) suggested that diurnal tides dominated the baroclinic energy in this area. However, modal structure of the internal tides in this region has not been considered yet. In this study, we use a highresolution data set to provide the first observation of the modal structure of the internal tides on the continental shelf of the northwestern SCS. It is shown that the second-mode signals dominate the semidiurnal internal tides in this area, which is quite different from the predomination of the first-mode semidiurnal variations in the northeastern area. The rich multimodal structure of semidiurnal internal tides has been rarely reported in the SCS. The shear variations induced by the semidiurnal internal waves are also examined in relate to the modal structure and it is suggested that the small-scale baroclinic M2-motions not only exist, but also contribute significantly to the shear field in our observational region.

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0.01  C and a time interval of 1 min were collected at 23 layers. Most of the temperature sensors were placed between 4 and 40 m below the sea surface with a vertical separation of less than 4 m, whereas the bottom two sensors were located at depths of 50 and 75 m. The barotropic current is defined here as the depth-averaged flow, and the baroclinic current as the residual once the barotropic current is removed. The barotropic tidal currents were estimated by applying a least-square fit method of harmonic analysis to the depth-averaged currents (Pawlowicz et al., 2002). Tidal harmonic analysis is also used to examine the vertical structure of the internal tidal currents. Additionally, due to the absence of temperature and density data covering the entire water column, we will use empirical orthogonal functions (EOF) method to investigate the detailed modal structure of the baroclinic signals. Furthermore, spectra properties of the shear current are calculated to examine the vertical scales of the multimodal tides, according to the method outlined by Emery and Thomson (2001). 3. Results

2. Data and methods

3.1. Barotropic tide

The data reported here are composed of a two-month long (from the 22nd of July to 20th of September, 2005) time series obtained from an acoustic Doppler current profiler (ADCP) and a thermistor chain deployed at Wenchang Station on the northwestern shelf of the SCS. The water depth at the station is 117 m. The study area and mooring position are indicated in Fig. 1. The 190 kHz down-looking ADCP was positioned at a depth of 8 m. The depth of the available current data measured by ADCP ranged from 10 to 114 m, with a vertical interval of 2 m. Current measurements were recorded with a precision of 1  104 m/s at a time interval of 10 min. The temperature sensor information with a precision of

The M2 is the largest barotropic tidal constituent, followed by the O1 and S2 with comparable magnitudes, and finally the K1 (Table 1). Generally, all the major axises of the main constituents are aligned with the cross-isobath direction to within a few degrees, except for the K1, with comparable cross-isobath and along-isobath components. The semidiurnal tidal currents are almost rectilinear, whereas the O1 and K1 tidal ellipses are a little circular, and the velocity vector rotates clockwise (Fig. 1). In the next section, we will use M2 and K1 to represent the semidiurnal and diurnal band motions, respectively, according to the focus of most previous studies in the northern SCS.

Fig. 1. Barotropic current ellipses for M2 and K1. Symbol * indicates the mooring position. Contours mark isobaths in meters.

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Table 1 Ellipse Properties of the Major Tidal Constituents. Constituent

Semimajor Axis, cm/s

Semiminor Axis, cm/s

Inclination, deg

Phase, deg

M2 O1 K1 S2

4.5 2.2 1.4 2.5

0.3 0.7 0.7 0.2

127 137 169 115

212 211 274 260

3.2. Internal tide Tidal-current ellipses of the two major constituents (M2 and K1) are derived from the harmonic analysis of the baroclinic current measurements (Fig. 2). In contrast to the domination of the semidiurnal currents for the barotropic tide, here the diurnal internal tidal currents are much larger than that of the semidiurnal constituents. Furthermore, the amplitudes of the diurnal baroclinic currents are generally larger than their barotropic counterparts, on the contrary, the semidiurnal baroclinic currents are smaller than their barotropic counterparts. The K1 baroclinic tide has comparable along-isobath and cross-isobath components, consistent with the direction of the barotropic K1 tide, whereas the M2 internal tide is mainly aligned with the zonal direction, but deflects slightly to the meridional direction. Generally, the M2 and K1 internal tides are shown to propagate in the northwest by west direction, but with an ambiguity of 180 . In addition, there are some remarkable and interesting differences of the modal structure between the diurnal and semidiurnal internal tides: the K1 resembles as a first-mode structure, i.e., with two separate layers oscillating 180 out of phase with each other around 45 m, whereas the M2 seems to exhibit a higher-mode structure with more oscillating layers around 35 and 70 m. To further examine the multi-mode structure of the M2 internal tide, we filtered the baroclinic current and temperature data by

Fig. 2. Baroclinic current ellipses at different depths for M2 (a) and K1 (b).

a band-pass filter with frequency band of [0.8, 1.2] M2. Fig. 3 shows an example of the semidiurnal internal tides of higher-mode on 1 August 2005. A second-mode internal tide signal can be clearly identified around 17:30, when the temperature profile shows increasing and then decreasing temperature in the upper layer at depth less than 40 m and the opposite temperature pattern in the lower layer. The current profile also displays a two currentreversal-structure in the vertical with the zero crossing points at 30 and 60 m, which is in qualitative agreement with the temperature pattern from Fig. 2 (oscillating layers around 35 and 70 m). The velocity above an isotherm trough is in the in-shore direction, visually indicating that the second-mode semidiurnal waves propagate northwestward, according to the internal wave theory. 3.3. EOF analysis In order to further characterize the vertical modal content of the internal tides, an EOF analysis is used to decompose the baroclinic tidal currents into dominant modes of variance. Considering that the east (u) baroclinic currents are much larger than the north (v) component, hereafter we will concentrate on the analysis of the u variations. Fig. 4 shows the vertical structure and spectral density of the first three modes. The first three dynamical modes account for more than 80% of the energy variance. The EOF modes apparently resemble corresponding baroclinic modes, according to the number of zero crossing layers of each mode. It should be noted that the shear layer around 105 m may be caused by a mean bottom mixed layer with the height of 10 m, but is not likely to represent a modal structure of the internal motions, which is beyond the scope of the present paper. The modal structure of the internal tides was also found to differ greatly between semidiurnal and diurnal constituents based on the EOF analysis (Fig. 4b). For the diurnal band frequency, the first mode is dominant, which is consistent with previous description of the baroclinic tides. In contrast, for the semidiurnal band frequency, the second mode is clearly more important than the first and third modes during the observation period, which is different from the overwhelming mode-1 signals in the northeastern SCS. Note that the modal structure of the baroclinic tides estimated from the EOF method is in good agreement with the results from the tidal harmonic analysis, and with the observational results from the filtered velocity and temperature data, which strongly suggests that the EOF analysis does demonstrate a qualitative convincible modal structure of the baroclinic tides, although the EOF method does not depend on any dynamical assumption, but only on the statistics of the data. In addition, the EOF analysis is also used to decompose the temperature data into dominant modes of variance. Notice that the temperature observations only span the upper water column, the gaps below 75 m to the bottom make the modal decomposition unstable for the higher modes. However, the modal decomposition based on the temperature data does exhibit a multimodal pattern of the semidiurnal tides (not shown). It is really interesting to find that the second-mode signals dominate the semidiurnal internal tides in our experiment. To the best of our knowledge, the phenomenon of rich multimodal structure and predomination of second-mode signals of semidiurnal internal tides during a long period is firstly reported in the SCS. Although the baroclinic energy is concentrated in the first-mode diurnal tides, in the next section, we will show that semidiurnal motions, especially higher-mode variations with small vertical scale also contribute significantly to the shear variations, which may play an important role in the local ocean mixing.

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Fig. 3. The semidiurnal east velocity component and north velocity component. The solid black lines denote the isotherms from 20  C (lowermost) to 28  C (uppermost).

Fig. 4. Results from EOF analysis of u baroclinic currents. (a) The vertical structure of the first three baroclinic modes. (b) Spectral density of the eigenfuction time series for the first three modes.

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3.4. Shear analysis Although the diurnal internal tidal currents are much larger than that of the semidiurnal constituents in our study area as described in the former sections, it is surprising to note that significant M2-shear S ¼ (vu=vz; vv=vz) does exist at certain depths over various small and large scales (Fig. 5). This similar phenomenon has been observed by Xie et al. (2008) in the northeastern SCS, where relatively smaller peaks appear at semidiurnal frequency both in the small-scale (4 m) and large scale (68 m) current difference spectra. They proposed that this feature was due to the barotropic or low-mode M2 baroclinic motions. Unfortunately, their study used observed velocities covering a little depth range of the entire water column over a short period, thus was unable to give a strong conclusion of the modal structure of the M2 internal tides. As we have previously described, for the M2 component in our study area, higher-mode, especially second-mode internal motions are more important than the first-mode variations. Since barotropic tides do not affect the shear field, thus we infer that the presence of significantly M2-shear over small and large scales at certain depths shown in Fig. 5 is probably due to the superposition of the internal variations of different modes. Particularly, small-scale M2-shear over various depths is most likely owing to the contributions from the higher-mode fluctuations. In order to compare the contributions to the shear field between the semidiurnal and diurnal baroclinic tides, we first calculated the M2 band and K1 band horizontal baroclinic currents (u and v) by a band-pass filter with frequency band of [0.8, 1.2] M2 and [0.8, 1.2] K1, respectively, then estimated the mean vector shear of the M2 band, K1 band, and raw horizontal baroclinic currents at 2 m vertical scale over the whole period, and finally made a comparison between them (Fig. 6). One can see that both semidiurnal and diurnal internal

tides make a relative contribution to the shear field. Around 45 m depth where the first-mode current reversal in the vertical happens, the shear induced by the diurnal internal tides is larger than that induced by the semidiurnal variations, while at the depths less than 45 m, the shear caused by the diurnal tides is comparable to that by semidiurnal tides and below 45 m depth the semidiurnal internal tides generally result in larger shear than the diurnal component. Although the diurnal internal tides are much stronger than the semidiurnal tides, the semidiurnal motions are shown to contribute significantly to the shear field, which might play an important role in local mixing. The strength and vertical range of the shear induced by the diurnal band and semidiurnal band variations vary slightly during the observational period, therefore, we select a 10-day period from 12 August to 22 August 2005 to investigate the variations of the shear field (Fig. 7). Combine the modal decomposition results, the shear field and baroclinic velocity (not shown) induced by the internal tides, one can see that the vertical scales of the diurnal internal tides are larger than that of the semidiurnal tides, and numerous small vertical scales of the semidiurnal variations can be discerned in the M2 band shear. Thus, the first-mode and highermode semidiurnal internal tides have smaller scales than that of the first-mode dominant diurnal variations, which are responsible for the enhancement of the shear at semidiurnal frequency. Both the first and higher baroclinic modes motions might play a role in the mean shear both for the semidiurnal and diurnal frequency band. For example, around the depth of 45 m, where first-mode zero crossing exists, both the semidiurnal and diurnal internal tides lead to strong shear. It should be noted that the higher-mode, especially the second-mode and third-mode semidiurnal motions also make a relative contribution to the shear enhancement at the semidiurnal frequency around this layer, thus enhancing the shear caused by the semidiurnal variations in

Fig. 5. Smooth spectrum of the holrizontal current difference over (a) 4 m, (b) 8 m, (c)16 m and (d) 32 m vertical scales at different depths.

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Fig. 6. Vertical structure of the mean shear caused by the (a) raw baroclinic currents and (b) M2 and K1 band baroclinic currents over 2 m vertical scale during the observational period.

a comparable order with the diurnal variations induced shear. But below 45 m depth the semidiurnal internal tides are generally shown to produce larger shear than that induced by the diurnal component, which is consistent with weaker higher-mode diurnal

signals and stronger higher-mode semidiurnal signals in the lower water column. Fig. 6 also shows that the diurnal and semidiurnal internal tides can not explain all shear field in the shelf seas. Other oceanic processes, such as the eddy, near-inertial band and other

Fig. 7. Time series of the shear field caused by the M2 and K1 band baroclinic currents over 2 m vertical scale during a 10-day period.

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harmonic tidal band motions might also contribute to the shear field in the observational region, which are not discussed here. In addition, note that a strong shear layer occurs near the bottom, but it is probably caused by the bottom layer stress, which is beyond the scope of this study. In summary, these features, consistent with the previous analysis, once again confirm that small-scale baroclinic M2-motions contribute significantly to the shear field, despite the much weaker M2 variations than that of the K1 component. 4. Discussion and conclusion Our observations show that the second-mode variations dominate the semidiurnal internal tides on the continental shelf in the northwestern SCS. Significantly M2-shear exists at certain depths over various small and large scales, and small-scale M2-shear contributes significantly to the shear filed. Previous studies in the SCS have suggested that the M2 internal tides are mainly low-mode (large scale), thus have no direct effect on ocean mixing and instead, the M2 internal tides can contribute to ocean mixing only when they are down to small dissipation scales via waveewave interaction. However, according to our study, the abundant highermode M2 internal tides in the shelf area of the SCS with small-scale can dissipate locally by shear instability and directly contribute to the local ocean mixing, besides via the other indirect processes. It is suggested that nearly all small-scale M2-motions will dissipate not very far from their topographic source (St. Laurent and Garrett, 2002; van Haren, 2007). In another word, outside source regions, internal tides predominantly have large vertical scales (low-mode). Numerical simulations in the northern SCS also suggest that higher baroclinic modes are almost invisible in the farfield (Vlasenko et al., 2010). In addition, the low-mode semidiurnal internal tides are mostly considered to originate from the Luzon Strait. Note that our mooring position is far away (more than 1 thousand kilometers) from the Luzon Strait. As a result, combined with previous suggestions, it seems that the abundant higher-mode semidiurnal internal tides observed in our study area are probably not directly generated at the Luzon Strait area, instead, they may be generated by the scattering or reflection process of the low-mode internal tides originated from the Luzon Strait. At present and with this data set it is rather difficult to explain why the semidiurnal internal tides exhibit a higher-mode structure. However, we can offer some tentative hypotheses. First, both reflection and scattering process can redistribute energy flux in wave-number space. Changes in stratification, background shear and significant nonlinear bottom drag may alter the modal content from low-mode to higher modes (St. Laurent and Garrett, 2002; Nash et al., 2004). Second, internal tides are dependent on the local stratification. Factors contributing to the structure of the internal tides also include stratification variations at the deep generation sites, mesoscale activity and the shoaling of a random internal wave field. In summer, the vertical structure of the water column in the northern SCS is intermittent in time and space and consists of several layers. Thickness of all layers varies through the continental slope and shelf, and it is notable that the thickness of the pycnocline layer is often comparable to or even larger than the thickness of the surrounding layers. Thus, the incident mode-one internal tides from the deep basin may integrate the effects of stratification changes, radiate out and disintegrate into higher modes during their long-range propagation to a variable stratification and mesoscale activity system on the shelf as observed in this study. In addition, some of the lowest-mode internal tides are also generated along the shelf break from local tidal-topography interactions, thus it is likely that these waves may also excite higher-mode signals during the propagation through the multilayer environment conditions. The interference pattern of the

internal tides from multiple sources might contribute to the variable and rich multimodal internal wave field, but it is unlikely to separate them with the present data set. Third, in the northern SCS, there are large regions that are near-critical to the diurnal tide and sub-critical to the semidiurnal tide (Klymak et al., 2011), and the internal tidal beam is more horizontal at the diurnal period than at the semidiurnal period under the same stratification (Shaw et al., 2009), indicating that the different harmonic constituents have different ray paths dependent on the temporal variability of the stratification structure, and the semidiurnal internal tides are more subjected to reflection from the surface or bottom and more energy are scattered to higher-mode motions than the diurnal tides. In this paper, we present the evidence for the multimodal semidiurnal internal tides and show that the second-mode signals dominate the semidiurnal variations in the northwestern SCS. The phenomenon of rich higher-mode semidiurnal variations is rarely reported, which is distinctly different from the predominance of the first-mode motions for the semidiurnal internal tides in the northeastern SCS. In spite of the weaker semidiurnal signals than the diurnal variations, the semidiurnal motions are shown to contribute significantly to the shear field and might be directly available for local ocean mixing, because of the superposition of the first-mode and higher-mode (small vertical scale) semidiurnal variations. However, the reasons for the multimodal structure observed in a complex ocean environment remain unclear; the investigation of these topics needs more concurrent in-situ observations and numerical simulations. Acknowledgments The funding for this study was provided by National Natural Science Foundation of China (No. 41106017, No. 41030855), the Knowledge Innovation Program of Chinese Academy of Sciences (No. KZCX1-YW-12), the National High Technology Research and Development Program of China (863 program) (No. 2008AA09A401). Helpful comments from two anonymous reviewers are gratefully acknowledged. References Alford, M.H., 2003. Redistribution of energy available for ocean mixing by longrange propagation of internal waves. Nature 423, 159e162. Alford, M.H., MacKinnon, J.A., Zhao, Z., Pinkel, R., Klymak, J., Peacock, T., 2007. Internal waves across the Pacific. Geophysical Research Letters 34. doi:10.1029/ 2007GL031566 L24601. Duda, T.F., Lynch, J.F., Irish, J.D., Beardsley, R.C., Ramp, S.R., Chiu, C.S., Tang, T.Y., Yang, Y.J., 2004. Internal tide and nonlinear internal wave behavior at the continental slope in the northern South China Sea. IEEE Journal of Oceanic Engineering 29, 1105e1130. Emery, W.J., Thomson, R.E., 2001. Data Analysis Methods in Physical Oceanography. second ed. revised. Elsevier Science, Amsterdam. Farmer, D., Li, Q., Park, J.H., 2009. Internal wave observations in the South China Sea: the role of rotation and non- linearity. Atmosphere-Ocean 47 (4), 267e280. Garrett, C., Kunze, E., 2007. Internal tide generation in the deep ocean. Annual Review of Fluid Mechanics 39, 57e87. Helfrich, K.R., Melville, W.K., 2006. Long nonlinear internal waves. Annual Review of Fluid Mechanics 38, 395e425. Jan, S., Chern, C., Wang, J., Chao, S., 2007. Generation of diurnal k1 internal tide in the luzon strait and its influence on surface tide in the South China Sea. Journal of Geophysical Research 112. doi:10.1029/2006JC004003. Klymak, J.M., Alford, M.H., Pinkel, R., Lien, R.C., Yang, Y.J., Tang, T.Y., 2011. The breaking and scattering of the internal tide on a continental slope. Journal of Physical Oceanography 41, 926e945. doi:10.1175/2010JPO4500.1. Lien, R.C., Tang, T.Y., Chang, M.H., D’Asaro, E.A., 2005. Energy of nonlinear internal waves in the South China Sea. Geophysical Research Letters 32. doi:10.1029/ 2004GL022012 L05615. Liu, A.K., Chang, Y.S., Hsu, M.K., Liang, N.K., 1998. Evolution of nonlinear internal waves in the east and south china seas. Journal of Geophysical Research 103 (C4), 7995e8008. Liu, A.K., Hsu, M.K., 2004. Internal wave study in the South China Sea using synthetic aperture radar (SAR). International Journal of Remote Sensing 25, 1261e1264.

Z. Xu et al. / Estuarine, Coastal and Shelf Science 95 (2011) 178e185 Liu, A.K., Hsu, M.K., Zhao, Y., 2008. Overview of internal waves in the south china sea. In: Liu, A.K., Ho, C.-R., Liu, C.-T. (Eds.), Chapter I, Satellite Remote Sensing of South China Sea. Tingmao Publish Co, Taipei, pp. 1e23. Liu, J.L., Cai, S.Q., Wang, S., 2010. Currents and mixing in the northern south china sea. Chinese Journal of Oceanology and Limnology 28 (5), 974e980. Moum, J.N., Caldwell, D.R., Nash, J.D., Gunderson, G.D., 2002. Observations of boundary mixing over the continental slope. Journal of Physical Oceanography 32, 2113e2130. Nash, J.D., Kunze, E., Toole, J.M., Schmitt, R.W., 2004. Internal tide reflection and turbulent mixing on the continental slope. Journal of Physical Oceanography 34, 1117e1134. Park, J.H., Andres, M., Martin, P.J., Wimbush, M., Watts, D.R., 2006. Second-mode internal tides in the East China Sea deduced from historical hydrocasts and a model. Geophysical Research Letters 33. doi:10.1029/2005GL024732 L05602. Pawlowicz, R., Beardsley, B., Lentz, S., 2002. Classical tidal harmonic analysis including error estimates in Matlab using T_Tide. Computers and Geosciences 28, 929e937. Rainville, L., Pinkel, R., 2006. Observations of the propagation and nonlinear interaction of the internal tide generated at the Hawaiian Ridge. Journal of Physical Oceanography 36, 1104e1122. St. Laurent, L., Garrett, C., 2002. The role of internal tides in mixing the deep ocean. Journal of Physical Oceanography 32, 2882e2899. Shaw, P.T., Ko, D., Chao, S.Y., 2009. Internal solitary waves induced by flow over a ridge: with applications to the northern South China Sea. Journal of Geophysical Research 114. doi:10.1029/2008JC005007 C02019.

185

van Haren, H., 2007. Shear at the critical diurnal latitude. Geophysical Research Letters 34. doi:10.1029/2006GL028716 L06601. Vlasenko, V., Stashchuk, N., Guo, C., Chen, X., 2010. Multimodal structure of baroclinic tides in the South China Sea. Nonlinear Processes in Geophysics 17, 529e543. doi:10.5194/npg-17-529-2010. Wang, Y.H., Lee, I.H., Liu, J.T., 2008. Observation of internal tidal currents in the Kaoping Canyon off southwestern Taiwan. Estuarine, Coastal and Shelf Sciences 80, 153e160. Wolanski, E., Colin, P., Naithani, J., Deleersnijder, E., Golbuu, Y., 2004. Large amplitude, leaky, island-generated, internal waves around Palau, Micronesia. Estuarine, Coastal and Shelf Sciences 60, 705e716. Xie, X.H., Chen, G.Y., Shang, X.D., Fang, W.D., 2008. Evolution of the semidiurnal (M2) internal tide on the continental slope of the northern South China Sea. Geophysical Research Letters 35 L13604. Yang, Y.J., Tang, T.Y., Chang, M.H., Liu, A.K., Hsu, M.K., Ramp, S.R., 2004. Solitons northeast of Tung-Sha Island during the ASIAEX pilot studies. IEEE Journal of Oceanic Engineering 29, 1182e1199. Zhao, Z., Klemas, V., Zheng, Q., Yan, X.H., 2004. Remote sensing evidence for baroclinic tide origin of internal solitary waves in the northeastern South China Sea. Geophysical Research Letters 31. doi:10.1029/2003GL019077 L06302. Zhao, Z., Alford, M.H., MacKinnon, J.A., Pinkel, R., 2010. Long-range propagation of the semidiurnal internal tide from the Hawaiian Ridge. Journal of Physical Oceanography 40, 713e736.