R.-C. Lien,1 T. Y. Tang,2 M. H. Chang,2 E. A. D’Asaro,1
Four sets of ADCP measurements were taken in the South China Sea (SCS); these results were combined with previ-ous satellite observations and internal-tide numerical model results. Analysis suggests that strong internal tides are gen-erated in Luzon Strait, propagate as a narrow tidal beam into the SCS, are amplified by the shoaling continental slope near TungSha Island, become nonlinear, and evolve into high-frequency nonlinear internal waves (NIW). Inter-nal waves in the SCS have geographically distinct charac-teristics. (1) West of Luzon Strait the total internal-wave energy (Eiw) is 10 × that predicted by Garrett and Munk spectra (EGM)(Levine, 2002). There is no sign of NIW. (2) Near TungSha Island Eiw = 13 ×EGM. Strong nonlinear and high-harmonic tides are present. Repetitive trains of large-amplitude NIW appear primarily at a semidiurnal pe-riodicity with their amplitudes modulated at a fortnightly tidal cycle. The rms vertical velocity of NIW shows a clear spring-neap tidal cycle and is linearly proportional to the barotropic tidal height in Luzon Strait with a 1.85-days time lag; this provides an estimate of NIW energy in the SCS.
The 1.85-day time lag is consistent with the travel time of internal tides from Luzon Strait to TungSha Island. (3) At the northern SCS shelfbreak, Eiw = 4 × EGM. Single de-pression waves are found, but no multiple-waves packets are evident. (4) On the continental shelf Eiw= 2 × EGM. Both depression and elevation NIW exist.
Introduction
Hsu and Liu (2000) and Zhao et al. (2004) collected satellite images between 1993 and 2001 in the SCS to re-veal the distribution of NIW (Fig. 1). Most of the long-crest, multiple-wave packets exist in a (200 km)2 area on the continental slope and shelf centering around TungSha Island. A single long-crest, multiple-wave packet was ob-served at the west of Luzon Strait on 1995 June 16. In the deep basin of the SCS only a few short-crest wave trains and single-depression waves exist. Recent in-situ measurements confirm the presence of NIW identified by satellite images (Ramp et al. 2004 and Yang et al. 2004).
The generation mechanism for NIW in the SCS remains controversial. Two hypotheses have been proposed: the in-ternal soliton/lee wave model, and the nonlinear inin-ternal tide model (Fig. 2)(Apel et al., 1997). According to the for-mer, lee waves are generated between the Batan Islands in Luzon Strait. When the current reverses, lee waves escape from the topography and develop into NIW (Fig. 2a). Ac-cording to the latter, internal tides are generated either on
1Applied Physics Lab, University of Washington, Seattle, WA 98105, USA
2Institute of Ocean Research, National Taiwan University, Taiwan
Copyright 2004 by the American Geophysical Union.
0094-8276/04/$5.00
shelf break or remotely on two ridges in Luzon Strait (Fig. 1) (Niwa and Hibiya, 2004). Those generated in Luzon Strait propagate across the SCS in a narrow tidal beam. They are amplified by the shoaling continental slope, become nonlin-ear, and evolve into NIW riding on the internal tide (Fig.
2b). For very strong barotropic tidal forcing in Luzon Strait, internal tides could be strongly nonlinear near their genera-tion sites so that NIW would evolve immediately (Fig. 2c).
19.5
115 116 117 118 119 120 121 122 123
Longitude (oE)
Figure 1. Map of South China Sea and positions of ADCP stations (blue dots). Black contours are 200, 500, 1000, 2000, and 3000-m isobaths. Red vectors are model results of depth-integrated semidiurnal internal tidal en-ergy flux produced by Niwa and Hibiya (2004). Green curves are internal wave packets derived from satellite images by Zhao et al. (2004). Solid green curves indicate multiple-wave packets and dashed green curves single-wave packets. Thick solid green curves west of Luzon Strait represent the ”big wave” event observed on 16 June 1995.
Here, we analyze a set of four ADCP measurements taken in different regions of the SCS. We will 1) describe internal wave characteristics, 2) discuss the generation mechanism of NIW, and 3) explore the relation between NIW in the SCS and barotropic tidal forcing in Luzon Strait.
Observations
In April 2000 three 150-kHz broadband ADCP moorings (L2, IW1, and IW3) and one 300-kHz narrowband bottom ADCP (IW2) were deployed in the SCS (Figs. 1 and 2) col-lecting data for ∼20 days. All ADCPs were upward-looking and recorded 1-min averages. The water depths at stations L2, IW1, IW3, and IW2 were 2080 m, 426 m, 468 m, and 110 m, respectively. The mooring ADCPs were mounted at a nominal depth of 237 m.
Internal Wave Characteristics
Internal waves observed in four locations within the SCS have different characteristics. Segments of 4-hr time series for six consecutive semidiurnal periods illustrate these dif-ferences (Fig. 3).
The L2 mooring was located west of a submarine ridge in Luzon Strait. ADCP observations were available between 30 and 220 m depths. The zonal current u dominated the 1
Ψ = R
dz(u − C), where a wave speed C=1.8 m s−1 is used (Yang et al., 2004). The zonal velocity between the sea surface and 30-m depth is assumed constant and equal to u(30m). The computed stream line provides a crude view of the isopycnal displacement. The streamline shows high-frequency variations riding on a low-high-frequency tidal bore;
but no NIW are evident. This is the first in-situ evidence confirming the absence of NIW near Luzon Strait. The ver-tical velocity measurements at L2 were contaminated by in-strument noise and are not shown.
115 116 117 118 119 120 121 122 123
0 Internal Soliton Model
Nonlinear Internal Tide Model
Luzon Strait
(c)Very Strong Nonlinear Internal Tide Model IW1
IW2 IW3 L2
Figure 2. Sketch of generation mechanisms for NIW in the SCS:(a) internal soliton model, (b) nonlinear in-ternal tide model, and (c) very strong nonlinear inter-nal tide model. The shading is the bathymetry across the South China Sea. The inset (d) shows the moor-ing ADCP configuration. Blue dots indicate locations of ADCP measurements.
At mooring IW1, large NIW were observed at a semidi-urnal period. The streamline followed the zonal shear very well, especially within the leading wave. The leading waves had a vertical displacement of 70–120 m, and a wave width of 10–20 minutes corresponding to a 1–2 km-width. These NIW had a first-mode appearance. Before the waves’ arrival, the current flowed eastward. During the waves’ passage, the zonal current in the upper layer fluctuated in alternating directions. The maximum westward current was > 1 m s−1. The vertical velocity at IW1 showed the unambigu-ous first-mode depression wave structure, with maximum speed at mid-depth, and downwelling followed by upwelling.
The vertical velocity reached 0.2 m s−1. NIW at IW1 were the strongest among our observations, as was expected from satellite images and numerical model results of internal tides (Fig. 1).
At mooring IW3, only single depression waves were ob-served. The largest depression wave was at 0300 on 21 April.
The zonal velocity of the wave was ∼0.5 m s−1, less than 1/2 of that observed at IW1. Mooring IW3 was located off shelf relative to the ASIAEX experiment site(Ramp et al., 2004).
Mooring IW2 was located on the continental shelf at
∼110-m depth. Two trains of elevation waves were iden-tified at 0300 on 18 April and 0548 on 19 April. A westward wave speed of 0.8 m/s was used to compute the stream func-tion, determined by matching the observed vertical velocity with the prediction from the stream function. The isopycnal displacement was generally <10 m. The most distinct char-acteristic of these elevation waves is the leading upwelling
at 0548 on 19 April.
Z (m)Z (m) 0 60 120180 mins L2
Figure 3. Zonal velocity and vertical velocity contours in 4-hr time segments for six consecutive semidiurnal pe-riods. Each segment is separated by a semidiurnal period 12.4 hr. The vertical velocity at L2 is not shown because it is contaminated by instrument noise. The beginning time for each time segment is shown on the lower line of the x-axis; upper line shows minutes elapsed from the beginning time. The black curve shows the streamline beginning at 100-m depth, assuming a westward wave speed of 1.8 m s−1for L2, IW1, and IW3, and 0.8 m s−1 for IW2.
Internal Wave Spectra
Velocity spectra are computed and WKB-normalized at each depth. Spectra are averaged over the upper 100 m and compared with the Garrett–Munk spectra (GM79) (Levine, 2002). The total energy spectrum (ΦE), horizontal velocity spectrum (Φu), vertical velocity spectrum (Φw), and po-tential energy spectrum (ΦP E) of GM79 are expressed as follows,
ΦP E=
2 ω2Φw, (4)
where B(ω) = 2f
πω(ω2−f2)1/2, ω is frequency, N the buoy-ancy frequency, and f the inertial frequency. Et = 2.9 mJ kg−1 is the total energy per unit mass. N0= 0.0052 s−1 is a reference buoyancy frequency. We compute the potential energy spectrum using the observed vertical velocity spec-trum following Eq. (4).
At mooring L2, both horizontal velocity spectra show dominant diurnal and semidiurnal peaks. They have a sim-ilar magnitude and show a ω−2 spectral shape until they meet the noise floor at about 0.003 s−1. The total inter-nal wave energy Eiw is 10 ×EGM, where EGM is the total energy of GM79 (Table 1).
10-4 10-2
Figure 4. Average velocity and energy spectra. Spectra are WKB-normalized and averaged over the upper 100 m.
Red, green, and black curves represent zonal, meridional, and vertical velocity spectra, respectively. Blue curves are total energy spectra. Black and red dashed curves are GM79 vertical and horizontal velocity spectra. The thick dashed gray lines represent the observed vertical velocity spectrum at IW3 averaged in 0.001 s−1< ω < N , plotted for reference. Frequencies of diurnal tide S1, semidiurnal tide M2, and the compound tide, M2+ S1 are labeled.
The dashed blue curve in the panel of IW1 represents the background high-frequency internal wave spectrum.
At mooring IW1 observed spectra exhibit peaks at diur-nal, semidiurdiur-nal, and compound tides, as well as higher tidal harmonics suggesting nonlinear internal tides. At frequen-cies greater than tidal harmonics, 1) the meridional velocity spectrum Φv shows a ω−2 shape below N ( 0.016 s−1), 2) Φu shows a plateau of 5 ×Φv, and 3) Φw shows a bump in 0.001 s−1< ω < N . Eiwis 5.76 × 10−2 m2s−2, 13 ×EGM
(Table 1). The vertical kinetic energy Wiw2 is 0.045 × 10−2 m2s−2, 54 × the vertical energy of GM (WGM2 )! The spec-tral plateau of Φuand the spectral bump of Φwbelow N are associated with the NIW. The strong nonlinear tide and the accompanying enhanced NIW suggest a direct dynamic link, consistent with the nonlinear internal tide model generation mechanism (Fig. 2b).
At mooring IW3 spectral peaks exist at diurnal, semidi-urnal, and compound tides, as well as higher tidal harmonic frequencies, similar to IW1 but of weaker magnitudes. Be-yond the tidal harmonics, the two horizontal velocity spec-tra have the same specspec-tral level with a specspec-tral slope slightly greater than -2, and Φw is white below N. Eiw is 4 ×EGM, and Wiw2 is 25 ×WGM2 . Fundamental differences from IW1
Φw at IW3, 2) the total internal wave energy and vertical kinetic energy at IW3 is < 1/2 of those at IW1.
At mooring IW2, all velocity spectra show peaks at the diurnal and semidiurnal frequencies. In 0.001 s−1< ω < N , all spectra exhibit a bump 10 times the background level as-sociated with the mixed elevation and depression NIW (see Fig. 3). Eiwis 2 ×EGM, and Wiw2 is 15 ×WGM2 .
The presence of strong NIW at IW1 and their absence at L2 shown in time series and spectral properties suggest that NIW in the SCS are generated via the nonlinear internal tide model (Fig. 2b), not the lee wave model (Fig. 2a).
NIW Energy and Tidal Forcing
NIW contain more than 80% of the vertical energy in the internal wave band (Table 1). Therefore, the vertical energy is an ideal index for NIW energy. The vertical ve-locity variances at IW1, computed in 1-hr intervals, show a semidiurnal periodicity (Fig. 5b). The barotropic tidal height in Luzon Strait, computed using Oregon Tidal Inver-sion Software (OTIS) (Egbert and Erofeeva, 2002) is also dominated by the semidiurnal tide (Fig. 5a). Both vari-ables show a fortnightly modulation and are correlated with a 1.85-day phase lag lead by the tide (Fig. 5c). Niwa and Hi-biya (2004) show that the M2energy flux emanates mostly from the western submarine ridge, 300–350 km from IW1.
Considering the 1.85-day phase lag as the travel time, the speed of the semidiurnal internal tide should be 1.88–2.20 m s−1, a reasonable estimate. The correlation between the rms tidal amplitude in Luzon Strait (σH) and the rms ver-tical velocity at IW1 (σw) is 0.89 and the linear regression fit (Fig. 5d) yields
σw(m/s) = 0.11σH(m) − 0.01(m/s). (5) This relation provides a simple model to predict the energy of NIW near TungSha Island based on the barotropic tide at Luzon Strait. The correlation increases to 0.96 and the linear regression fit is improved if the linear trend of σw is removed (Fig. 5d).
Figure 5. Time series of (a) the barotropic tide east of Luzon Strait HLS((black curve) and the 1.7 × the rms tidal amplitude computed in 24-hr intervals σHLS (red curve); (b) the vertical velocity variance computed in 1-hr intervals σ2w (black curve), and the 1.85-day forward shifted HLS (red curve); (c) the rms vertical velocity σw
computed in 24-hr intervals (gray curve) and the 1.85-day forward shifted σHLS (red curve). The blue curve in (c) is the detrended σw. The inset (d) shows the scatter plot between 1.85-day shifted σHLS and σw (red dots), and between 1.85-day shifted σHLS and detrended σw (blue dots). The black line represents the linear regression fit.
Generation Mechanisms
Observed internal wave properties combined with a com-posite map of NIW from satellite images and results of nu-merical internal tide models supports the hypothesis that the nonlinear internal tide is the primary generation mecha-nism for NIW observed in the SCS (Fig. 2b). Strong inter-nal tides are generated in Luzon Strait. They propagate into the SCS in a narrow tidal beam (Fig. 1). They are ampli-fied by the shoaling continental slope near TungSha, become nonlinear, and evolve into NIW (Figs. 3 and 4). Observed NIW are not escaping lee waves (Fig. 2a) because they are not observed at L2, contradicting the internal-soliton model.
Within the internal tidal beam (e.g., IW1), NIW evolve primarily from the amplification of the trans-basin internal tides. At mooring IW1, the internal wave energy is 13×GM, the vertical energy is 54×GM, and NIW of O(100m) ampli-tude are observed repeatedly. Outside of the internal tidal beam (e.g., IW3), NIW may evolve from the locally gener-ated internal tides (Ramp et al., 2004).
Big Wave near Luzon Strait
A long-crest NIW was captured by a satellite image on 16 June 1995 (Hus and Liu, 2000). During this event, the barotropic tidal current in Luzon Strait was one of the strongest of 1995 (Fig. 6). The ”big wave” west of Luzon Strait may have been generated by an abnormally strong barotropic tidal forcing. These events occur only a few days each year. The chance is small for satellite images to cap-ture these events; only one appears in the satellite record of nearly 10 years.
Figure 6. Barotropic zonal tidal current in Luzon Strait in 1995 produced by OTIS (Egbert and Erofeeva, 2002).
Energy Conversion and Dissipation of NIW
At mooring IW1, the total energy in the high-frequency regime (10−3 s−1 < ω < N ) is ∼16% of the total inter-nal wave energy (Table 1). The total energy of “non-NIW”
high-frequency internal waves is computed by integrating the background internal wave spectrum, constructed by ex-trapolating a ω−2spectrum from the observed spectral level at 10−3 s−1 to N (blue dashed curve in Fig. 4). It is
∼3% of the total internal wave energy. Therefore, the en-ergy conversion rate from internal tides to NIW is ∼13%.
Niwa and Hibiya (2004) report an internal tidal energy flux of 4.2 GW into the SCS (Fig. 1). Applying a 13% con-version rate, NIW contain an energy flux of 0.54 GW. If all NIW dissipate within the (200 km)2 area centered at TungSha Island in the 1–10m-thick interface, the turbulence kinetic energy dissipation rate ε associated with breaking NIW would be ∼ 10−6–10−5W kg−1and an eddy diffusiv-ity Kρ= 0.2εN−2=∼ 10−3–10−2m2s−1, at least 100 times that in typical oceanic thermocline.
The energy content of NIW depends on 1) the conver-sion rate from the barotropic to internal tides, 2)the con-version rate from internal tides to NIW, 3) the tidal beam properties, and 4) the dissipation of NIW. These processes are modulated by the barotropic tides, by the background shear and stratification associated with Kuroshio, mesoscale eddies, and by the surface wind and buoyancy forcing in the SCS including Luzon Strait. The simple relation (5) includes only one of many important parameters, implying invariant energy conversion rates. The fair success of this simple re-lation is because other parameters are nearly invariant in a monthly time scale, and at mooring IW1 internal tides generated remotely in Luzon Strait dominates those gener-ated locally. The linear trend of σw (Fig. 5c) represents the effects of processes overlooked by Eq. (5). Further ob-servations and numerical models are needed to improve our understanding of the details of these processes, and improve the prediction of NIW.
Acknowledgments. We wish to thank Drs. Yoshihiro Niwa and Toshiyuki Hibiya for providing their model results of inter-nal tidal energy flux in the South China Sea. Discussions with Drs. Wen-Ssn Chuang, Matthew Alford, and Zhongxiang Zhao were very helpful. This work is supported by the Office of Naval Research of US and the National Science Council of Taiwan.
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R.-C. Lien, Applied Physics Lab, University of Washington, Seattle, WA 98105, USA. ([email protected])
stations in the SCS averaged in the upper 100 m: Wiw, ver-tical kinetic energy in the internal wave band; Eiw, total in-ternal wave energy; W
2 iw
WGM2 , the ratio of Wiw2 to the GM79 vertical kinetic energy WGM2 ; EEiw
GM, the ratio of Eiw to GM total energy EGM; WN IW2 , the vertical kinetic energy in the high-frequency regime (10−3s−1< ω < N ); EN IW, the total energy in the high-frequency regime; %W2
N IW, the percentage of WN IW2 in Wiw2 ; and %EN IW, the percentage of EN IW in Eiw.
Stn Wiw2 Eiw W
2 iw WGM2
Eiw EGM W2
N IW EN IW %W2
N IW %EN IW (cm2
s2 ) (cm2
s2 ) (cm2
s2 ) (cm2
s2 ) (%) (%)
L2 NA 546 NA 10.2 NA NA NA 10
IW1 4.5 576 53.5 12.9 4 92 89 16
IW3 2.1 243 24.8 4.3 1.7 26 81 11
IW2 1.3 140 14.7 2.4 1.2 20 93 14