Observations of a mode-2 nonlinear internal wave on the northern Heng-Chun Ridge south of Taiwan

Transcription

1 JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 117,, doi: /2011jc007662, 2012 Observations of a mode-2 nonlinear internal wave on the northern Heng-Chun Ridge south of Taiwan S. R. Ramp, 1 Y. J. Yang, 2 D. B. Reeder, 3 and F. L. Bahr 4 Received 5 October 2011; revised 7 February 2012; accepted 8 February 2012; published 30 March [1] A research cruise was carried out over the Heng-Chun Ridge during June 27 July 1, 2010, near N, E, about 35 km south of Taiwan. The goal of the cruise was to determine if the location is an active generation site for internal tides and high-frequency nonlinear internal waves (NLIWs) in the northeastern South China Sea (SCS). The method was to sample a series of across-ridge sections using an underway conductivity-temperature-depth (UCTD) profiler and to conduct a time series at a fixed point atop the ridge using a CTD with lowered acoustic Doppler current profiler (LADCP) instrumentation. A hull-mounted ADCP and acoustic backscatter device were also operated throughout the cruise. The site was a very high energy region, with the northward Kuroshio Current exceeding 100 cm s 1 and the primarily zonal barotropic tidal currents exceeding 140 cm s 1. The most remarkable feature observed was a convex-type mode-2 NLIW with a westward-propagating core centered near 100 m depth. The wave was clearly visible in the velocity and backscatter data and had surface expressions visible both on radar and with the naked eye. The horizontal and vertical velocity structure was a good match for theoretical mode-2 waves in the SCS. The wave generation was consistent with local lee wave dynamics, which favored mode-2 generation over mode-1 at peak ebb tide given the currents, stratification, and bottom slope at the site. The wave could not be tracked farther west, and apparently did not escape the opposing Kuroshio. Citation: Ramp, S. R., Y. J. Yang, D. B. Reeder, and F. L. Bahr (2012), Observations of a mode-2 nonlinear internal wave on the northern Heng-Chun Ridge south of Taiwan, J. Geophys. Res., 117,, doi: /2011jc Introduction [2] Over a period of ten years, a series of joint programs between Taiwan and the United States have been studying the world s largest high frequency nonlinear internal waves (NLIWs) in the northeastern South China Sea. Early observations of the far-field wave arrivals on the Chinese continental shelf north of Dongsha Island documented the existence of these waves and their basic arrival patterns [Duda et al., 2004; Liu et al., 2004; Ramp et al., 2004; Yang et al., 2004]. Subsequent observations and theoretical studies localized the generation regions for these transbasin waves to the vicinity of the Batan Islands, Philippines [Alford et al., 2010; Ramp et al., 2010]. These islands sit upon the eastern (Lan-Yu) ridge between Taiwan and the Philippines in the Luzon strait and are separated by a multitude of shallow sills and straits where nonlinear internal waves might be generated. The westward barotropic tidal flux through this region converts enormous energy into the 1 Soliton Ocean Services, Inc., Carmel Valley, California, USA. 2 Department of Marine Science, Naval Academy, Kaohsiung, Taiwan. 3 Department of Oceanography, Naval Postgraduate School, Monterey, California, USA. 4 Monterey Bay Aquarium Research Institute, Moss Landing, California, USA. Copyright 2012 by the American Geophysical Union /12/2011JC internal tide [Niwa and Hibiya, 2004; Jan et al., 2008], which subsequently steepens and becomes increasingly nonlinear as it propagates westward, ultimately spawning the high frequency NLIWs [Farmer et al., 2009; Buijsman et al., 2010a, 2010b; Zhang et al., 2011]. NLIWs can also be locally generated by a lee wave mechanism [Maxworthy, 1979; Farmer and Smith, 1980; Apel et al., 1985]. The extent to which these processes are operative in the Luzon Strait is still an active research topic. It seems that given the wide range of tidal forcing and bottom topography, both mechanisms may be operative at different locations and different phases of the tide [Ramp et al., 2010; Zhang et al., 2011]. Most of the observational effort to date has focused on the Lan-Yu ridge, particularly in the very active strait between Batan and Itbayat Islands, Philippines. [3] An interesting and still unresolved issue is how the western (Heng-Chun) ridge impacts the wave generation process. The west ridge runs southward from the tip of Taiwan nominally 100 km west of the Lan-Yu Ridge. The west ridge is for the most part much deeper than the eastern ridge but shoals northward toward Taiwan where it becomes shallower than the eastern ridge. Some investigators have suggested that the west ridge dampens the waves [Chao et al., 2007] while others find that a tidal resonance between the two ridges actually enhances the internal wave amplitudes [Buijsman et al., 2010a, 2010b; Zhang et al., 2011]. This effect may depend on the latitude being studied. Due primarily to 1of11

2 eastern ridge centered near N, E just north of Babuyan Island in the Balintang Channel, and one on the northern Heng-Chun Ridge where the water is less than 500 m deep. Since no in situ observations had been made at the Heng-Chun site, a pilot cruise was organized to the area during June 27 July 1, 2010 on the Research Vessel OCEAN RESEARCHER 2. Despite the short cruise duration, several time series of temperature, salinity, velocity, and backscatter were collected and used to construct spatial and temporal displays of these variables. These sections captured a highvelocity, high-turbulence region during the spring tide that included a portion of the Kuroshio Current. Most interestingly, a clear mode-2 nonlinear internal wave was documented propagating from east to west across the top of the ridge. While mode-2 waves had been observed in the far field [Yang et al., 2009, 2010], they had not been previously observed near the generating ridges. The remainder of this paper describes how this feature was observed with suggestions as to its likely generation mechanism. 2. Data and Methods Figure 1. Locator maps showing the study area on the Heng-Chun Ridge south of Taiwan. The black line is the UCTD transect and the white square is the anchor station. The color bars indicate the bottom depth in meters. Top base map courtesy of Tswen Yung David Tang, National Taiwan University. differences in the ridge geometry, tidal resonance between ridges appears likely along 21.5 N, but unlikely at 21.0 N and 19.5 N [Farmer et al., 2009]. Another recent theoretical study finds that the large mode-1 depression waves are generated at the eastern ridge while higher-mode waves stem from the western ridge [Vlasenko et al., 2010]. These waves then interact as they propagate westward to form the observed transbasin waves. An inverted echo sounder with pressure (PIES) placed between the ridges at 20.5 N observed a nonlinear internal tide but no NLIW energy between ridges [Farmer et al., 2009]. They ascribed this to inadequate time and distance from the source for nonlinear steepening of the mode-1 depression waves to occur [Farmer et al., 2009]. [4] Recent theoretical studies suggest that multiple sources interact to create the observed far-field wavefronts, which are surprisingly linear in nature [Vlasenko et al., 2010; Zhang et al., 2011]. These sites include the Batan/ Itbayat site already mentioned, one farther south on the [5] The site chosen for study was atop the Heng-Chun Ridge about 35 km south of Taiwan (Figure 1). While the bottom topography was generally rough, a relatively smooth zonal channel 9 km wide was located along N with a sill depth of 580 m located toward the eastern end. When viewed in cross-section, the region resembled a ridge about 15 km wide by 400 m high, sitting atop the main ridge which topped out at about 1000 m depth (Figure 2). Between 580 and 800 m, the bottom slope to the east was about twice the bottom slope to the west. The tidal current forecast (Figure 3) was constructed using the tidal constituents calculated from a time series collected nearby during a previous experiment [Ramp et al., 2010] using the Foreman analysis method [Foreman, 1978]. The tide can be characterized as mixed, diurnal dominant, with a strong diurnal inequality. The cruise dates from June 27 to July 1, 2010 sampled the ridge during the spring tide (Figure 3) when the largest barotropic tidal currents and greatest internal wave activity were expected. [6] The first activity upon arrival at the site was to conduct a 21-h anchor station on top of the sill at N, E using a conductivity-temperature-depth (CTD) package equipped with a lowered Acoustic Doppler Current Profiler (LADCP). During this activity, the ship held position atop the sill to obtain a time series of observations at that point. The LADCP was configured as two Teledyne RDI 300 khz broadband units with a downward-looking master and upward-looking slave. Each profile took nominally 38 min to complete, and both down and up casts were used, resulting in 34 profiles during the anchor station. The LADCP data were processed using the velocity inversion method with bottom tracking [Visbeck, 2002; Thurnherr, 2010]. The algorithms are publically available from a web site at IFMGEOMAR at the University of Kiel, Germany. The CTD/ LADCP package returned complete time series of temperature, salinity, velocity, and derived parameters over the full sampling period. Underway data were collected continuously throughout the cruise using the ship s hull-mounted ADCP, a Teledyne RDI 150 khz Ocean Surveyor unit with a basic averaging interval of 5 min. Acoustic backscatter 2 of 11

3 Figure 2. Cross-sectional view of the transect highlighted by the black line in Figure 1. The view is toward the north with east on the right and west on the left. The bottom depths were obtained from the ship s echo sounder. The heavy black line is the anchor station and the thin lines indicate the UCTD profile positions. Data were collected to the bottom at the anchor station and to 500 m at the UCTD positions. The dashed line indicates the origin of the lee wave as suggested by the analysis. data at 38 and 120 khz were also collected continuously using a Simrad EK500 echo sounder sampling at 2 Hz. [7] Upon completion of the anchor station, three acrossridge transects were completed using an Oceanscience underway CTD (UCTD). The UCTD is a free-falling CTD probe that can be deployed and retrieved while the vessel is steaming at up to ten knots [Rudnick and Klinke, 2007]. The basic operating principle is similar to an expendable bathythermograph (XBT): The thin Spectra line spools off from both a deck-mounted reel, which lays line out along the sea surface, and from the tail of the probe, which allows the probe to fall straight down. Advantages over an XBT are many, including higher-quality sensors, the addition of salinity, the use of pressure to determine depth rather than fall rate, and the ability to retrieve the probe following each cast. Back on deck, the data were downloaded to a PC via Bluetooth while the probe tail was rewound in preparation for the next cast. For this application, profiles were collected to 500 m with the vessel steaming at four knots. With some practice, the entire cycle could be reliably accomplished in about twenty minutes, resulting in profiles nominally every 2.5 km (Figure 2). 3. Results [8] The UCTD temperature and salinity sections provided the large-scale oceanographic context for the observations (Figure 4). Each section required about four hours to complete and thus showed some aliasing by internal waves. The dominant large-scale feature present was the Kuroshio Current, easily discernable by the salinity maximum >34.8 near 100 m depth. Only the western edge of the current was visible in the section, placing it over the eastern slope of the ridge. A strong salinity front was present in the upper 75 m between the coastal water (blue) and the Kuroshio water (red). The position of the front moved about from section to section, likely influenced by the tides which flowed predominantly east-west across the ridge. [9] The complexity of the currents and water mass structure on top of the ridge is revealed by the time series data (Figure 5). The ribbon of high salinity water >34.8 (Figure 5b) was well correlated with the northward current ranging from 50 to 100 cm s 1 in the same depth range (Figure 5d) and represents the Kuroshio Current. Below 200 m depth, the currents were dominated by the tides (Figure 5c). The flood tide toward the SCS (blue) from 1600 June 28 to 0400 June 29 was followed by a stronger ebb tide toward the Pacific (red) from 0400 June 29 to the end of sampling. The tidal currents were primarily zonal across the ridge but also had a southward component on ebb. The maximum values exceeded 70 cm s 1 on flood and 140 cm s 1 on ebb. The thermohaline structure (Figures 5a and 5b) rose and fell with the tidal currents. Toward the end of the record, two strong bulges developed in the 16 C water. The first event at 0900 on June 29 depressed the 16 C isotherm 85 m in 30 min, followed by an even more rapid depression at 1030 that forced the isotherms 100 m down. The appearance of these features roughly coincided with the turn of the tide, which reached maximum ebb at about 0820 on June 29. 3of11

4 Figure 3. Predicted barotropic tide computed using a Foreman analysis of a two-year velocity time series collected in the Batan Islands near 20.5 N, W (see Figure 1). The vertical dashed lines indicate the start and stop times for the anchor station. All times throughout the paper are reported in Coordinated Universal Time (UTC). [10] A higher resolution view of the upper ocean was recorded during the anchor station by the EK500 and the ship s hull-mounted ADCP. Both data sets required some additional processing to produce a clean image. Since the backscatter data contained some high-frequency white noise, a smoother based on discrete cosine transforms [Garcia, 2010] was applied to the data first horizontally and then vertically. The effect of the smoother was to reduce the amplitude of the white noise by two orders of magnitude at 1 min, resulting in a much sharper image. Based on the displacement of the scatterers (Figure 6), a clear convex mode-2 nonlinear internal wave was observed passing beneath the vessel. The wave was centered near 100 m depth and reached its peak amplitude at 1024 on June 29, when the scattering layers were displaced about 50 m upward and m downward. Smaller leading and trailing waves were also observed in the backscatter data, separated by about 10 min time. Coincident with the wave passage, a band of breaking waves was observed on the sea surface, propagating westward toward the motionless vessel. Closer inspection revealed a leading surface slick, indicative of a convex mode-2 wave, whose surface signature closely resembles a mode-1 elevation wave [Liu et al., 1998; Yang et al., 2009, 2010]. These features were easily visible to the naked eye and on the ship s radar. The radar and visual best estimates indicated an along-crest length of only 1 km. This may indicate that the wave was observed close to the source, since the crests typically spread radially downstream from the generation point. [11] The east-west (u) and vertical (w) components of the wave velocity from the hull-mounted ADCP were overlaid on the backscatter data to show the wave-induced circulation patterns with respect to the wave amplitude as indicated by the backscatter signal (Figure 6). To construct this plot it was first necessary to extract the wave signal from the total velocity as observed by the ADCP. This can be a difficult task, but given the short times series and dynamic local environment, filtering was deemed the best method as opposed to beamwise removal or modal regression [Mirshak and Kelly, 2009]. The background flow was determined by horizontally averaging a section of the undisturbed velocity ahead of the wave for each bin depth. The wave-induced circulation patterns shown in the plot are the result of subtracting this averaged background flow (Figure 6b, inset) from the total velocity as observed by the ADCP. This procedure revealed circulation cells in the main wave that were an excellent match for a convex mode-2 wave [Yang et al., 2010, Figure 6]. The horizontal velocities (Figure 6a) were westward in the wave core (the direction of wave propagation) at over 90 cm s 1, and eastward at over 40 cm s 1 above and below. The vertical velocities (Figure 6b) exceeded 10 cm s 1 and were upward (downward) ahead of the wave in the upper (lower) portion of the mode-2 structure. The two velocity components were consistent since the vertical velocity zero crossing was aligned with the horizontal velocity maximum. The horizontal velocities produced a surface current divergence ahead of the wave core and a convergence behind [Hsu and Liu, 2000] 4of11

5 Figure 4. The UCTD sections along the transect indicated by the black line in Figure 1. The view is toward the north with east on the right and west on the left. The sections were occupied continuously from June 29, 2010 at 2124 to June 30, 2010 at 1014, with each transect taking about 4 h to complete. The direction of ship travel is indicated by the arrow on the salinity plot. The 18 C isotherm is boldfaced in the temperature plots. which were consistent with the observed positions of the smooth and rough water on the sea surface respectively. [12] One of the smaller leading waves in the backscatter signal reached its maximum amplitude at 1002 on June 29 and displaced the scattering layers about 20 m upward and 50 m downward. This wave had a weaker velocity signal than the main wave but also resembled a mode-2 structure. There was a westward core exceeding 30 cm s 1 near 100 m depth with weaker eastward velocities above and below. The associated vertical velocities were order 6 cm s 1 just ahead of the wave, upward above 90 m depth and downward below. The observed surface velocities were weakly divergent ahead of the wave and convergent behind it but did not produce any visible surface signatures. The small trailing waves occurring after 1030 in the backscatter signal did not produce any discernable velocity signatures in the ADCP data. [13] The velocity patterns observed by the ADCP appeared to be lagged about two to three minutes behind the backscatter data. This is within the 5-min sampling window of the ADCP, but might also be due to the highly sheared background flow, and/or beam spreading in the ship s 150 khz hull-mounted ADCP. The heaving of the background flow by the wave induces velocity fluctuations on time scales comparable to the wave itself that are difficult to remove [Mirshak and Kelly, 2009]. Correcting for beam spreading [Scotti et al., 2005; Chang et al., 2011] would be difficult with only one realization and has not been attempted for a mode-2 wave. 4. Discussion [14] In this section, the generation and fate of the wave is examined, along with the issue of why only a mode-2 wave was observed, when much larger mode-1 waves dominate all the other known SCS generation sites. The primary possibilities for generation are a) that it evolved from a locally generated lee wave, or b) that it was generated in the vicinity of the eastern ridge and propagated to the western ridge as a steepening nonlinear internal tide which eventually spawned highfrequency nonlinear internal waves. While the latter possibility cannot be ruled out by the existing data, remote generation of the observed mode-2 wave seems unlikely. Observations and theory suggest that the distance between the two ridges along 21.6 N is insufficient to allow NLIWs to form by 121 E via nonlinear steepening [Farmer et al., 2009]. Furthermore, the bottom slope of the eastern ridge is gentler than the western ridge and not conducive to higher-mode wave generation [Vlasenko et al., 2010]. The mode-2 waves observed farther west on the Chinese continental slope during previous studies were found to be quite transient, and did not propagate large distances like the mode-1 waves do [Yang et al., 2004, 2010]. The ephemeral nature of mode-2 waves was also observed on 5 of 11

6 Figure 5. Depth versus time plots of (a) temperature, (b) salinity, (c) u-current component, and (d) v-current component at the anchor station indicated by the white square in Figure 1 and the heavy black line in Figure 2. The bottom depth varied from 518 m to 591 m and the data have been plotted to the deepest common depth. Scales are indicated by the color bars on the right. The 18 C isotherm is boldfaced in the temperature plot. the continental shelf off New Jersey [Shroyer et al., 2010]. This discussion will therefore focus on a complete local analysis of the lee-wave possibility. [15] Lee waves form on the ebb tide, trapped behind the generating topographic feature until they are released to propagate downstream when the tide turns to flood. Three useful parameters to discern the possibility of lee waves are the tidal excursion parameter s, the topographic steepness parameter ɛ, and the internal Froude number F. The excursion parameter s ¼ U0 kb =w ð1þ where U0 is the velocity scale, kb = 1/Lb is the scale of the bottom topography, and w is the operative frequency 6 of 11

7 Figure 6. (a) Zonal and (b) vertical velocity data from the ship s ADCP overlain on the 120 khz backscatter data (db) from the EK500 echo sounder. Black contours are westward (down) and white eastward (up) for the zonal and vertical velocity components (cm s 1) respectively. The solid magenta line at 1024 indicates the time of maximum wave amplitude as indicated by the backscatter data, while the dashed line at 1027 indicates the wave core position as indicated by the horizontal velocity maxima and the zero crossing of the vertical velocity component. To emphasize the wave in the backscatter and velocity data, both data sets were processed as described in the text. The insert shows the background current profile that was removed from the u (solid line) and w (dashed line) data. (diurnal or semidiurnal), determines if there is sufficient tidal advection to transport a wave off the top of the ridge [Vlasenko et al., 2005; Garrett and Kunze, 2007; Zhang et al., 2011]. The excursion parameter needs to be significantly greater than one for lee waves to occur, while smaller values less than one favor tidal beams. The local topography at the observation site consisted of a smaller ridge with a relief of order 400 m and length scale 15 km sitting atop the much larger main ridge. The excursion parameter for the smaller ridge using U0 order 100 cm s 1 (Figure 5) and the semidiurnal tidal frequency was order 3 at the study site, which favors lee wave formation rather than tidal beams [Garrett and Kunze, 2007; Klymak et al., 2010; Zhang et al., 2011]. Note this is a significant departure from the Batan/ Itbayat sill, which at 30 km wide, has a tidal excursion parameter of order 0.4, which favors tidal beams. [16] The steepness parameter ɛ [Garrett and Kunze, 2007; Legg and Klymak, 2008; Klymak et al., 2010], is defined as the ratio of the bottom slope to the slope of the internal wave rays (a). The parameter a is calculated using the wellknown expression: 7 of 11 a¼ w2 f 2 N 2 w2 1=2 ð2þ

8 where f is the Coriolis parameter, N is the buoyancy frequency, and w is the internal wave frequency. The portion of the water column between 600 and 1000 m where the stratification intersects the bottom topography was not well sampled during 2010 but was very well sampled during A time series of 12 CTD casts to the bottom were collected during August 2011 near N, E, on the same transect as For the depth range m, the mean value of N 2 was nearly the same in both years, s 2 in 2010 and s 2 in For 2011 the mean value of N 2 in the deep water was s 2 with little temporal variation. Using this value of N 2 and f = s 1, the calculated ray slope was for the M2 tidal frequency and for the K1. Together with the bottom slope of 0.04 (Figure 2), this gives a slope parameter order 1.4 or greater, meaning that the topography was supercritical to both tides. Supercritical bottom slopes are consistent with turbulent lee wave formation [Klymak et al., 2010] and scattering of internal wave energy into higher modes [Buijsman et al., 2010b; Vlasenko et al., 2010]. [17] The Froude number, given by the ratio of the flow speed to the free wave speed, estimates the hydraulic control of a flow. For a multilayer system, the composite Froude number can be calculated as G 2 ¼ Xn Fi 2 i¼1 where n defines the number of layers being considered, and F 2 i ¼ u2 i c 2 i where u i and c i are the velocity and free wave speed in each layer. For quasi-steady flows with well-defined layers, the free wave speeds may be calculated as c 2 i ¼ g h i where g is the reduced gravity determined by the density ratios between layers and h i is the thickness of each layer. This approach was used to determine the critical conditions in the Straits of Gibraltar for the two-layer case [Farmer and Armi, 1988; Armi and Farmer, 1988] and the three-layer case [Sannino et al., 2002, 2007]. The concept can be extended by writing F 2 ni ¼ u2 i c 2 n where F n is now the Froude number for each internal mode n. Each F ni now becomes an expression of the critical flow condition with respect to each mode in each layer. The mode speeds were computed for each CTD profile as a solution to the Sturm-Liouville equation governing the vertical motions in a non-rotating, hydrostatic, zero-shear fluid with wave frequency much higher than the inertial frequency [Apel et al., 1985; Apel et al., 1997; Alford et al., 2010]. d 2 W n dz 2 þ N 2 ðzþ c 2 W n ¼ 0 n ð3þ ð4þ ð5þ ð6þ ð7þ Subject to the boundary conditions W n ð0þ ¼ W n ð HÞ ¼ 0 ð8þ where the subscript n indicates the mode number. The mode speeds were compared against the mean velocities in each layer, computed by vertically averaging each LADCP profile over depth ranges chosen to match the modal amplitude zero crossings. The layers used were m and 200 m bottom for mode-1; and 0 75 m, m, and 300 m bottom for mode-2. [18] The resulting time series of the composite Froude number (3) show that the flow across this portion of the Heng-Chun Ridge was generally subcritical to both modes except during the peak ebb tide at the end of the record when the flow was supercritical with respect to mode-2 but not mode-1 (Figure 7). The results for the two-layer case (Figures 7a and 7b) were similar to the three-layer case (Figures 7c and 7d). Both scenarios show supercritical flow for mode-2 after 0600, with most of the contribution coming from the strong currents in the bottom layer. This corresponds to the time when the mode-2 NLIW was observed, propagating westward in the middle layer. [19] The three-layer calculation was also carried out using the density ratio method [Sannino et al., 2002] to compute the free-wave speed in each layer. The results were very similar to Figure 7c, not surprisingly since the weighted sum of the three free wave speeds was 1.7 cm s 1, versus 1.6 cm s 1 for the mode-1 calculation averaged over all 34 profiles. The density ratios also allow estimation of whether mode-1 or mode-2 is supercritical. Since the interface perturbations are of like sign for a mode-1 wave and opposite sign for a mode-2 wave, then and 2 2 F 1 þ F2 > ð r2 r 1 Þ= ðr 3 r 1 Þ ð9þ 2 2 F 2 þ F3 > ð r3 r 2 Þ= ðr 3 r 1 Þ ð10þ if the first mode is critical and the opposite if the second mode is critical [Lane-Serff et al., 2000; Sannino et al., 2007]. For the Heng-Chun site, F 1 2 +F 2 2 was order 0.1 and the density ratio was order for the top two layers; and F 2 2 +F 3 2 was order and the density ratio was order 0.4 for the lower layers. These values all indicate that the second mode was critical but not the first. [20] The results above suggest a likely source for the observed wave. If the wave was released when the tide turned at 0820, was observed at the ship at 1024, and propagated at the mean mode-2 free wave speed (equation (7)) of 0.84 m s 1, then the wave would have originated about 6 km to the east of the sill over the steepest part of the sloping topography (Figure 2). This is entirely consistent with a locally generated wave. The ship steamed westward after the wave passed by, but no surface slicks, breaking waves, or wave-like backscatter signals were observed. It seems that the wave was generated locally, was very strong for a short while, but was quickly mixed away. This may be due to the very strong northeastward background current at 100 m depth (Figure 5c), which opposed the westward velocity in the wave core. A strong velocity front resulted at the head of the wave (Figure 6) suggesting that the wave may already have been ready to break as it passed beneath the vessel. The 38 khz 8of11

9 Figure 7. Time series of the internal Froude number for a (a, b) two-layer and (c, d) three-layer system. The lines represent the composite (solid), lower layer (dotted), upper layer (dashed), and middle layer (dot-dashed, Figures 7c and 7d only) results. The critical value (1) is highlighted by the bold horizontal line. backscatter data (not shown) indicated extensive mixing and turbulence along the transect, possibly due to breaking internal waves. This realization of the mode-2 wave appears not to have traveled very far; however both the strength of the tidal currents and the position of the Kuroshio [Centurioni et al., 2004; Liang et al., 2008] are highly variable with time. The known barotropic tidal pattern (Figure 3) suggests that the generation conditions will likely be met 6 8 times per fortnight. It is possible that other mode-2 waves could escape the ridge when the background flow is weaker or supportive. It is also possible that mode-1 waves could appear during times when the prevailing tidal currents are stronger. 5. Summary and Conclusions [21] A zonal channel on the northern Heng-Chun Ridge (sill depth 580 m) was investigated as a potential site for highly nonlinear internal wave generation. The observations consisted of two parts: A 21-h anchor station using a CTD with lowered ADCP (LADCP) was conducted near the top of the sill, followed by three rapid transects across the sill sampled using an underway CTD (UCTD). The Kuroshio flowed northward over the eastern flank of the ridge at about 100 cm s 1. The tidal currents were mixed, diurnal dominant, with maximum observed velocities near the bottom exceeding 70 cm s 1 on flood and 140 cm s 1 on ebb. About two hours after the ebb tide turned, a well-formed mode-2 nonlinear internal wave was observed propagating westward in all the observed variables including backscatter, velocity, temperature, salinity, and surface roughness. There was a leading surface slick ahead of the wave in the divergent zone, and a band of breaking surface waves just behind the wave crest in the convergent zone. The velocity profiles were an excellent match with the expected theory for a 9of11

10 convex mode-2 wave, except that the velocity field was offset from the backscatter data by about two-three minutes. This was attributed to the 5-min sampling window of the ADCP or possibly due to an opposing (eastward) mean current near the wave core. The along-crest extent of the wave, as observed visually and on the ship s radar, was only about 1 km, much smaller than the more common mode-1 waves that have often been observed in the northeastern South China Sea. This is attributed to the restrictions imposed by the local channel width and nearness to the source. [22] The excursion parameter, steepness parameter, and Froude number all favored mode-2 lee wave generation but not mode-1, which explains the lack of a mode-1 wave. The wave timing suggests that the wave formed about 6 km east of the edge of the sill on the ebb tide, over a steep portion of the ridge slope, and was released to propagate westward when the tide turned to flood. More observations are needed to determine the variation over a spring/neap tidal cycle and the importance of this process to the overall energy budget in the South China Sea. [23] Acknowledgments. This work was funded by the U. S. Office of Naval Research (ONR) under the Internal Waves in Straits Experiment (IWISE) Departmental Research Initiative (DRI), and by the National Science Council (NSC) of Taiwan. We are grateful to the officers and crew of the Research Vessel OCEAN RESEARCHER 2 for their skillful assistance conducting the work at sea. Careful comments by three reviewers improved the quality of the manuscript. References Alford, M. H., R.-C. Lien, H. Simmons, J. Klymak, S. R. Ramp, Y.-J. Yang, T.-Y. Tang, D. Farmer, and M.-H. Chang (2010), Speed and evolution of nonlinear internal waves transiting the South China Sea, J. Phys. Oceanogr., 40, , doi: /2010jpo Apel, J. R., J. R. Holbrook, J. Tsai, and A. K. Liu (1985), The Sulu Sea internal soliton experiment, J. Phys. Oceanogr., 15, , doi: / (1985)015<1625:tssise>2.0.co;2. Apel, J. R., et al. (1997), An overview of the 1995 SWARM shallow-water internal wave acoustic scattering experiment, IEEE J. Oceanic Eng., 22, , doi: / Armi, L., and D. M. Farmer (1988), The flow of Mediterranean water through the Strait of Gibraltar, Prog. Oceanogr., 21, 1 103, doi: / (88) Buijsman, M. C., Y. Kanarska, and J. C. McWilliams (2010a), On the generation and evolution of nonlinear internal waves in the South China Sea, J. Geophys. Res., 115, C02012, doi: /2009jc Buijsman, M. C., J. C. McWilliams, and C. R. Jackson (2010b), East-west asymmetry in nonlinear internal waves from Luzon Strait, J. Geophys. Res., 115, C10057, doi: /2009jc Centurioni, L. R., P. P. Niiler, and D.-K. Lee (2004), Observations of inflow of Philippine Sea surface water into the South China Sea through the Luzon Strait, J. Phys. Oceanogr., 34, , doi: / (2004)034<0113:ooiops>2.0.co;2. Chang, M.-H., R.-C. Lien, Y. J. Yang, and T. S. Tang (2011), Nonlinear internal wave properties estimated with moored ADCP measurements, J. Atmos. Oceanic Technol., 28, , doi: /2010jtecho Chao, S.-Y., D.-S. Ko, R.-C. Lien, and P.-T. Shaw (2007), Assessing the west ridge of Luzon Strait as an internal wave mediator, J. Oceanogr., 63, , doi: /s Duda, T. F., J. F. Lynch, J. D. Irish, R. C. Beardsley, S. R. Ramp, C.-S. Chiu, T.-Y. Tang, and Y.-J. Yang (2004), Internal tide and nonlinear internal wave behavior at the continental slope in the northern South China Sea, IEEE J. Oceanic Eng., 29, , doi: / JOE Farmer, D. M., and L. Armi (1988), The flow of Atlantic water through the Strait of Gibraltar, Prog. Oceanogr., 21,1 103, doi: / (88) Farmer, D. M., and J. D. Smith (1980), Tidal interaction of stratified flow with a sill in Knight Inlet, Deep Sea Res., Part A, 27, Farmer, D., Q. Li, and J.-H. Park (2009), Internal wave observations in the South China Sea: The role of rotation and non-linearity, Atmos. Ocean, 47, , doi: /oc Foreman, M. G. G. (1978), Manual for tidal currents analysis and prediction, Pac. Mar. Sci. Rep., 78-6, 57 pp., Inst. of Ocean Sci., Sidney, B. C., Canada. Garcia, D. (2010), Robust smoothing of gridded data in one and higher dimensions with missing values, Comput. Stat. Data Anal., 54, , doi: /j.csda Garrett, C., and E. Kunze (2007), Internal tide generation in the deep ocean, Annu. Rev. Fluid Mech., 39, 57 87, doi: /annurev.fluid Hsu, M. K., and A. K. Liu (2000), Nonlinear internal waves in the South China Sea, Can. J. Remote Sens., 26, Jan, S., R.-C. Lien, and C.-H. Ting (2008), Numerical study of baroclinic tides in the Luzon Strait, J. Oceanogr., 64, , doi: / s Klymak, J. M., S. Legg, and R. Pinkel (2010), A simple parameterization of turbulent tidal mixing near supercritical topography, J. Phys. Oceanogr., 40, , doi: /2010jpo Lane-Serff, G. F., D. A. Smeed, and C. R. Postlethwaite (2000), Multi-layer hydraulic exchange flows, J. Fluid Mech., 416, , doi: / S Legg, S., and J. M. Klymak (2008), Internal hydraulic jumps and overturning generated by tidal flow over a tall steep ridge, J. Phys. Oceanogr., 38, , doi: /2008jpo Liang, W.-D., Y. J. Yang, T.-Y. Tang, and W.-S. Chuang (2008), Kuroshio in the Luzon Strait, J. Geophys. Res., 113, C08048, doi: / 2007JC Liu, A. K., Y. S. Chang, M.-K. Hsu, and N. K. Liang (1998), Evolution of nonlinear internal waves in the East and South China Seas, J. Geophys. Res., 103, , doi: /97jc Liu, A. K., S. R. Ramp, Y. Zhao, and T.-Y. Tang (2004), A case study of internal wave propagation during ASIAEX-2001, IEEE J. Oceanic Eng., 29, , doi: /joe Maxworthy, T. (1979), A note on the internal solitary waves produced by tidal flow over a three-dimensional ridge, J. Geophys. Res., 84, , doi: /jc084ic01p Mirshak, R., and D. E. Kelly (2009), Inferring propagation direction of nonlinear internal waves in a vertically sheared background flow, J. Atmos. Oceanic Technol., 26, , doi: /2008jtecho Niwa, Y., and T. Hibiya (2004), Three-dimensional numerical simulation of the M2 internal tides generated around the continental shelf edge in the East China Sea, J. Geophys. Res., 109, C04027, doi: / 2003JC Ramp, S. R., C. S. Chiu, H.-R. Kim, F. L. Bahr, T.-Y. Tang, Y. J. Yang, T. Duda, and A. K. Liu (2004), Solitons in the northeastern South China Sea part I: Sources and propagation through deep water, IEEE J. Oceanic Eng., 29, , doi: /joe Ramp, S. R., Y. J. Yang, and F. L. Bahr (2010), Characterizing the nonlinear internal wave climate in the northeastern South China Sea, Nonlinear Processes Geophys., 17, , doi: /npg Rudnick, D. L., and J. Klinke (2007), The underway conductivitytemperature-depth instrument, J. Atmos. Oceanic Technol., 24, , doi: /jtech Sannino, G., A. Bargagli, and V. Artale (2002), Numerical modeling of the mean exchange through the Strait of Gibraltar, J. Geophys. Res., 107(C8), 3094, doi: /2001jc Sannino, G., A. Carillo, and V. Artale (2007), Three-layer view of transports and hydraulics in the Strait of Gibraltar: A three-dimensional model study, J. Geophys. Res., 112, C03010, doi: /2006jc Scotti, A., R. Butman, R. C. Beardsley, P. S. Alexander, and S. Anderson (2005), A modified beam-to-earth transformation to measure shortwavelength internal waves with an acoustic Doppler current profiler, J. Atmos. Oceanic Technol., 22, , doi: /jtech Shroyer, E. L., J. N. Moum, and J. D. Nash (2010), Mode 2 waves on the continental shelf: Ephemeral components of the nonlinear internal wavefield, J. Geophys. Res., 115, C07001, doi: /2009jc Thurnherr, A. M. (2010), A practical assessment of the errors associated with full-depth LADCP profiles obtained using Teledyne RDI Workhorse acoustic Doppler current profilers, J. Atmos. Oceanic Technol., 27, , doi: /2010jtecho Visbeck, M. (2002), Deep velocity profiling using lowered acoustic Doppler current profilers: Bottom track and inverse solutions, J. Atmos. Oceanic Technol., 19, , doi: / (2002)019<0794: DVPULA>2.0.CO;2. Vlasenko, V., N. Stashchuk, and K. Hutter (2005), Baroclinic Tides, Theoretical Modeling and Observational Evidence, 351 pp., Cambridge Univ. Press, New York. Vlasenko, V., N. Stashchuk, C. Guo, and X. Chen (2010), Multimodal structure of baroclinic tides in the South China Sea, Nonlinear Processes Geophys., 17, , doi: /npg of 11

11 Yang, Y.-J., T. Y. Tang, M. H. Chang, A. K. Liu, M.-K. Hsu, and S. R. Ramp (2004), Solitons northeast of Tung-Sha Island during the ASIEAX pilot studies, IEEE J. Oceanic Eng., 29, , doi: / JOE Yang, Y. J., Y. C. Fang, M.-H. Chang, S. R. Ramp, C.-C. Kao, and T.-Y. Tang (2009), Observations of second baroclinic mode internal solitary waves on the continental slope of the northern South China Sea, J. Geophys. Res., 114, C10003, doi: /2009jc Yang, Y. J., Y. C. Fang, Y.-T. Chang, T. Y. Tang, and S. R. Ramp (2010), Convex and concave types of second baroclinic mode internal solitary waves, Nonlinear Processes Geophys., 17, , doi: /npg Zhang, Z., O. B. Fringer, and S. R. Ramp (2011), Three-dimensional, nonhydrostatic numerical simulation of nonlinear internal wave generation and propagation in the South China Sea, J. Geophys. Res., 116, C05022, doi: /2010jc F. L. Bahr, Monterey Bay Aquarium Research Institute, Moss Landing, CA 95039, USA. S. R. Ramp, Soliton Ocean Services, Inc., Carmel Valley, CA 93924, USA. D. B. Reeder, Department of Oceanography, Naval Postgraduate School, Monterey, CA 93943, USA. Y. J. Yang, Department of Marine Science, Naval Academy, Kaohsiung 813, Taiwan. 11 of 11