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CITATION Farmer, D.M., M.H. Alford, R.-C. Lien, Y.J. Yang, M.-H. Chang, and Q. Li. 2011. From Luzon Strait to Dongsha Plateau: Stages in the life of an internal wave. Oceanography 24(4):64–77, http:// dx.doi.org/10.5670/oceanog.2011.95.
DOI http://dx.doi.org/10.5670/oceanog.2011.95
COPYRIGHT This article has been published inOceanography , Volume 24, Number 4, a quarterly journal of The Oceanography Society. Copyright 2011 by The Oceanography Society. All rights reserved.
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From Luzon Strait to Dongsha Plateau Stages in the Life of an Internal Wave
By David M. Farmer, Matthew H. Alford, Ren-Chieh Lien, Yiing Jiang Yang, Ming-Huei Chang, and Qiang Li
A rainbow and tropical clouds over the aft deck of R/V Revelle during the 2010 IWISE (Internal Waves in Straits Experiment) pilot cruise. The yellow steel sphere in the foreground provided flotation for one of the moorings discussed in the text.
64 Oceanography | Vol.24, No.4 Abstract. Tidal currents in Luzon Strait south of Taiwan generate some of the prey that can impact the biological envi- largest internal waves anywhere in the ocean. Recent collaborative efforts between ronment, have motivated intense study. oceanographers from the United States and Taiwan explored the generation, Moreover, their inherent nonlinearity evolution, and characteristics of these waves from their formation in the strait to presents a fascinating scientific challenge their scattering and dissipation on Dongsha Plateau and the continental slope of to those seeking to explain and predict mainland China. Nonlinear internal waves affect offshore engineering, navigation, their properties and behavior. biological productivity, and sediment resuspension. Observations within Luzon Although various mechanisms can Strait identified exceptionally large vertical excursions of density (as expressed generate nonlinear internal waves, the primarily in temperature profiles) and intense turbulence as tidal currents interact primary source is typically strong tidal with submarine ridges. In the northern part of the strait, the ridge spacing is close to currents leading to dynamic interaction the internal semidiurnal tidal wavelength, allowing wave generation at both ridges between stratified water and topographic to contribute to amplification of the internal tide. Westward radiation of semidiurnal features, such as submarine ridges internal tidal energy is predominant in the north, diurnal energy in the south. The and the continental slope. They are, competing effects of nonlinearity, which tends to steepen the stratification, and therefore, most common near abrupt or rotational dispersion, which tends to disperse energy into inertial waves, transform irregular topography in coastal waters. waves traveling across the deep basin of the South China Sea. Rotation inhibits The internal waves generated just south steepening, especially for the internal diurnal tide, but despite the rotational effect, of Taiwan in Luzon Strait are among the the semidiurnal tide steepens sufficiently so that nonhydrostatic effects become largest observed anywhere in the ocean important, leading to the formation of a nonlinear internal wave train. As the waves and can often be tracked by remote encounter the continental slope and Dongsha Plateau, they slow down, steepen sensing as they cross the deep basin further, and are modified and scattered into extended wave trains. At this stage, the of the South China Sea. The remotely waves can “break,” forming trapped cores. They have the potential to trap prey, which sensed patterns are associated with may account for their attraction to pilot whales, which are often seen following the short-period nonlinear internal waves. waves as they advance toward the coast. Interesting problems remain to be explored These waves do not form in the deep and are the subjects of continuing investigations. basin on all tides, but invariably occur as the internal tide starts to interact with Introduction which tends to spread it out, so that the the continental shelf of mainland China With the increasing extent and quality waves retain their distinctive shape as where they slow down, can form trapped of remotely sensed images of the ocean, they travel (see also Box 1). Individual cores, and scatter and decay. A collabora- the widespread occurrence of patterns waves can exist in isolation, and thus tion of many scientists supported by the caused by nonlinear internal waves (also are described as internal solitary waves, Physical Oceanography Program of the called internal solitary waves) in coastal internal solitons, or just “solitons.” They US Office of Naval Research, together waters becomes ever more apparent. The form some of the most striking features with prominent scientific and logistical nonlinearity in this case is expressed in of the ocean surface, modulating surface backing from Taiwan, is currently the progressive distortion of the shape roughness to produce great arcs that, focusing efforts on understanding the of the internal tide, with consequent in extreme cases, can stretch hundreds origin, evolution, physical behavior, and steepening of density surfaces to the of kilometers while typically retaining biological effects of these waves. Here, point where nonhydrostatic dispersion, a width of ~ 5 km or less. The waters we provide an overview of some of the associated with vertical acceleration of around Taiwan generate prominent results and draw attention to outstanding the fluid, becomes important, and short- examples of these waves. Their impor- features that await further investigation. period waves are formed. Once formed, tance to navigation, offshore engi- Our focus is on recent measurements these waves approximate a balance neering, underwater acoustical propaga- in Luzon Strait (an energetic source of between the nonlinearity, which tends to tion, and sediment suspension, as well as internal tides; Alford et al., 2011), obser- concentrate the energy, and dispersion, the mixing, stirring, and aggregation of vations, and simplified analysis of the
Oceanography | December 2011 65 Box 1. Nonlinear Fluid Dynamical Behavior waves’ transformation as they propagate westward, including formation of short- Nonlinearity in this article refers to nonlinear fluid dynamical behavior. period nonlinear internal waves in the Nonlinear terms are present in the equations of motion of fluid dynamics. deep basin (Li and Farmer, 2011), their For example, terms may be of the form “velocity, or vertical displacement interaction with the shoaling seafloor of a density interface, multiplied by a gradient of the same property.” and with Dongsha Island (Lien, 2005), Although these terms are always present, for some problems they can and evidence of biological interactions. be neglected. However, they can also be important, even dominant, in While the generation, propagation, and certain situations, and this is true for internal waves that are steep; for a fate of the waves has attracted much given wave length, nonlinearity increases with amplitude. Nonlinear waves study in recent years, our selective focus exhibit many characteristics that distinguish them from the linear wave on these features provides three diverse approximation. For example, the slope of the wave can change with time views of the waves from their origin in (i.e., gets steeper or less steep depending on whether the slope is positive Luzon Strait to their interaction with the or negative and depending on water depth and density stratification). One Dongsha Plateau. consequence of this behavior is that an initially sinusoidal wave can evolve into a sawtooth wave. When the wave becomes sufficiently steep, vertical Tidal Interaction and acceleration becomes important, and the resulting vertical motions lead Turbulence in Luzon Strait to the formation of higher-frequency waves (a process referred to as The internal waves radiating westward nonhydrostatic dispersion). Thus, a consequence of nonlinearity is that across the deep basin of the northern the shape of the internal tide can change as the interface between less- South China Sea have their origin dense water near the surface and denser water at depth becomes distorted, in Luzon Strait, south of Taiwan. eventually forming internal waves that exhibit a much shorter period than Surprisingly, there is little evidence in that of the internal tide from which they evolved. Thus, the nonlinearity, remotely sensed images, either in the combined with nonhydrostatic dispersion, creates the short-period waves Pacific to the east or within Luzon Strait we see in the deep basin of the South China Sea. itself, of the narrow elongated surface That’s one part of the wave evolution problem. Another part is that features so clearly seen in remotely Earth’s rotation disperses energy from the steepening internal tide into sensed images of the deep basin further motions initially transverse to the wave propagation (rotational disper- west (Figure 1). The sharp western sion) to form “inertial waves.” There is a competition between the boundary of the northward-flowing nonlinearity that steepens the internal tide and the rotation that extracts Kuroshio is a prominent feature of energy from the internal tide. The rotational dispersion is greater for the the strait that occasionally intrudes diurnal tide because its period (24 h) is closer to the inertial period (33 h) in a great loop into the South China than is true for the semidiurnal tide. Sea, but more often skirts Luzon Strait between the two submarine ridges (Rudnick et al., 2011, in this issue). The Kuroshio, although likely influencing their generation, changes its shape on a scale of weeks to months and is unlikely to be the direct source of the waves we observe. In contrast, the barotropic tidal currents, primarily running east-west, force the thermally stratified waters of the strait across a complex topography characterized by two ridges, Heng-Chun to the west and Lan-Yu to the east. The
66 Oceanography | Vol.24, No.4 western ridge is shallower to the north, 23°N and the eastern ridge is shallower to the south and punctuated by islands; the two ridges are closer to each other in the 22°N south. It is one of the intriguing conse- quences of nonlinear evolution of the 21°N A3 internal tides that the highly irregular A2 MPN and complex topography of Luzon N2 Strait can lead to the smoothly shaped A1 coherent features characteristic of 20°N remotely sensed images in the far field. S2 A major challenge to those seeking 19°N to model the generation and evolution a of these internal waves is the wide range of scales involved. The topography of 18°N Luzon Strait is rugged and complex, and 0 the depth of the South China Sea varies 1000 SCS from ~ 4,000 m in the deep basin to 2000
Depth (m) 3000 HCR LYR 100–300 m on the Dongsha Plateau and b 115°E 116°E6°E 117°E117°E 118°E 119°E 120°E 121°E 122°E the continental shelf of mainland China. Figure 1. (a) Chart of South China Sea superimposed on a MODIS remotely sensed image Moreover, nonlinearity transforms the illustrating the surface signature of nonlinear internal waves and measurement locations. internal tides with scales of 100–200 km Red lines: 2010 observations of Luzon Strait. A1, A2, and A3 show 2007 PIES (pressure-sensor into trains of large-amplitude, steep equipped inverted echosounders) deployments. Yellow rectangle: ship-based observations of shoaling internal waves. (b) Bathymetry along 21°N. SCS = South China Sea. HCR = Heng- internal waves. A comprehensive Chun Ridge. LYR = Lan-Yu Ridge. model must be three dimensional and nonhydrostatic, with sufficient resolution to handle the nonlinear transforma- occurs over the eastern ridge and that (which occur as nonlinear internal tion. Zhang et al. (2011) show that such the variable ridge orientation from north wave packets in the deep basin) and modeling is now becoming possible. to south preferentially radiates waves B-waves (which initially evolve as single Their model results lead to some impor- in different directions into the South large-amplitude waves), and show that tant insights, confirming, for example, China Sea. They distinguish between A-waves are preferentially radiated from that the primary internal tide generation the generation of so-called A-waves the southern part of Luzon Strait, where diurnal internal tidal beams augment the David M. Farmer ([email protected]) is Professor Emeritus, The Graduate School of semidiurnal wave, and propagate into Oceanography, University of Rhode Island, Narragansett, RI, USA. Matthew H. Alford is the northern portion of the South China Senior Oceanographer and Associate Professor, Applied Physics Laboratory, University of Sea basin, whereas B-waves, which are Washington, Seattle, WA, USA. Ren-Chieh Lien is Principal Oceanographer and Affiliate reinforced by the ridge spacing and Professor, Applied Physics Laboratory, University of Washington, Seattle, WA, USA. slopes, are preferentially radiated into Yiing Jiang Yang is Associate Professor, Department of Marine Science, Naval Academy, the southern portion. Reconciliation of Tsoying, Kaohsiung, Taiwan. Ming-Huei Chang is Assistant Professor, Department such comprehensive model calculations of Marine Environmental Informatics, National Taiwan Ocean University, Keelung, with the finely resolved measurements Taiwan. Qiang Li was a PhD candidate at the Graduate School of Oceanography, in Luzon Strait discussed below—as University of Rhode Island, Narragansett, RI, USA, and is currently Assistant Professor, well as more recent observations— Center for Ocean Science and Technology, Graduate School at Shenzhen, Tsinghua remains a task for the future. However, University, Shenzhen, China. given the hydrodynamics of a complex
Oceanography | December 2011 67 environment such as the South China these inversions is related to the outer shows an example at two sample stations Sea, simplified models can also prove scale of turbulence. By sorting them as (N2 and S6) on the eastern flank of the helpful, and in a subsequent section we described by Thorpe (1977), it is possible western ridge with velocity, represented include results from a simplified two- to estimate the turbulent kinetic energy by color (left two panels) and dissipa- layer model that help explain some of dissipation rate. This approach provides tion rate (right panel). Each station the observed features. results consistent with direct micro- was occupied twice: once at a time of A diverse array of measurements structure measurements (Dillon, 1982; predominantly semidiurnal forcing (first and third rows) and once when diurnal signals were dominant (second and fourth rows). Density contours in each With the increasing extent and quality panel show the vertical displacement of isopycnals, which can reach 500 m of remotely sensed images of the ocean, the close to the steep face of the western widespread occurrence of patterns caused ridge at the northern station. The “ by nonlinear internal waves (also called measurements are generally consistent internal solitary waves) in coastal waters with the expected ebb and flood of the tides, with large turbulence dissipa- becomes ever more apparent. tions observed each 12 and 24 hours, respectively. Superimposed on these energetic tidal currents, the northward flow of the Kuroshio appears as a red acquired in a short but intensive obser- Alford et al., 2006) and is especially patch in the upper 500 m, especially vational program during the summer of appropriate” for rapid estimates over noticeable during both occupations of 2010 have already revealed important the full water column in this intensely the northern station. features of tidal interaction with the turbulent environment. (Although these As expected for this region of intense topography in Luzon Strait (Alford et al., comparisons were carried out for smaller tidal interaction with topography, the 2011). The goal was to acquire prelimi- overturns than presented here [overturns magnitude of the baroclinic velocity nary observations of the internal tide in occur when dense water moves up and is ~ 1 m s–1 peak-to-peak, the vertical the strait so as to estimate energy and over less-dense water, a process that displacement of isopycnals in the energy fluxes of the semidiurnal and takes energy and leads to some degree of weakly stratified water below 1,000 m is diurnal components, as well as the rate mixing], the relationships appear to hold 200–500 m, and dissipation rates are up of turbulent kinetic energy dissipation. for these large overturns, as indicated to 10–5 W kg–1, much stronger than open- Observations were made along two lines by preliminary comparisons with simul- ocean conditions. Dissipation rates are shown in Figure 1 and included repeated taneous temperature microstructure greatest at N2 and are some of the largest conductivity-temperature-depth (CTD) measurements. Detailed comparisons are observed, implying vertical diffusivity and acoustic Doppler current profiler the topic of ongoing work.) exceeding 10–1 m2 s–1, over 10,000 times (ADCP) measurements that yielded Repeated profiling at each loca- that of typical open ocean values (Gregg, profiles of temperature, salinity, density, tion for 36 hours can reliably separate 1989) and a thousand times that of and current velocity over almost the semidiurnal and diurnal signals. These Munk’s (1966) 1D global estimate. entire water column at approximately measurements are important in Luzon The spatial pattern of dissipation can hourly intervals. Strait, where both semidiurnal and be seen from profiles along the northern Numerous inversions in the measured diurnal tides are significant and the and southern lines (Figure 3). Left and density profiles are interpreted as regions timing of astronomical forcing leads to right panels refer to semidiurnal and where turbulence has swept dense periods where one or the other tide is diurnal energy and energy flux signals water upward, and the vertical scale of dominant (see Figures 2 and 4). Figure 2 (light and dark gray, respectively),
68 Oceanography | Vol.24, No.4 discussed below. Each panel shows Buijsman, Geophysical Fluid Dynamics Buijsman et al. (2010a) have explored profiles of the logarithm of total dissipa- Laboratory, Princeton University, pers. the resonance that can occur in such tion rate (not separated by frequency) comm., 2011) match the magnitude and environments. Resonance encompasses with a yellow/green color map. phase of the observed velocity, isopycnal a broad range of processes, but for our Dissipation increases toward the bottom displacement, and dissipation signals purposes here, we loosely define it as at all stations, where the internal tide and quite well at some locations such as N2, wave generation between the two ridges topography can be expected to interact pointing to the role of internal hydraulic leading to reinforcement of the signal. most strongly. In spite of observational processes and wave breaking on the Returning to Figure 3, the potential limitations, the northern ridge appears steep western ridge. Ridge separation in for resonance of the northern and more dissipative. northern Luzon Strait is comparable to southern lines is seen by overplotting Preliminary two-dimensional the semidiurnal internal tide wavelength. internal-wave characteristics (lines numerical simulations (Maarten Echeverri and Peacock (2010), and with slopes corresponding to the angle
Eastward Velocity Northward Velocity Dissipation Rate 0
500
100 N2a
Depth (m) 1500
239.5 240.0 239.5 240.0 239.5 240.0 0
500
100 N2b
Depth (m) 1500
245.5 246.0 245.5 246.0 245.5 246.0 0
500
100 S6a Depth (m) 1500
232.5 233.0 233.5 232.5 233.0 233.5 232.5 233.0 233.5 0
500
100 S6b Depth (m) 1500
251.0 251.5 252.0 251.0 251.5 252.0 251.0 251.5 252.0 YeardayYeardayYearday
–1 –1 m s log10 (ε/W kg )
–1.0 –0.5 0.0 0.5 1.0 –10 –9 –8 –7 –6 –5 Figure 2. Top row: Time series of eastward (left) and northward (middle) velocity, and Thorpe-inferred turbulent dissi- pation rate (right) for station N2a. The superimposed density contours (black lines) are evenly spaced in the resting depth of each isopycnal. Lower three rows: same for stations N2b, S6a, and S6b, respectively.
Oceanography | December 2011 69 at which internal waves travel as they baroclinic energy assists in identifica- panels of Figure 3 by plotting profiles propagate upward or downward from tion of radiation from the two ridges of energy flux (dark gray) and energy their sources). The slope depends on and their interference with one another. (light gray) at each station. Semidiurnal stratification and frequency, which is It is calculated from the correlation and diurnal signals are shown at left why the curves have greater slope at between baroclinic velocity u and baro- and right, respectively. greater depth. Likewise, the semidiurnal clinic pressure p (i.e.,
0 N1 LS01 N2 LS02 MPN LS03 A1 X1 NSE N1 LS01 N2 LS02 MPN LS03 A1 X1 NSE −500 Northern Line Northern Line −1000 D1 D2 −1500 −2000
Depth (m) –2 −2500 Energy: 100 Jm log ε (W kg–1) –9 10 –5.5 −3000 Flux: 100 Wm–2 −3500 –2 C (W m–2) 2
0 MPS S7 S6 S8 S4 S5 MPS S7 S6 S8 S4 S5 −500 Southern Line Southern Line −1000 D1 D2 −1500 −2000
Depth (m) −2500 −3000 −3500 0 20 40 60 80 100 120 140 160 0 20 40 60 80 100 120 140 160 Distance (km) Distance (km)
Figure 3. Bathymetry and measured energy flux (dark gray), energy (light gray), and dissipation (colors) for each constituent along each line. Cross sections of model bathymetry (gray shading) and conversion (red/blue) are plotted along the northern line (top panels) and the southern line (bottom), plotted versus distance from the western end of each line (see Figure 1). Left and right panels are for diurnal and semidiurnal components, respectively. Characteristics (see text) computed from the measured stratification are indicated in each panel. At each station, along-line synoptic energy flux profiles are plotted in dark gray, with energy plotted as lighter gray, increasing to the right. Reference bars are given in the upper left panel. Time-mean dissipation rate for each station is plotted in green/yellow at each location (color scale at upper right). Conversion is provided courtesy of Harper Simmons, University of Alaska.
70 Oceanography | Vol.24, No.4 one of the strongest energy flux values speed is less than the first mode internal signatures in the South China Sea are observed anywhere in the world ocean. wave speed). Zhang et al.’s (2011) consistent with this interpretation has This energy flux is concentrated in the calculations, and their analysis using been amply demonstrated by observa- density-stratified water within the upper a simplified model of the first internal tions. Short-period nonlinear internal 500 m and corresponds to the internal mode response, support the notion that waves always occur as the internal tide tide that is radiated into the deep basin internal hydraulic and also lee wave interacts with the continental slope of of the South China Sea. contributions are likely to be weak. Local mainland China, but their occurrence in To summarize the results of these topography may favor higher modes, the deep basin depends on the character recent measurements in Luzon Strait, but further observations are required to of the tidal forcing. intense tidal interaction with topog- resolve this response. This interpreta- Remotely sensed wave positions raphy leads to a variety of responses. tion is also consistent with the absence collected by Jackson (2009) over nearly At the northern end of the strait, of well-defined surface manifestations four years show that they first become where the ridge spacing is close to one of nonlinear internal waves in remote apparent at ~ 120.5°E, with more internal semidiurnal wavelength, there sensing imagery within Luzon Strait. frequent occurrences west of 120.0°E. is evidence of a standing internal wave The large internal tides radiating Initially, the remotely sensed waves between the ridges. The observations westward from the strait into the deep extend in a north-south arc spanning reveal little net energy flux measured basin of the South China Sea evolve in 100–200 km centered at ~ 20.5°N. Their in the center of the strait. The deeper a way that depends upon the competing orientation implies propagation to the western ridge at the northern line influences of rotational dispersion and west or west-northwest. The position allows enhanced westward radiation of nonlinear steepening. For the internal of a remotely sensed wave depends on semidiurnal internal tidal energy, but diurnal tide, rotational effects dominate, the time of the satellite overpass, but the there is only modest radiation of diurnal and steepening is inhibited. Internal distribution of observed wave positions energy. In contrast, along the southern semidiurnal tides also respond to rota- provides support for the conclusion line, the ridge spacing is less and does tional effects, but in this case, the steep- that short nonlinear waves form about not match the semidiurnal wavelength, ening proceeds until nonhydrostatic 180 km west of the prominent Lan-Yu but there is strong radiation of the effects become important. Ridge and slightly west of the Heng- diurnal signal, with most of the energy Internal tides radiating into the South Chun Ridge. As they approach the conti- trapped in the upper 500 m. China Sea from Luzon Strait are long nental shelf, they slow down and are
(~ 135 km for M2) relative to the vertical refracted, presenting a more complicated Tidal Evolution from scale of stratification (~ 500 m) or the picture, with further generation and Luzon Strait into the water depth (2–3 km), and do not imme- reflection of the internal tide by the local South China Sea Basin diately produce a pronounced surface topography (Klymak et al., 2011). To first order and in particular for manifestation sufficient to generate the The steepening of an internal tide the first internal mode, conditions for sharply defined lines seen in remotely and subsequent generation of a train of internal tide generation appear consis- sensed images (Figure 1). Signatures short nonlinear internal waves has been tent with those predicted for the mixed of this kind, so clearly identified both widely observed in coastal environments. tidal lee wave type (Vlasenko et al., in synthetic aperture radar and visible However, Earth’s rotation influences this 2005). Although internal hydraulic wavelength imagery, depend upon process, and in the South China Sea the processes may occur at discrete loca- modulation of surface waves by strong waves take approximately one inertial tions, such as in the northern part of surface current divergence produced by period (33 h at this latitude) to cross the the Heng-Chun Ridge and in a shal- short, steep internal waves. Such waves deep basin, providing sufficient time for lower feature south of Sabtang Island are the result of nonlinear transforma- rotation to influence their evolution. (Warn-Varnas et al., 2010), the present tion of the internal tide and have been Observations of the waves at three evidence points toward predominantly the subject of extensive modeling and locations (Figure 1) in Luzon Strait subcritical flow over the ridges (i.e., flow theoretical analysis. That these surface and the deep basin to the west were
Oceanography | December 2011 71 acquired over seven months using removed in the vertical integration. basin, based on high-pass filtering of the pressure-sensor equipped inverted Removal of the higher modes has the PIES time series; only the leading wave echosounders (PIES). Placed on the benefit of allowing the first mode to be of a wave packet is shown. Comparison seafloor, these instruments transmit an clearly revealed in a way that would not with the predicted tidal currents shows acoustic pulse to the sea surface and be possible if higher modes were also a tendency for short-period nonlinear detect the time it takes for the echo to present. Higher-mode waves undoubt- internal waves in the deep basin to return. Changes in stratification due edly exist in the South China Sea and coincide with maxima in the semi- to passage of an internal wave produce are of interest, but they are usually left diurnal tidal current rather than the corresponding changes in acoustic travel behind by the fast-moving first mode diurnal current, even though the latter time. Background temperature/salinity response and are generally less energetic. can be stronger than the semidiurnal profiles acquired during the study, By tracking waves as they pass successive signal. There is also a tendency for the together with simultaneous pressure instruments, we can observe the progres- strongest internal solitons to occur measurements to correct for changes in sive evolution of the internal tide from when the diurnal and semidiurnal sea surface elevation, allow inversion its initial formation in Luzon Strait to currents are in phase. to recover time-series measurements its subsequent transformation under the Theoretical models provide insight of fluctuations in stratification. Such influence of nonlinearity and rotation. into the combined effects of nonlinearity measurements have been widely used The tidal currents in Luzon Strait and rotation. In the South China Sea, to study mesoscale ocean processes. change between predominantly diurnal a useful simplification, consistent with By adapting the instrument to sample and predominantly semidiurnal, the limitation of our measurements rapidly (every 6 s), it is possible to separated by a transition period of to the first internal mode, represents measure the shape of a passing internal mixed tides. This change is illustrated stratification as a two-layer system wave. Following a pilot study in 2005, in Figure 4 (upper panel) where the with a warm surface layer overlying a analysis of internal waves measured with predicted tidal current is separated into deeper cold layer. Nonlinearity distorts collocated inverted echosounders and diurnal (red) and semidiurnal (blue), the wave as it travels. For example, in recording thermistor strings showed based on the four leading constituents the absence of rotation, a sinusoidal consistent results (Li et al., 2009). The in each case. Figure 4 (lower panel) internal tide generated by harmonic inverted echosounder measurement shows the occurrence and amplitude forcing initially evolves toward a saw- is restricted to the first internal mode, of the short-period nonlinear internal tooth shape as an interface with posi- as all modes but the first are effectively waves observed at station A3 in the deep tive slope progressively steepens and
K + O + P + Q 1 1 1 1 : M + S + N + K a 2 2 2 2 0.2 ) @ LZ –1 0.0
U (m s –0.2 50 50 Sep 29 b 0 0
–50 η (m) –50 η (m) @ A3 A3 –100 –100 Apr May Jun Jul Aug Sep Oct Nov Time (month in 2007 UTC)
Figure 4. Upper panel: Tidal current predictions (TPXO) for Luzon Strait broken into diurnal (red) and semidiurnal (blue) components, each based on the four leading constituents. Lower panel: Occurrence and range of nonlinear waves derived from high-pass filtered PIES time series. Only the leading wave of a wave train is shown. Nonlinear internal waves tend to occur when the semidiurnal tidal current envelope in Luzon Strait is at its maximum. Dashed lines indicate the period of observations shown in Figure 6. Adapted from Li and Farmer, 2011
72 Oceanography | Vol.24, No.4 an interface of negative slope becomes long before that could happen. depth by Helfrich (2007). This simpli- less steep. The greater the amplitude of A useful scaling parameter, referred fied description applies to a single tidal the initial wave, the more rapidly the to as the Ostrovsky number Os, is found component. The more realistic combina- nonlinear transformation occurs. When from the ratio of nonlinear to rota- tion of diurnal and semidiurnal internal the interfacial slope becomes sufficiently tional terms in the weakly nonlinear tides leads to a more subtle interaction steep, vertical acceleration plays a role two-layer case: and Equation 1 no longer strictly applies,
(the “nonhydrostatic effect”), and short- 2 2 2 although we can use an approximation Os = 36π Ag'(|h1 – h2| / h1 + h2) / f λ , (1) ~ period waves are generated. It is these Os based on the initial (positive) interface short nonlinear waves of large amplitude where A is the internal wave amplitude, slope (Farmer et al., 2009). Moreover, that are responsible for the surface signa- g' = g Δρ/ρ– is the reduced gravity (Δρ/ρ– the waves in the South China Sea are tures seen so clearly in remotely sensed is the relative density difference between large and can be steep, justifying a fully images (Figure 1). layers), λ is the wavelength, and h1 and nonlinear analysis.
Earth’s rotation plays a different role. h2 are the upper and lower layer depths, Figure 5 illustrates results of an
As the interface steepens, the flow is respectively. For Os >> 1, the waves analysis by Li and Farmer (2011), deflected to the right in the Northern steepen and “break,” whereas for Os << 1, based on Hibiya’s (1986) solution for
Hemisphere, dispersing energy from no breaking occurs. For 1 < Os < ~ 2, internal tide generation. The resulting the internal tide into internal inertial rotation inhibits steepening, the steepest internal tide provides initial conditions waves, thus tending to inhibit further part of the interface shifts forward, for analysis of the nonlinear evolution steepening. The rotational effect for and the internal tide approximates a using Helfrich’s (2007) fully nonlinear semidiurnal tides in the South China Sea parabolic or “corner wave” as predicted wave evolution model. Meridionally is small enough that steepening is dimin- by Ostrovsky (1978) and explored in averaged topography, including both ished but not halted, continuing until vertical acceleration becomes important 0.2 0.2 and short-period internal solitary waves a d 0.4 g 0.1 0.1 ) are generated. For diurnal internal tides, –1 0.2 0.0 0.0 which have a period closer to the inertial U (m s 0.0 –0.1 –0.1 period, rotation inhibits steepening and –0.2 –0.2 –0.2 0 5 10 15 20 0 5 10 15 20 0 5 10 15 20 the internal tide assumes a cusp shape, Time (hr) Time (hr) Time (hr) with the downward-pointing cusp iden- 40 e 50 b 20 h tified as a “corner wave.” This interpreta- 20 tion helps explain the increased tendency 0 0 0 for nonlinear internal waves to be more –20
Displacement (m) –20 closely associated with semidiurnal –40 –50 350 400 450 500 550 400 450 500 550 600 450 500 550 600 650 rather than diurnal currents, although, x (km) x (km) x (km) as noted above, nonlinear internal 0 c f 20 0 i waves always form further west as they –50 slow down over the continental slope. 0 –50 –100 Modeling (Helfrich, 2007) shows that Displacement (m) –150 –20 –100 these shape changes are not permanent 350 400 450 500 550 400 450 500 550 600 450 500 550 600 650 features; over a long enough time period, x (km) x (km) x (km) Figure 5. Two-layer model solutions for internal tides generated in Luzon Strait. Top row: Three the inertial energy would be returned to representative tidal current conditions in Luzon Strait corresponding to (a) predominantly semi- the internal tide and the process of steep- diurnal, (d) predominantly diurnal, and (g) mixed forcing. Middle row: Interface displacement ening and rotational dispersion repeated. solutions to Hibiya’s (1986) internal tide generation model for a two-ridge system representa- tive of the strait at 21°N, evaluated for each example in the top row. Bottom row: Evolution In the South China Sea, however, inter- of internal tide for each internal tide shown in the middle row, calculated for station A3 using action with the continental shelf occurs Helfrich’s (2007) fully nonlinear model. Adapted from Li and Farmer, 2011
Oceanography | December 2011 73 ridges between 20°N and 21°N, is a characteristic feature also observed in 2006; Alford et al., 2010). To the east included in the internal tide genera- the South China Sea. of Dongsha Plateau, these westward- tion, with a ridge spacing matching Figure 6 shows a short section of propagating nonlinear internal waves the semidiurnal wavelength. The the PIES time series during a period slow down and become unstable as they calculations are for three idealized but of mixed tidal forcing, referenced in encounter a steep slope, from ~ 2,500 m representative tidal current conditions Figure 4, illustrating the alternating char- depth east of 118°E to ~ 300 m on the in Luzon Strait: a purely semidiurnal acter of the response predicted for the Dongsha Plateau at 117°E, forming recir- tide (a, b, c), a diurnal tide (d, e, f), and idealized case (g, h, i) shown above. The culating cores, with individual waves sometimes being scattered into multiple waves and even becoming inverted. In 2005, a Nonlinear Internal Wave Luzon Strait and the South China Sea Initiative pilot study tracked the evolu- provide an ideal laboratory for studying the tion of shoaling nonlinear internal waves on the steep slope between 117.5°E generation, evolution, and ultimate fate of and 117°E (yellow box in Figure 1) “ large-amplitude internal waves. with shipboard profiling of currents, salinity, and temperature (ADCP and CTD), using the Taiwanese research vessel Ocean Researcher 3. Figure 7 a mixed tide (g, h, i). The top row shows internal tides that traverse the deep basin shows an example of a large-amplitude the prescribed zonal current in Luzon of the South” China Sea are progressively nonlinear internal wave measured by a Strait for each case, with the second row transformed by nonlinearity and rota- rapidly profiling CTD at 21°N, 117.25°E, showing the corresponding internal tide tion in this way, until they approach the acquired in water of 440 m depth. that is generated, and the bottom row continental shelf where the changing Based on 10 CTD profiles, the isopycnal giving the modeled nonlinearly evolved depth becomes the dominant factor in surface of 1,024 kg m–3 descends from wave after it has travelled 30 h, which is their further evolution. 50 m depth before the arrival of the the approximate distance to station A3 nonlinear internal wave to 200 m depth (Figure 1). For the semidiurnal example, Interaction of Nonlinear at the center of the wave, a vertical
Os = ~ 2 and the waves have steepened Internal Waves with the excursion of ~ 150 m. The wave has a to form solitary wave packets. For the Dongsha Plateau width of ~ 1 km. Within the wave, a diurnal case Os = ~ 1, the internal tide Nonlinear internal waves propagate gravitationally unstable overturn exists has evolved into a “corner wave.” For the predominantly westward at a speed of between ~ 100 m and 175 m depth. In ~ –1 mixed example, Os alternates between 2–3 m s across the deep South China sharp contrast to the gradual steepening ~ 1 and ~ 2, leading to an alternating Sea basin without losing much of their process and generation of short-period pattern of single and multiple waves, energy and identity (Klymak et al., nonlinear internal waves described
125 3.320 Figure 6. Example time series of PIES acoustic travel time at station A3 75 3.318 during mixed tidal currents. The 25 3.316 measurement period is shown by vertical dashed lines in the lower
–25 3.314 Delay (s) panel of Figure 4. The travel time (right-hand scale) has been converted Vertical Excursion (m) –75 3.312 to displacement of vertical stratifica- tion (left-hand scale) based on a first –125 3.310 Apr 20 04:00 08:00 12:00 16:00 20:00 Apr 21 04:00 08:00 12:00 16:00 20:00 Apr 23 internal mode analysis. Time in 2007 (UTC)
74 Oceanography | Vol.24, No.4 above, this wave exhibits an extreme breaking process and has formed a 23 recirculating trapped core in the center 50 of the wave. Breaking of internal waves, 24 defined as occurring when the particle 100 velocity (current associated with the wave) exceeds the wave’s propagation 25 speed (Lamb, 2002), is a specific feature 150
of these observations. Moreover, the Depth (m) ADCP measurements show closed 200 streamline flow, and repeated CTD profiles reveal overturning of the density 250 stratification. This is the internal wave 26 analog of breaking surface waves when 300 they shoal near the beach and the crest –1.0 –0.5 0.0 0.5 1.0 1.5 advances faster than the trough, but x (km) with an amplitude 10–100 times greater. Figure 7. A large-amplitude nonlinear internal wave observed from a shipboard conductivity- Echosounder images proved effective temperature-depth survey around 21°N, 117.25°E. Color shadings and contour lines are –3 –3 at tracking the waves as they moved at isopycnals at 0.25 kg m interval. Isopycnal surfaces of 1,023, 1,024, 1,025, and 1,026 kg m are labeled. 1–2 m s–1 across Dongsha Plateau. Waves propagating across the plateau dissipate most of their energy before reaching Active movement of the prey likely If there is an intrusion of the Kuroshio the continental shelf (Lien et al., 2005; plays a role in the aggregative process. into the South China Sea, an additional Chang et al., 2006). Prey availability for pilot whales and the effect comes into play due to Doppler The nonlinear internal waves in the marine ecosystem in the South China Sea shifting of the radiated internal tides by South China Sea (Chang et al., 2008) are likely influenced by the characteristics the zonal component of the background strongly modulate the surface waves. of nonlinear internal waves, which in current (Li and Farmer, 2011). These Strong horizontal convergence in the turn are modulated by the spring neap predictions need to be tested against leading portion of the wave often leads tidal cycle (Moore and Lien, 2007). observations over periods long enough to surface-wave breaking on the slope to include variability in the Kuroshio of Dongsha (Figure 8) where strong Outstanding Problems together with time series measurements surface scattering intensity is detected in While the broad concepts of genera- east of the eastern ridge to observe waves remotely sensed synthetic aperture radar tion, evolution, and dissipation of these radiating into the Pacific. images and shipboard radar. Behind the remarkable and widely distributed waves wave, horizontal divergence and boils are apparent, there are many subtleties Detailed understanding of wave generation, associated with upwelling are present. yet to be resolved, including: including generation of intense turbulence Schools of pilot whales are often observed over ridges, generation of higher-mode in the boil region. Nonlinear internal The role of the Kuroshio in modulating components, nonlinear interaction of waves waves appear to lead to the aggregation internal wave generation. Model calcula- in Luzon Strait, and related phenomena. of prey as they entrain small fish and tions (Buijsman, 2010b) predict how The pioneering observations in Luzon squid within convergence zones. These westward shoaling of stratification asso- Strait described above could not resolve boils occur near the leading part of the ciated with the Kuroshio enhances the some important details of the generation wave, accompanied by downwelling, and amplitude and nonlinearity of internal process. Are there locations of hydrauli- at greater depth in the trailing portion tides traveling into the South China Sea cally controlled flow, and if so, how of the wave, accompanied by upwelling. relative to those traveling into the Pacific. important are these flows to the far-field
Oceanography | December 2011 75 How to use described biological effects of the
Boil internal waves to make quantitative esti- mates of the role these waves play in biolog- ical productivity in the South China Sea. Vertical mixing associated with the internal waves brings nutrients into the Calm Breaking Surface Waves euphotic zone. The extent to which this Boil fertilization of near-surface waters occurs Pilot Whales in the South China Sea and the resulting
Fishes and Squids biological impact represent a potentially Planktons Nutrients important feature of this highly produc- ~160 m tive part of the ocean. Internal Solitary Wave Luzon Strait and the South China Sea provide an ideal laboratory for studying Isopycnal the generation, evolution, and ultimate fate of large-amplitude internal waves. ~ 1 km While the observations and analyses of Figure 8. Snapshots of varying sea-surface conditions associated with internal waves coupled to a sche- recent studies have greatly improved matic diagram showing the associated spatial scale. Arrow sequence indicates current pattern associated with overturning of the wave core. Strong horizontal convergence and vertical downwelling in the front our understanding, much remains to be portion of the internal wave leads to breaking surface waves; horizontal divergence and upwelling in the learned about these energetic and ocean- rear portion of the wave, where pilot whales were seen, create surface boils and may entrain fish, squid, ographically significant phenomena. plankton, and nutrients, and thus the pilot whales.
Acknowledgements The work described here owes much to internal wave properties? Are lee waves model calculations are required to the encouragement and support of the generated in some areas, and how do understand how spatial variations among US Office of Naval Research Physical they evolve? What fraction of energy different components interact to form Oceanography Program’s Nonlinear goes into higher modes? What role do the far-field signal. Internal Waves Initiative and Internal these higher modes play in contributing Waves in Straits Experiment, which to turbulence, mixing, and far-field Tidal interaction with Dongsha Plateau have in turn benefitted greatly from the internal wave characteristics? and the continental slope, which not only US-Taiwanese collaboration, including intensifies and dissipates internal waves important Taiwanese scientific and The far-field consequences of predominant that have propagated across the deep logistical support. We thank the captains diurnal internal tide radiation from the basin from the east but also is a source of and crews of all the US and Taiwanese southern portion of the strait (see Figure 3) additional internal tide generation, turbu- research vessels conducting this research, and how wave generation at different lence, and mixing. Observations show a as well as the technical staffs of each frequencies (diurnal and semidiurnal) complex pattern of nonlinear internal institution, for their skill and expertise— at different locations combines to form waves over the shelf and shelf break. without which the fieldwork would not the observed features in the deep basin. Interesting effects can be expected due to have been possible. We also thank the Diurnal and semidiurnal internal the interaction of waves propagating in many colleagues and technical support tides respond quite differently to the different directions. staff who have played important roles in combined effects of nonlinearity and ensuring the success of our research. rotation. Further observations and
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