Cross-shelf variation of internal tides west of the Dongsha Plateau in the northern South China Sea

We examine the cross-shelf variation of internal tides(ITs)west of the Dongsha Plateau in the northern South China Sea based on observations from 4 moorings deployed between August 2017 and September 2018.On the slope,the amplitude of diurnal baroclinic current ellipses are 5 times larger than that of barotropic currents.The baroclinic energy quickly dissipates during cross-shelf propagation,and barotropic currents become dominant on the shelf outside of the Zhujiang River Estuary,with the amplitude of semidiurnal barotropic current ellipses being 10 times larger than that of the baroclinic ones.Dynamic modal decomposition indicates the first baroclinic mode is dominant for both diurnal and semidiurnal ITs.The total horizontal kinetic energy(HKE)of the first three baroclinic modes shows spatiotemporal differences among the 4 moorings.On the slope,the HKE for diurnal ITs is stronger in summer and winter,but weaker in spring and autumn;for semidiurnal ITs there is a similar seasonal variation,but the HKE in winter is even stronger than that in summer.On the shallow shelf,both diurnal and semidiurnal ITs maintain a certain intensity in summer but almost disappear in winter.Further analysis shows that only the upper water column is affected by seasonal variation of stratification on the slope,variation of diurnal ITs is thus controlled by the semi-annual cycle of barotropic energy input from the Luzon Strait,while the incoherent baroclinic currents make a major contribution to the temporal variation of semidiurnal ITs.For the shelf region,the water column is well mixed in winter,and the baroclinic energy largely dissipates when ITs propagate to the shelf zone despite of a strong barotropic energy input from the Luzon Strait.

Observation of Internal Tides in the Qiongzhou Strait by Coastal Acoustic Tomography

In this study,power spectral density and inverse analyses were performed to obtain the frequency characteristics and spatial distribution of temperature in the Qiongzhou Strait using reciprocal sound transmission data obtained in a coastal acoustic tomo-graphy experiment conducted in 2013.The results reveal three dominant types of internal tides(diurnal,semidiurnal,and terdiurnal).Spectral analysis of the range-average temperature deviation along the northern and southern transmission paths shows that along the northern path,the energy of the diurnal internal tides was significantly larger than that of the semidiurnal tides.The semidiurnal internal tides,in contrast,were more pronounced along the southern path.A terdiurnal spectrum with an energy level equivalent to that of the semidiurnal internal tide was discernable for both the northern and southern paths.These three types of internal tides can also be recognized in the time variation of the zonal-average temperature deviation.The diurnal internal tides were strengthened along the northern coast,implying their westward propagation and the existence of coastally trapped effects.The other two types of internal tides,which have smaller wavelengths than the diurnal internal tides,were less resolved over the entire tomographic domain due to the insufficient resolution of the inversion.The data quality was verified to be satisfactory by error estimation.

Characteristics of Semi-diurnal Internal Tides in the Western Equatorial Pacific Ocean Around 1°45′S,156°E

The analyses of a data series obtained during TOGA- COARE show the existence of remarkable semi-diurnal intemal tides in the western equatorial Pacific Ocean around 1°45＇S, 156°E. Some characteristic parameters of the internal tides are vertical wavenumber -1.6×10^-3 m^-1, horizontal wavenumber （wavelength） 3.3×10^-2 km^-1 （210 km）, vertical propagation speed -3.8 cm/s and horizontal propagation speed 2.0 m/s. The waveforms propagate downwards slantingly, that is, the wave energy transfers upwards slantingly. Depth-distribution of the＇rotary spectral levels is a saddle-shape. The depths of the trough and the deeper peaks are almost coincident with those of the south boundaries of the South Equatorial Current and the Equatorial Undercurrent, respectively. The mean orientation of the rotary spectral ellipse changes with depth： 30° from north to east at 40 m, and changes into 14° from east to south at 324 m, and generally, it points to northeastward, which indicates ＂that waves come from the southwest.

Internal tides in the northern South China Sea from 20-day in-situ mooring observations in 1998

20-day in-situ ADCP current and CTD data are used to investigate the characteristics and energy of the internal tides in the northern South China Sea （NSCS）. The results show that the O1, K1, M2 and S2 constituents of internal tides are energetic and diurnal constituents （O1 and K1） are dominating. In the observational period, the current vectors of these four constituents all rotate clockwise and the maximum semi-major axe of internal tidal ellipses is more than 14 cm/s. The variation of ocean temperature shows that the internal tides present obvious quasi-diurnal oscillation and the average amplitude reaches 50 m. Furthermore, these internal tides carry high energy and appear to be intermittent. The maximum values of KE （PE） during the observational period are up to 2 （3.5） k J/m^2 for diurnal internal tides, and up to 1 （1.5） k J/m^2 for semidiurnal internal tides.

A study of SAR remote sensing of internal solitary waves in the north of the South China Sea:Ⅰ.Simulation of internal tide transformation

For settlement of the well-known problem of contemporary radar imaging models, i. e. , the problem of a general underestimation of radar signatures of hydrodynamic features over oceanic internal waves and underwater bottom topography in tidal waters at high radar frequency bands （ X-band and C-band）, the impact of the ocean surface mixed layer turbulence and the significance of strat- ified oceanic model on SAR remote sensing of internal solitary waves are proposed. In the north of the South China Sea by utilizing some observed data of background field the nonlinearity coefficient, the dispersion coefficient, the horizontal variability coefficient and the phase speed in the generalized K-dV equation are determined approximately. Through simulations of internal tide transfor- mation the temporal evolution and spatial distribution of the vertical displacement and horizontal velocity of internal wave field are obtained. The simulation results indicate that the maximum amplitudes of internal solitary waves occur at depth 35 m, but the maximum current speeds take place at depth 20 m in this area of the sea （about 20°30＇N, 114°E） in August. It was noticed that considering the effects of flood current and ebb current respectively is appropriate to investigate influence of the background shear flow on coefficients of the K-dV equation. The obtained results provide the possibility for the simulation of SAR signatures of internal solitary waves under considering the impact of ocean surface mixed layer turbulence in the companion paper.

An isopycnic-coordinate internal tide model and its application to the South China Sea

A three-dimensional isopycnic-coordinate ocean model for the study of internal tides is presented. In this model, the ocean interior is viewed as a stack of isopycnic layers, each characterized by a constant density. The isopycnic coordinate performs well at tracking the depth variance of the thermocline, and is suitable for simulation of internal tides. This model consists of external and internal modes, and barotropic and baroclinic motions are calculated in the two modes, respectively. The capability of simulating internal tides was verified by comparing model results with an analytical solution. The model was then applied to the simulation of internal tides in the South China Sea （SCS） with the forcing of M2 and K1 tidal constituents. The results show that internal tides in the SCS are mainly generated in the Luzon Strait. The generated M2 internal tides propagate away in three different directions （branches）. The branch with the widest tidal beam propagates eastward into the Pacific Ocean, the most energetic branch propagates westward toward Dongsha Island, and the least energetic branch propagates southwestward into the basin of the SCS. The generated KI internal tides propagate in two different directions （branches）. One branch propagates eastward into the Pacific Ocean, and the other branch propagates southwestward into the SCS basin. The steepening process of internal tides due to shoaling effects is described briefly. Meridionally integrated westward energy fluxes into the SCS are comparable to the meridionally integrated eastward energy fluxes into the Pacific Ocean.

Observation of interactions between internal tides and near-inertial waves after typhoon passage in the northern South China Sea

During the observational period of our study, Typhoon Hagupit passed over the mooring site and induced strong near-inertial waves （NIWs）, which provided an opportunity to investigate the interactions between internal tides （ITs） and NIWs. Based on the mooring data, we compared the current spectra during the typhoon period and non-typhoon period in the northern South China Sea, and found that the high- frequency waves （fD1 and fD2） were evident during the former. Moreover, the observations of the current revealed that fD1 and fD2 occurred near the depth of strong vertical shear in the NlWs. In order to confirm the generation mechanism of fD1 and fD2, we compared the positions of strong vertical shear in the NIWs and strong vertical velocity in the ITs. It was established that the vertical shear of the horizontal current of the NIWs and the vertical current of the ITs contributed to the generation of fDt and fD2.

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

A fully nonlinear,three-dimensional nonhydrostatic model driven by four principal tidal constituents(M2,S2,K1,and O1) is used to investigate the spatial-temporal characteristics and energetics of internal tides in Luzon Strait(LS).The model results show that,during spring(neap) tides,about 64(47) GW(1 GW=109 W) of barotropic tidal energy is consumed in LS,of which 59.0%(50.5%) is converted to baroclinic tides.About 22(11) GW of the derived baroclinic energy flux subsequently passes from LS,among which 50.9%(54.3%) flows westward into the South China Sea(SCS) and 45.0%(39.7%) eastward into the Pacific Ocean,and the remaining 16(13) GW is lost locally owing to dissipation and convection.It is revealed that generation areas of internal tides vary with the spring and neap tide,indicating different source areas for internal solitary waves in the northern SCS.The region around the Batan Islands is the most important generation region of internal tides during both spring and neap tides.In addition,the baroclinic tidal energy has pronounced seasonal variability.Both the total energy transferred from barotropic tides to baroclinic tides and the baroclinic energy flux flowing out of LS are the highest in summer and lowest in winter.

INTERNAL TIDES, SOLITARY WAVES AND BORES IN SHALLOW SEAS

Remote sensing and in situ observations of internal tides, solitary waves and bores in shallow water are briefly reviewed in this paper. The emphasis is laid on interpreting SAR images based on oceanographic measurements, and analyzing characteristics of internal waves in the China Seas. Directions for future research are discussed.

Seasonal characteristics of internal tides and their responses to background currents in the Luzon Strait

The spatial-temporal characteristics of internal tides （ITs） in the southwest Luzon Strait are examined, based on 9-month mooring current records from autumn 2008 to summer 2009. The results of spectral analysis show that the ITs in diurnal and semidiurnal frequencies are prominent at the mooring site, especially for the clockwise rotary component. The diurnal ITs are mostly dominated by the first mode except for that in spring when the second mode is relatively predominant. The semidiurnal ITs display a variable multimodal structure. Moreover, an apparent difference is detected in the kinetic energy of diurnal ITs. The energy is strongest in winter, and followed by that in summer, whereas the value is smallest in spring and autumn. It is suggested that the incoherent motions are responsible for the significant seasonal variations of diurnal ITs, reflecting interaction between diurnal ITs and the varying background conditions. However, the semidiumal ITs are independent of seasonal change, whose energy is smaller and only one-third of the diurnal energy in winter. Nevertheless, the abnormal variations of semidiurnal ITs are also related to the variable background conditions. The incoherent semidiurnal constituent accounts for about 37% of the total semidiurnal tidal kinetic energy, but the diurnal tidal motions contain fewer incoherent component （22.2%）.

Numerical study of M_2 internal tide generation and propagation in the Luzon Strait

Based on the z-coordinate ocean model HAMSOM,we introduced the internal-tide viscosity term and applied the model to numerically investigate the M2 internal tide generation and propagation in the Luzon Strait （LS）.The results show that （1） in the upper 250 m depth,at the thermocline,the maximum amplitude of the generated internal tides in the LS can reach 40 m;（2） the major internal tides are generated to the northwest of Itbayat Island,the southwest of Batan Island and the northwest of the Babuyan Islands;（3） during the propagation the baroclinic energy scattering and reflection is obvious,which exists under the effect of the specific topography in the South China Sea （SCS）;（4） the westward-propagating internal tides are divided into two branches entering the SCS.While passing through 118 E,the major branch is divided into two branches again.The strongest internal tides in the LS are generated to the northwest of Itbayat Island and propagate northeastward to the Pacific.However,to the east of 122 E,most of the internal tides propagate southeastward to the Pacific as a beam.

Estimation of the Reflection of Internal Tides on a Slope

Reflection occurs when internal tides impact on a steep continental slope. Separating reflected internal tide signals from incident ones is crucial to develop the parameterization of internal tide-driven turbulent mixing on the continental slopes. In this study, the performances of three different methods for estimating internal tide reflections are examined by using two different cases. The Hilbert transform-based method is found to be more suitable than two other methods for both cases considered in this study. The two other methods are effective for westward-propagating mode-1 internal tides impacting a slope, but inappropriate in the case where internal tides radiate from a Gaussian ridge impact the slope because of their inaccurate estimation of incident internal tides in the latter case. Such inaccurate estimation further influences the extraction of reflected signals and calculation of the reflected and cross term of energy fluxes. In addition, it should be noted that, due to the use of filtering, the method based on Hilbert transform may result in slight bias when assessing the incident and reflected signals near topographic features.

Theoretical study of the effect of topographic height and width on generation of internal tides

Internal tides generated upon two-dimensional Gaussian topographies of different sizes and steepness are investigated theoretically in a numerical methodology.Compared with previous theoretical works,this model is not restricted by weak topography,but provides an opportunity to examine the influence of topography.Ten typical cases are studied using different values of height and/or width of topography.By analyzing the baroclinic velocity fields,as well as their first eight baroclinic modes,it is found that the magnitude of baroclinic velocity increases and the vertical structure becomes increasingly complex as height increases or width decreases.However,when both height and width vary,while parameter s(the ratio of the topographic slope to the characteristic slope of the internal wave ray) remains invariant,the final pattern is influenced primarily by width.The conversion rate is studied and the results indicate that width determines where the conversion rate reaches a peak,and where it is positive or negative,whereas height affects only the magnitude.High and narrow topography is considerably more beneficial to converting energy from barotropic to baroclinic fields than low and wide topography.Furthermore,parameter s,which is an important non-dimensional parameter for internal tide generation,is not the sole parameter by which the baroclinic velocity fields and conversion rate are determined.

Three-dimensional numerical simulation of M_2 internal tides in the Luzon Strait

A three-dimensional isopycnic-coordinate internal tidal model is employed to investigate the generation, propagation, vertical structure and energy conversion ofM2 internal tides in the Luzon Strait （LS） with mooring observations. Simulated results, especially the tidal current amplitudes, agree well with observations, demonstrating the reasonability and accuracy of the model. Results indicate that M2 internal tides mainly propagate into three directions horizontally, i.e., eastward towards the western Pacific Ocean, westward towards the Dongsha Island and southwestward towards the South China Sea Basin. In the horizontal direction, tidal current amplitudes decrease as distance increases away from the LS; in the vertical direction, they show an obvious decreasing tendency with depth. Between the double ridges of the LS, a clockwise gyre of M2 baroclinic energy flux appears, which is caused by reflections of M2 internal tides at supercritical topographies, and resonance of M2 internal tides happens along 19.5° and 21.5°N due to the heights and separation distance of the double ridges. The total energy conversion in the LS is about 14.20 GW.

Seasonal variation and modal content of internal tides in the northern South China Sea

A nine-month mooring record was used to investigate seasonal variation and modal content of internal tides(ITs) on the continental slope in the northern South China Sea(SCS). Diurnal tides at this site show clear seasonal change with higher energy in winter than in spring and autumn, whereas semidiurnal tides show the opposite seasonal pattern. The consistency of ITs with barotropic tides within the Luzon Strait, which is the generation region of the ITs, implies that the seasonal variation of ITs depends on their astronomical forcing, even after extended propagation across the SCS basin. Diurnal tides also differ from semidiurnal tides in relation to modal content; they display signals of high modes while semidiurnal tides are dominated by low modes. Reflection of the diurnal tides on the continental slope serves as a reasonable explanation for their high modes. Both diurnal and semidiurnal tides are composed of a larger proportion of coherent components that have a regular 14-day spring-neap cycle. The coherent components are dominated by low modes and they show obvious seasonal variation, while the incoherent components are composed mainly of higher modes and they display intermittent characteristics.

Temporal variations in internal tide multimodal structure on the continental shelf, South China Sea

Temporal variations in multimodal structures of diurnal( D_1) and semidiurnal( D_2) internal tides were investigated on the continental slope of the Dongsha Plateau, based on 2-month moored acoustic Doppler current profiler observations. Harmonic analysis indicated that the D_1 components( K_1 and O_1) dominated the internal tide field. The vertical structure of the K_1 constituent presented a first-mode structure while the M_2 constituent seemed to exhibit a high-mode structure. Amplitude spectra analysis of the current data revealed differences in baroclinic current amplitudes between different water depths. Temporal variations in modal structures ware analyzed, based on the D_1 and D_2 baroclinic tides extracted from the baroclinic velocity field with band-pass filters. Analysis showed that the magnitude of the D_1 internal tide current was much larger than the D_2 current, and temporal variations in the modal structure of the D_1 internal tide occurred on an approximately fortnightly cycle. The EOF analyses revealed temporal transformation of multimodal structures for D_1 and D_2 internal tides. The enhancement of the D_1 internal tide was mainly due to the superposition of K_1 and O_1, according to the temporal variation of coherent kinetic energy.

Coherent and incoherent internal tides in the southern South China Sea

Coherent and incoherent internal tides(CITs and ICITs) in the southern South China Sea were investigated from two sets of _18-month mooring current records. The CITs were mainly composed of diurnal Q _1, O _1, P _1 and K _1 and semidiurnal M_2. The observed diurnal internal tides(ITs) were more coherent than the semidiurnal constituents. Coherent diurnal variance accounted for approximately 58% of the diurnal motion, whereas semidiurnal tides contained a much smaller fraction(35%) of coherent motion. The ICITs mainly consisted of motion at non-tidal harmonic frequencies around the tidal frequency, and showed clear intermittency. The modal decomposition of CITs and ICITs showed that CITs were dominated by mode-1, whereas mode-1 and higher modes in ICITs signals showed comparable amplitudes. CITs and ICITs accounted for approximately 64% and 36% of the total kinetic energy of internal tides, respectively.

Three-dimensional numerical simulation of internal tides that radiated from the Luzon Strait into the Western Pacific

Recent satellite altimeter observations have indicated that internal tides （ITs） from the Luzon Strait （LS） propagate more than 2 500 km into the Western Pacific （WP）. This study used a high-resolution three-dimensional numerical model to reproduce and examine the ITs radiation process. The propagation of diurnal and semidiurnal ITs showed different patterns and variations. Diurnal ITs with lower frequency were affected more by the earth＇s rotation and they were bent more toward the equator than semidiurnal ITs. ITs phase speeds are functions of latitude and diurnal ITs showed greater distinctions of phase speeds during propagation. For M2 ITs, the wavelength remained nearly unchanged but the beam width increased significantly during propagation away from the LS. For diurnal ITs （K1 and O0, the wavelength decreased noticeably with latitude, while the beam width varied little during propagation because of blocking by land. Baroclinic energy was also examined as a complement to satellite results reported by Zhao （2014）. The magnitude of the generated baroclinic energy flux reduced remarkably within 300 km from the generation site but it then decayed slowly when propagating into abyssal sea. Baroclinic energy of diurnal ITs was found to dissipate at a slower rate than semidiurnal ITs along the main propagation path in the WP.

The slanting property of semi-diurnal internal tide propagation in the Pacific Ocean at 1°45′S,156°E

By analyzing a data set collected using a moored instrument array and CTD during TOGA-COARE, it is found that there exist remarkable internal tides in the western equatorial Pacific Ocean around 1°45′S, 156°E, whose horizontal wavenumber （wavelength）, vertical wavenumber, h 156° orizontal propagation speed and vertical propagation speed are 3.3×10^-2 km^-1 （210 km）, - 1.6×10^-3m, 2.0 m/s and -3.8 cm/s, respectively, that is, the waveform propagates downwards slantingly. Moreover, the propagating direction rotates statistically clockwise as the depth increases and its cause is unclear.

Seasonal Variability of Internal Tides Northeast of Taiwan

The spatial-temporal characteristics of the barotropic tides and internal tides(ITs) northeast of Taiwan Island are examined, based on a 1-year mooring current observations from May 23, 2017 to May 19, 2018. The results of harmonic tidal analysis show that the barotropic tides are dominated by semidiurnal tides, which is mainly controlled by M2 tidal components. Moreover, the vertical structures of diurnal and semidiurnal ITs show that the semidiurnal IT shows notable seasonal variation, whereas seasonal variations of the diurnal IT energy is not significant. The semidiurnal IT energy in winter half year is twice that in summer half year. The seasonal variation of semidiurnal IT is mainly modulated by the direction change of the current rather than by the topographic features and stratification. In summer(winter) half year cyclonic(anti-cyclonic) eddies meanly control at this point, so the flow direction is mainly in the southwest(northeast) direction, causing the background flow to flow along(perpendicular to) the isobath. When crossing the isobath, the ITs are generated by the interaction of the barotropic tide and the topography, resulting in the increase of the tidal energy in the winter half year.