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.

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.

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 effect of internal tides on the vertical structure of tidal current in the North Huanghai Sea

The tidal current is generally predominant in China's offshore areas. The vertical structure of the observedtidal current is quite complicated with the presence of seasonal thermocline. The observed tidal current may be divided into two parts, an averaged barotropic tide current and a variation tide current. A method for studying the vertical structure of tidal current is developed from the constitution and distribution of energy, and the vertical structure of the observed tide current in the North Huanghai Sea is studied on the basis of the method. The result shows that the reason why the energy of the tidal current is concentrated on the neighbourhood of the thermocline mainly lies in the internal tides i under certain conditions, the fact that the direction of the internal tide current above the thermocline is opposite to the one below the thermocline will be able to cause the rotary directions of the observed tidal current above and below the thermocline to be in opposite. The interaction between the averaged barotropic and the variation tide current plays an important role in forming the vertical structure of the tidal current, and it is mainly the interaction that results in the inho-mogeneous distribution of the tide current energy in the entire water column ; the ratio between the total energies of the internal tide current above the thermocline and the variation tide current in the entire water column is greater than the ratio between the total energies of that below the thermocline and the variation's. In a strong internal tide area such as the neighbourhood of Station L4, at diurnal tide frequency, the above-mentioned corresponding ratios are about 38. 82% and 29. 88%, respectively, and the energy of the internal tide current is about 68. 70%of the energy of the variation tide current; at semidiurnal tide frequency, the above-mentioned corresponding ratios are about 26. 61 % and 19. 73% , respectively, and the total internal tide current energy is about 46. 36% of the total variation tide current energy.

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.

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.

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%）.

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.

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.

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.

Turning depths of internal tides in the South China Sea inferred from profile data

Theoretically,propagating internal tides in the ocean may reflect at turning depths,where buoyancy frequencies equal tidal frequencies,before colliding with the air-sea interface or rugged bottom topography.Globally,the internal tide lower turning depths(ITLTDs)in the open ocean have been mapped;however,knowledge of the presence of ITLTDs in the South China Sea(SCS)is lacking.In this study,2125 high-quality temperature-salinity profiles(including 58 deep-sea hydrographic measurements with observational depths exceeding 3000 m)are collected and analyzed to investigate the existence of ITLTDs in the SCS.Furthermore,the concept of the upper turning depth is first introduced in the context of internal tides,and internal tide upper turning depths(ITUTDs)are also investigated.ITLTDs are found to exist at several abyssal stations;these stations are distributed mostly in the southern part of the SCS basin,possibly due to the greater water depths there.Fewer locations show the presence of ITLTDs for K_(1) versus M_(2) tidal frequencies because of the lower tidal frequency.The distance between ITLTDs and the seafloor ranged from 270 m to more than 1200 m,implying the possible existence of multiple internal wave evanescent regions in the abyssal bottom.ITUTDs of tens of meters are ubiquitous in the SCS;stations with the presence of ITUTDs are located mainly in the northeastern SCS due to the intensive observations there.However,the calculated ITUTDs have large uncertainties;they are sensitive to the selected bin values.The horizontal propagation directions of internal tides in the SCS change dramatically,and as a result,the estimated turning depths under the full Coriolis force definition are different compared to that under the traditional approximation.

A Model Study on the Generation of Internal Tides by Tidal Flows Over a Submerged Seamount in the Channel

It is known that the submerged seamount/ridge is a source for the generation of internal tides.In this paper,a three-dimensional two-layer model is set up to study the generation of internal tides by tidal flows over a submerged seamount/ridge in the channel.Several numerical experiments with different topographic features,upper layer depths,tidal flows and background currents are carried out to study the variations of the induced internal tides.It is shown that,for the specific stratification,the seamount feature,the slope,the initial upper layer depth and the imposing driven force determine the Froude number near the seamount peak.Once when the Froude number is supercritical,the associated maximum amplitude of the induced internal tide is so large that the internal tide begins to disintegrate,which brings about severe variations of the current velocity and the water elevation fields,and the associated induced baroclinic tidal energy around the seamount peak is much larger than the barotropic one.The Richardson number greater than 1/4 is a criterion for stability of shear flow.Since the maximum tidal velocity changes within 0∼360◦with time in a period around the seamount peak,the induced internal tide does not stride the seamount peak before it disintegrates,which is different from the two-dimensional modeled results.The asymmetrical slope of the submerged seamount is a mechanism for the asymmetrical internal tide generation.

Effects of internal tidal dissipation and self-attraction and loading on semidiurnal tides in the Bohai Sea, Yellow Sea and East China Sea： a numerical study

A parameterized internal tide dissipation term and self-attraction and loading(SAL) tide term are introduced in a barotropic numerical model to investigate the dynamics of semidiurnal tidal constituents M_2 and S_2 in the Bohai Sea, Yellow Sea and East China Sea(BYECS). The optimal parameters for bottom friction and internal dissipation are obtained through a series of numerical computations. Numerical simulation shows that the tide-generating force contributes 1.2% of M_2 power for the entire BYECS and up to 2.8% for the East China Sea deep basin. SAL tide contributes 4.4% of M_2 power for the BYECS and up to 9.3% for the East China Sea deep basin. Bottom friction plays a major role in dissipating tidal energy in the shelf regions, and the internal tide eff ect is important in the deep water regions. Numerical experiments show that artifi cial removal of tide-generating force in the BYECS can cause a signifi cant dif ference(as much as 30 cm) in model output. Artifi cial removal of SAL tide in the BYECS can cause even greater diff erence, up to 40 cm. This indicates that SAL tide should be taken into account in numerical simulations, especially if the tide-generating force is considered.

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.