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.

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.

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%）.

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.

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.

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.

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.

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.

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.

Performance Evaluation of Three Parameterizations on Internal Tidal Mixing in the Northern Pacific

The accurate assessment of the energy dissipation of internal tides(ITs)is of great importance because ITs contribute significantly to abyssal mixing.Thus,in this study,the IT-driven dissipation and diapycnal diffusion in the northern Pacific are esti-mated using parameterizations proposed by St.Laurent et al.(2002),Koch-Larrouy et al.(2007),and de Lavergne et al.(2020)(hereaf-ter referred to as LSJ02,KL07,and dL20,respectively).The performances of the three parameterizations are evaluated by comparing the calculated results with fine structure observations.In particular,the dissipation estimated by LSJ02 parameterization shows a bottom-intensified characteristic,with the patterns showing good agreement with the observations near seamounts.Moreover,43%of the results calculated using the LSJ02 parameterization have errors lower than one order of magnitude in the generation sites of ITs.Meanwhile,the strongest dissipation estimated by the KL07 parameterization shifts to the thermocline,with the results showing the highest level of consistency with observations in the generation sites.The proportion of results with errors lower than one order of magnitude is 80.7%.Furthermore,the results calculated by dL20 parameterization agree well with the observations in the upper and middle layers,with the parameterization showing an accurate estimation of the remote dissipation.The percentages of the errors lower than one order of magnitude between the dL20 parameterization and observations account for 77.1%and 88.7%in the genera-tion sites and far-field regions,respectively.

A study of internal solitary waves observed on the continental shelf in the northwestern South China Sea

Based on in-situ time series data from the acoustic Doppler current profiler （ADCP） and thermistor chain in Wenchang area, a sequence of internal solitary wave （ISW） packets was observed in September 2005, propagating northwest on the continental shelf of the northwestern South China Sea （SCS）. Corresponding to different stratification of the water column and tidal condition, both elevation and depression ISWs were observed at the same mooring location with amplitude of 35 m and 25 m respectively in different days. Regular arrival of the remarkable ISW packets at approximately the diurnal tidal period and the dominance of diurnal internal waves in the study area, strongly suggest that the main energy source of the waves is the diurnal tide. Notice that the wave packets were all riding on the troughs and shoulders of the internal tides, they were probably generated locally from the shelf break by the evolution of the internal tides due to nonlinear and dispersive effects.

A study of SAR remote sensing of internal solitary waves in the north of the South China Sea:Ⅱ.Simulation of SAR signatures of internal solitary waves

A new model developed from the full-spectrum model of Lyzenga and Bennett （ 1988 ） is built up by us preliminarily through considering the impact of the ocean surface mixed layer turbulence on SAR remote sensing of internal solitary waves. In the partial differential equation of the action spectral density of the surface gravity-capillary waves the source function representing the contribution of the turbulence is added besides the usual source function representing the contribution of the wind. The source function is determined by applying the κ - ε model and adopting the Nasmyth spectrum of oceanic turbulence （ Nasmyth, 1970; Oakey, 1982; Fan, 2002） on the basis of the previous simulation results of internal tide transformation obtained in the companion paper （Fan et al. ,2008）. Either under relatively high wind speed, or under low wind speed, our model predicts significant large modulations of radar backscatter at all three bands （ L, C and X bands） for both VV and HH polarization. These results prove that considering the impact of ocean surface mixed layer turbulence on SAR remote sensing of internal solitary waves is reasonable and appropriate for settlement of the well-known problem of contemporary radar imaging models.

Mooring observed mode-2 internal solitary waves in the northern South China Sea

The mode-2 internal solitary waves(ISWs)generated by mode-2 internal tide(IT)are identified by mooring observations in the northern South China Sea(SCS)from 2016 to 2017.Two mode-2 ISWs with a re-appearance period of 24.9 h observed on 29 and 30 July 2016 are characterized by type-b ISWs.They occurred when the isotherms compressed obviously in the vertical direction.Modal decomposition of IT horizontal currents shows that the vertical compression of the isotherms is mainly caused by diurnal mode-2 IT.The analysis of the role of the density stratification reveals that a deeper and thinner pycnocline is favorable for generation of mode-2 ISWs rather than pycnocline intensity.By comparing the mode-2 nonlinear,dispersion coefficients and the Ursell numbers calculated based on the stratification associated with different kinds of ITs with the observation results,it is shown that the diurnal mode-2 IT plays a crucial role in the generation of the mode-2 ISWs.When the diurnal mode-2 IT interacts with the semidiurnal IT and causes a deeper and thinner pycnocline,the mode-2 ISWs are easily excited.

Is the small-scale turbulence an exclusive breaking product of oceanic internal waves

On the basis of the theoretical research results by the author and the literature published up to date, the analysis and the justification presented in this paper show that the breaking products of oceanic internal waves are not only turbulence, but also the fine-scale near-inertial internal waves （the oceanic reversible finestructure） for inertial waves and the internal solitary waves for internal tides respectively. It was found that the oceanic reversible finestructure may be induced by the effect of the horizontal component f （f = 2Ωcosφ） of the rotation vector on inertial waves. And a new instability of the theoretical shear and strain spectra due to the effect of f occurs at critical vertical wavenumber β c ≈ 0.1 cpm. It happens when the levels of shear and strain of the reversible finestructure are higher than those of inertial waves, which is induced by the effect of f along an ＂iso-potential-pycnal＂ of internal wave. If all breaking products of internal waves are taken into account, the average kinetic energy dissipation rate is an order of magnitude larger than the values of turbulence observed by microstructure measurements. The author’s theoretical research results are basically in agreement with those observed in IWEX, DRIFTER and PATCHEX experiments. An important impersonal fact is that on the mean temporal scale of thermohaline circulation these breaking products of internal waves exist simultaneously with turbulence. Because inertial waves are generated by winds at the surface, and internal tides are generated by strong tide-topography interactions, the analysis and justification in this paper support in principle the abyssal recipes Ⅱ：energetics of tidal and wind mixing by Munk Wunsch in 1998, in despite of the results of microstructure measurements for the turbulent kinetic energy dissipation rate and the diapycnal turbulent eddy diffusivity.

The influence of background waves on internal solitary waves after the transit of Typhoon Neast in the northern South China Sea

On the basis of the time series observations from a temperature chain and an acoustic Doppler current profiler on the continental shelf of the northern South China Sea, a sequence of internal solitary waves （ISWs） and background waves （BWs, including internal tides and near-inertial waves） on the continental shelf were captured simultaneously after the transit of Typhoon Neast in October 2011. These measurementsprovided a unique opportunity to explore the influence of BWs on the ISWs. The BWs appeared a conversion on the current strength and vertical mode structure during the observational period. The BWs were dominated by weak and mode-one waves before October 2 and then turned to strong and high-mode waves after that time. Meanwhile, the ISWs displayed different wave structures before and after October 2, which was closely related to BWs＇ changes. According to the current profiles of BWs, the high-mode wave structure with strong current could significantly strengthen the vertical shear of ISWs in the near-surface layer and promote the breaking of ISWs, and thus it may play an important role in affecting the background current condition.

Observations of semidiurnal M 2 internal tidal parametric subharmonic instability in the northeastern South China Sea

Near-diurnal vertically-standing waves with high vertical wavenumbers k z were observed in the velocity and shear fi elds from a set of 75-d long ADCP moored in the northeastern South China Sea(SCS)away from the“critical”latitude of 28.8°.These enhanced near-diurnal internal waves followed a fortnightly spring-neap cycle.However,they always happened during semidiurnal spring tides rather than diurnal springs although strong diurnal internal tides with the fortnightly spring-neap cycle were prevailing,suggesting that they were generated via subharmonic instability(PSI)of dominant semidiurnal M 2 internal tides.When two semidiurnal internal tidal waves with opposite vertical propagation direction intersected,both semidiurnal subharmonic and super harmonic waves were largely intensifi ed.The observed maximum diurnal velocity amplitudes were up to 0.25 m/s.The kinetic energy and shear spectra further suggested that frequencies of daughter waves were not always perfectly equal to M 2/2.The superposition of two daughter waves with nearly equal frequencies and nearly opposite k z in a PSI-triad leaded to the vertically-standing waves.

Plane wave fitting of the internal tidal sea-surface height signatures extracted from the TOPEX/Poseidon altimeter data along satellite tracks

The sea-surface height （SSH） signatures of internal tides extracted from the TOPEX/Poseidon （T/P） altimeter data along satellite tracks are fitted with superposition of several plane waves which have different wavenumber vectors. The key problem of plane wave fitting with iterative method is how to determine the initial value of wavenumber of each plane wave. The previous solving method is to analyze the internal tidal SSH signatures along each track with wavenumber spectrum. But it is found that the problem cannot be solved completely with the wavenumber spectrum analysis method only. The method based on the combination of wavenumber spectrum analysis method and the exhaustive method is proposed to determine the initial values of wavenumbers for iteration. Numerical results indicate that the proposed method is not only reasonable and feasible but also better than the previous method. The proposed method is an improvement of the previous one, which is beneficial to improving the precision of plane wave fitting of the T/P internal tidal SSH signatures and deepening the understanding of the internal tides in ocean.