Directional spectra and eigen-solutions of vertically standing wavemodes of internal waves in shallow seas

Some approximate formulas, based on the internal- wave directional spectral model established by Schott and Willebrand (1973), of vertically standing wavemode eigenfunctions and a dispersion relation of internal waves in shallow seas are presented. An optimization method to estimate internal wave directional spectra is described and the confidence interval expression of the estimates is established. The GM spectral model of oceanic internal waves cannot be used in shallow seas (01 bers, 1983). Internal waves in shallow seas have two origins: oceanic (those generated in and propagating from the deep sea and ocean) and local (Phillips, 1977). As both reveal obvious propagation orientations, it is important to investigate the directional properties of the internal wave field. Though cross correlation function or cross-spectrum analyses can reveal the directional properties in some degree (Fang et al., 1984, and Fang, 1987), internal- wave directional spectrum analysis can further estimate the main propagation directions of wave components with different modenumbers and frequencies. So the latter is a more effective analysis tool. Because internal- wave directional spectrum analysis requires high quality data and long computer time, there are very few study reports so far on this subject. Among them. Schott and Willebrands' (1973) work is noteworthy. On the supposition, of linearization, they derived an internal- wave directional spectrum model. Internal-wave directional-spectra in shallow seas are investigated in the present study with their work as reference. Project supported by the National Natural Science Foundation of China.     

Laboratory Experiments on an Internal Solitary Wave over a Triangular Barrier

Laboratory experiments were conducted to investigate the evolution of interfacial internal solitary waves(ISWs) incident on a triangular barrier. ISWs with different amplitudes were generated by gravitational collapse. The ISW energy dissipation and turbulence processes were calculated as waves passed over the triangular barrier. Experimental results showed that ISWs were reflecting back off the triangular barrier, and shoaling ISWs led to wave breaking and mixing when waves propagated over the obstacle. Wave instability created the dissipation of energy as it was transmitted from waves to turbulence. The rate of ISW energy dissipation, the maximum turbulent dissipation, and the buoyancy diffusivity linearly increased with the increase in the incident wave energy.     

Modeling of low-frequency seismic waves in a shallow sea using the staggered grid difference method

Elastic waves in the seabed generated by low-frequency noise radiating from ships are known as ship seismic waves and can be used to detect and identify ships.To obtain the propagation characteristics of ship seismic waves,an algorithm for calculating seismic waves at the seafl oor is presented based on the staggered-grid fi nite diff erence method.The accuracy of the algorithm was tested by comparison with analytical solutions.Numerical simulation of seismic waves generated by a low-frequency point sound source in a typical shallow sea environment was carried out.Using various source frequencies and locations in the numerical simulation,we show that the seismic waves in the near fi eld are composed mostly of transmitted S-waves and interface waves while transmitted P-waves are weak near the seafl oor.However,in the far fi eld,the wave components of the seismic wave are mainly normal modes and interface waves,with the latter being relatively strong in the waveforms.As the source frequency decreases,the normal modes become smaller and the interface waves dominate the time series of the seismic waves.     

Response of internal waves to 2005 Typhoon Damrey over the northwestern shelf of the South China Sea

Continuous observation of sea water temperature and current was made at Wenchang Station (19°35′N, 112°E) in 2005. The data collected indicate vigorous internal waves of both short periods and tidal and near-inertial periods. The temperature and current time series during 18-30 September were examined to describe the upper ocean internal wave field response to Typhoon Damrey (0518). The strong wind associated with the typhoon, which passed over the sea area about 45 km south of Wenchang Sta- tion on 25 September, deepened the mixed layer depth remarkably. It decreased the mixed layer temperature while increasing the deep layer temperature, and intensified the near-inertial and high-frequency fluctuations of temperature and current. Power spectra of temperature and current time series indicate significant deviations from those obtained by using the deep ocean internal wave models characterized by a power law. The frequency spectra were dominated by three energetic bands: around the inertial frequency (7.75× 10-6 Hz), tidal frequencies (1.010-25 to 2.4×10-5 Hz), and between 1.4×10-4 and 8.3 × 10-4 Hz. Dividing the field data into three phases (before, during and after the typhoon), we found that the typhoon enhanced the kinetic energy in nearly all the frequency bands, es- pecially in the surface water. The passage of Damrey made a major contribution to the horizontal kinetic energy of the total surface current variances. The vertical energy density distribution, with its peak value at the surface, was an indication that the energy in- jected by the strong wind into the surface current could penetrate downward to the thermocline.     

An investigation of the properties of low-frequency internal waves in the northeastern China Seas

A simple and practical method for separating low-frequency internal waves from low-frequency barotropic waves was employed to analyze the observation data. Analysis of some data gathered in the northestern China Seas revealed strong semidiurnal internal tides and near-inertial internal waves at the stations in the East China Sea and near-inertial waves but no semidiurnal internal tides at the station in the centre of the Yellow Sea. The geographic properties of low-frequency internal waves in the region are discussed primarily on the basis of the mechanism of internal tide generation on the continental shelfbreak, and the mechanisms of local generation and global generation. Project supported by the National Natural Science Foundation of China.     

STATISTICAL PROPERTIES OF HIGH-FREQUENCY INTERNAL WAVES IN QINGDAO OFFSHORE AREA OF THE YELLOW SEA

Densely-sampled thermistor chain data obtained from a shallow-water acoustics experiment in the Yellow Sea off the coast of Qingdao were analyzed to examine the statistical properties of the 6 to 520 cpd frequency band internal waves observed. The negative skewness coefficients and the greaterthan-3 kurtosis coefficients indicated non-Gaussianity of the internal waves. The probability distributions were negatively skewed and abnormally high peaks. Nonlinear properties, as exemplified by the asymmetric waveshapes of the internal waves in the offshore area are described quantitatively.     

A continuously stratified nonlinear model for internal solitary waves in the northern South China Sea

A continuously stratified nonlinear model is set up to study the impact of topographical character on the generation of internal solitary waves over a sill by tidal flow. One of the reasons why almost all of the generated internal solitary waves propagate westward in the northern South China Sea is explained. The model simulations describe the generation and propagation of internal waves well. When the strength of imposed barotropic tides and the water stratification stay unchanged, the steepness of the sill slope can control both (a) whether or not the waves induced over a sill by tidal flow are linear internal waves or nonlinear internal solitary waves, and (b) the amplitude of the internal solitary waves generated. If the steepness of the sill is asymmetric, the nonlinear internal solitary waves may be induced on the steeper side of the sill. These conclusions are supported by a numerical experiment with a monthly-mean stratification and an actual seafloor topography from the Luzon Strait.     

Study on suspended matter in seawater in the Southern Yellow Sea

Distribution of suspended matter in seawater in the Southern Yellow Sea is investigated in five regions: 1) the Northern Jiangsu bank, the highest TSM (total suspended matter) content region; 2) the high TSM content region off the Changjiang River mouth; 3) the high TSM content region off the Chengshan Cape; 4) the low TSM region off Haizhou Bay; 5) the central part of the Southern Yellow Sea, a low TSM content region. The vertical distribution of TSM is mainly characterized by a spring layer of suspended matter, written as “suspended-cline” whose genesis is related to storms in winter. In this paper, non-combustible components and grain sizes in suspended matter, relationship between suspended matter and bottom sediments, and salinity in seawater are described. Investigation result shows that, in this area, suspended matter comes mainly from resuspended bottom sediment and secondarily from present discharge loads from rivers and biogenic materials. Discharged sediments from the Huanghe River move around the Chengshan Cape and affect the northwestern region of this area. Sediments from the Changjiang River affect only the southern part and have little or no direct influence on the central deep region. Wave is the main factor affecting distribution of suspended matter. Water depth controls the critical depth acted on by waves. The cold water mass in the central region limits horizontal and vertical dispersions of terrigenous materials. Suspended matter here has the transitional properties of the epicontinental sea. Its concentration and composition are different from those of a semi-closed sea (such as the Bohai Sea) and those of the East China Sea outer continental shelf or those near oceanic areas.     

Development of a High-Resolution Coastal Circulation Model for the Ocean Observatory in Lunenburg Bay

An advanced ocean observatory has been established in Lunenburg Bay of Nova Scotia, Canada as part of an interdisciplinary research project of marine environmental prediction. The development of a high-resolution coastal circulation model is one of important components of the observatory. The model horizontal resolution is 60m and the vertical resolution is about 1 m. The coastal circulation model is used to simulate the semi-diurnal tidal circulation and associated nonlinear dynamics with the M2 forcing specified at the model open boundaries. The model is also used to simulate the storm-induced circulation in the bay during Hurricane Juan in September 2003, with the model forcing to be the combination of tides and remotely generated waves specified at the model open boundaries and wind stress applied at the sea surface. The model results demonstrate strong interactions between the local wind stress, tidal forcing, and remotely generated waves during this period. Comparison of model results with the surface elevation and current observations demonstrates that the coastal circulation model has reasonable skills in simulating the tidal and storm-induced circulation in the bay.     

Numerical simulation and preliminary analysis on ocean waves during Typhoon Nesat in South China Sea and adjacent areas

Using the wave model WAVEWATCH III(WW3), we simulated the generation and propagation of typhoon waves in the South China Sea and adjacent areas during the passage of typhoon Nesat(2011). In the domain 100°–145°E and 0°–35°N, the model was forced by the cross-calibrated multi-platform(CCMP) wind fi elds of September 15 to October 5, 2011. We then validated the simulation results against wave radar data observed from an oil platform and altimeter data from the Jason-2 satellite. The simulated waves were characterized by fi ve points along track using the Spectrum Integration Method(SIM) and the Spectrum Partitioning Method(SPM), by which wind sea and swell components of the 1D and 2D wave spectra are separated. There was reasonable agreement between the model results and observations, although the WW3 wave model may underestimate swell wave height. Signifi cant wave heights are large along the typhoon track and are noticeably greater on the right of the track than on the left. Swells from the east are largely unable to enter the South China Sea because of the obstruction due to the Philippine Islands. During the initial stage and later period of the typhoon, swells at the fi ve points were generated by the propagation of waves that were created by typhoons Haitang and Nalgae. Of the two methods, the 2D SPM method is more accurate than the 1D SIM which overestimates the separation frequency under low winds, but the SIM method is more convenient because it does not require wind speed and wave direction. When the typhoon left the area, the wind sea fractions decreased rapidly. Under similar wind conditions, the points located in the South China Sea are affected less than those points situated in the open sea because of the infl uence of the complex internal topography of the South China Sea. The results reveal the characteristic wind sea and swell features of the South China Sea and adjacent areas in response to typhoon Nesat, and provide a reference for swell forecasting and offshore structural designs.     

Density Perturbation and Energy Flux of Internal Waves from Velocity Data

Internal waves play a crucial role in ocean mixing, and density perturbation and energy flux are essential quantities to investigate the generation and propagation of internal waves. This paper presents a methodology for calculating density perturbation and energy flux of internal waves only using a velocity field that is based on linearized equations for internal waves. The method was tested by numerical simulations of internal waves generated by tidal flowing over a Gaussian topography in a stratified fluid. The density perturbations and energy fluxes determined using our method that only used velocity data agreed with density perturbations and energy fluxes determined by the equation of state based on temperature data. The mean relative error (MRE) and root mean square error (RMSE) between the two methods were lower than 5% and 10% respectively. In addition, an experiment was performed to exam our method using the velocity field measured by Particle Image Velocimetry (PIV), and the setup of the experiment is consistent with the numerical model. The results of the experiments calculated by the methods using PIV data were also generally equal to those of the numerical model.     

Wind-forced equatorial wave dynamics of the Pacific Ocean during 2014/2015 and 2015/2016 E1 Ni?o events

The equatorial wave dynamics of interannual sea level variations between 2014/2015 and2015/2016 El Nino events are compared using the Laboratory of Numerical Modeling for Atmospheric Sciences and Geophysical Fluid Dynamics,Institute of Atmospheric Physics Climate Ocean Model(LICOM) forced by the National Centers for Environmental Prediction(NCEP) reanalysis I wind stre s s and heat flux during 2000-2015.In addition,the LICOM can reproduce the interannual variability of sea surface temperature anomalies(SSTA) and sea level anomalies(SLA) along the equator over the Pacific Ocean in comparison with the Hadley center and altimetric data well.We extracted the equatorial wave coefficients of LICOM simulation to get the contribution to SLA by multiplying the meridional wave structure.During 2014/2015 El Nino event,upwelling equatorial Kelvin waves from the western boundary in April2014 reach the eastern Pacific Ocean,which weakened SLA in the eastern Pacific Ocean.However,no upwelling equatorial Kelvin waves from the western boundary of the Pacific Ocean could reach the eastern boundary during the 2015/2016 El Nino event.Linear wave model results also demonstrate that upwelling equatorial Kelvin waves in both 2014/2015 and 2015/2016 from the western boundary can reach the eastern boundary.However,the contribution from stronger westerly anomalies forced downwelling equatorial Kelvin waves overwhelmed that from the upwelling equatorial Kelvin waves from the western boundary in 2015.Therefore,the western boundary reflection and weak westerly wind burst inhibited the growth of the 2014/2015 El Nino event.The disclosed equatorial wave dynamics are important to the simulation and prediction of ENSO events in future studies.     

A numerical study on the generation of a distinct type of nonlinear internal wave packet in the South China Sea

A distinct type of nonlinear internal-wave packet, with the largest internal solitary wave in the middle of the packet, was regularly observed in the South China Sea during the Asian Seas International Acoustics Experiment in 2001. Data analysis shows that the occurrence of the distinct internal wave packet is closely related with the occurrence of lower-high internal tides; the internal tides are mixed in the experimental area and, thus, there is diurnal inequality between the heights of two neighboring internal tides. Modeling of internal tides and internal solitary waves in a shoaling situation suggests that this type of wave packet can be generated in the South China Sea by the large shoaling of internal solitary waves and internal tides. Both the internal solitary waves and the internal tides come from the direction of Luzon Strait. The initial large internal solitary waves contribute to the occurrence of the largest internal solitary wave in the middle of the packet and the waves behind the largest internal solitary wave, while the shoaling internal tides bring about the nonlinear internal waves in front of the largest internal solitary wave via interaction with the local shelf topography.     

PROGRESS OF STUDIES ON THE INTERNAL TIDE GENERATED BY THE PASSAGE OF BAROTROPIC TIDE OVER CONTINENTAL SHELF/SLOPE

Various aspects of studies on internal tides are reviewed .Both beam-like structure and modal structure of internal tides may exist in the ocean . Bottom intensifications are caused by many factors .e.g. upstream blocking , which is the result of nonlinear interaction among waves . The energy may decay very fast so that internal tides are mostly locally generated .Internal tides may have considerable residual currents.In a 3-D frame, numerical study revealed that internal waves may interfere with each other to cause strong motions fer from the generation sources.The mechanism that determines how the lee waves break to form various nonlinear waves such as solitary waves, hydraulic jumps and internal surges or bores remains unclear. Analytic study is difficult , so numerical method may be effective . A radiation condition on the open boundary must be employed. A complete 3-D model may gain interesting result.Study on internal tides in China is limited to field observations and data analysis .     

A TWO-DIMENSIONAL VORTICITY MODEL OF INTERNAL TIDES GENERATED ON THE CONTINENTAL SHELF/SLOPE

A two-dimensional spectral-difference mode (with vorticity and density equations) of internal tides isdeveloped for studying the genration and propagration of internal tides generated at the continentalshelf/slope. In general, internal tides propagate seaward in deep sea regions and shoreward on the shelf,and are dissipated rapidly. When the Vaisala frequency decreases vertically, waves may be mostly limited to thecontinental slope region. in deep sea region, motions may have either boam-like structure or modal structure,depending on the stratification strerigth and structure, whereas a modal structure may always exist onthe shelf. Waves show strong bottom intensification on the slope when strong stratification exists on thebottom. The barotropic tidal advection may affed the temporal character of internal tides at thecontinental slope, shelf break and shelf regions. but may have little influence on the energy density and energy flux of internal tides. ln the case of strong stratification, waverforms of     

Growth,reproduction & population structure of the freshwater crabSinopotamon yangtsekiense bott, 1967, from Zhejiang,China

Monthly investigations were mae on the population of Chinese freshwater crab,Sinopotamon yangtsekiense Bott, 1967 from April, 1984 to March, 1985. The data on 4413 specimens show that the growth was affected mainly by temperature. During the April to November growth period, the crabs' major development occurred from June through October. One year was required for a fine white oocyte to develop into a mature egg. The reproduction period was June–October. Females bearing eggs were taken from June–August, and crabs with young were found from July–October. The females reproduced once a year but could for more than one year. The number of eggs carried by a female varied greatly according to the size of the crab, ranging from 30 to 100 eggs. New-born crabs become mature after 1–2 years. The sex ratio was approximately 1∶1 in the overall population. However, the larger crabs are predominantly male. The age distribution ofS. yangtsekinese was estimated from size frequency histograms. There were more adult crabs (over 70%) from June to October and more immature crabs (over 50%) from November to May.     

Mechanism of sea ice formation based on comprehensive observation data in Liaodong Bay,China

Sea ice disaster is one of the principal natural hazards that affect some coastal areas of China, and the formation of ice cover in a wave field has important characteristics. However, analysis of the mechanism in which waves affect the thermodynamic process of sea ice is lacking, and the influence of waves is not taken into consideration in numerical models of sea ice, largely because of a lack of simultaneous observations of waves and sea ice. Using observational data of the sea ice cycle in the coastal waters of Liaodong Bay(China), we analyzed the characteristics of hydrology, meteorology, and sea ice thickness during the formation of sea ice, and explored the changes in the interrelationships among heat fluxes, waves, and sea ice under actual sea conditions. The results could provide a decision-making support as a reference to the establishment and improvement of China's early warning system to sea ice disasters, and the protection of ice drilling operations and production platform safety.     

Nonlinear interactions among internal tidal waves in the northeastern South China Sea

We used a set of 75-day long ADCP data from the northeastern South China Sea (SCS) to investigate nonlinear interactions among freely propagating internal tidal waves. The kinetic energy spectra displayed significant peaks at some higher tidal frequencies, such as O₁M₂ (O₁+M₂), and M₄ (M₂+M₂), where O₁ is the lunar diurnal internal tide, M₂ is the lunar semidiurnal internal tide, and M₄ is the first higher harmonic frequency of M₂. These higher tidal harmonic frequency peaks, as well as the fundamental tidal harmonic peaks, show a σ ^−2.3 spectral falloff rate with frequency. In addition, we explored the possible generation mechanism of higher tidal harmonics. Analysis on the rotary and bicoherence spectra suggests that strong forced non-resonant interaction induced by nonlinear advections was the dominant physical mechanism that induced these higher tidal harmonics. Moreover, the energetic, freely propagating semidiurnal (M₂) internal tidal wave played the most crucial role in these interactions. These results indicate that strong nonlinear forced non-resonant interactions among internal tides can be one of the processes responsible for the redistribution of energy in the internal wave spectrum.     

A three-dimensional nonlinear hydrodynamic model with variable eddy viscosity in shallow seas

Considerable scientific and practical interest exists in ascertaining the dynamic processes in shallow seas. This is especially true for China having a vast area of shallow seas. To simulate the observed data and study the dynamical mechanism of waves and currents in shallow seas a numerical model is developed in this paper. In view of the notable nonlinearity of shallow sea waves and currents, and in order to solve the current distribution in the vertical direction, and to examine the effect of variable eddy viscosity, the model proposed is a three-dimensional nonlinear one with variable eddy viscosity. The eddy viscosity can be considered as a physically acceptable arbitrary function of depth, which is realized in terms of a Sturm-Liouville System. The currents are expressed by using the eigenfunctions satisfying the Sturm-Liouville System just mentioned. A boundary-value problem (or an initio-boundary-value problem) of free surface elevation is derived. And then, the application of the proposed shallow sea model to nonlinear tides, ultra-shallow water storm surges and steady circulation is given, respectively. Finally, a generalized linear law between the bottom friction and the transport is derived. This paper was presented at the Joint Oceanographic Assembly (J.O.A.) held at Halifax, Canada, August 2–13, 1982, and included in “Poster Abstract” Vol. I.     

Objective analysis and classification of the ten-day mean sea surface temperature variation in the East China Sea using singular value decomposition technique

The seasonal changes of the ten-day mean sea surface temperature in the East China Sea for the years 1953–1972 were studied using the singular value decomposition technique. Main results obtained are as follows: In the singular vector analysis of the ten-day mean sea surface temperature in the East China Sea, the first three singular vectors (or seasonal march functions) account for 97.76% of the variance of the data. The geographical distribution in the weightings (or spatial pattern functions) on these vectors shows a remarkable regional organization. An objective classification of the surface water mass in the East China Sea was based on the mode of its seasonal temperature changes. Contribution No. 801 from the Institute of Oceanology, Academia Sinica. An abstract of this paper was presented at an IAPSO Session of XVII IUGG held at Canberra, Australia, December 1979.