Depression and elevation internal solitary waves in a two-layer fluid and their forces on cylindrical piles

Both large amplitude depression and elevation internal solitary waves (ISWs) were observed on the continental shelf of the northwest South China Sea (SCS) during the Wenchang Internal Wave Experiment. In this study, we investigate the characteristics of depression and elevation ISWs based on comparisons between observational results and internal wave theories. It is suggested that the large amplitude depression wave is better represented by the extended Korteweg-de Vries (EKdV) theory than by the KdV model, whereas the large amplitude elevation wave is in better agreement with the KdV equation than with the EKdV theory. Wave-induced forces on a supposed small-diameter cylindrical pile by depression and elevation waves are also estimated using the internal wave theory and Morison formula. The wave-induced force by elevation ISWs is rarely reported in the literature. It is found that the force induced by the elevation wave differs significantly from that by the depression wave, and the elevation wave generally produces greater force on the pile in the lower water column than the depression wave. These results show that ISWs in the study area can present a serious threat to ocean engineering structures, and should not be ignored in the design of oil platforms and ocean operations.     

Highly nonlinear internal solitary waves over the continental shelf of the northwestern South China Sea

Large amplitude internal solitary waves (ISWs) often exhibit highly nonlinear effects and may contribute significantly to mixing and energy transporting in the ocean. We observed highly nonlinear ISWs over the continental shelf of the northwestern South China Sea (19°35′N, 112°E) in May 2005 during the Wenchang Internal Wave Experiment using in-situ time series data from an array of temperature and salinity sensors, and an acoustic Doppler current profiler (ADCP). We summarized the characteristics of the ISWs and compared them with those of existing internal wave theories. Particular attention has been paid to characterizing solitons in terms of the relationship between shape and amplitude-width. Comparison between theoretical prediction and observation results shows that the high nonlinearity of these waves is better represented by the second-order extended Korteweg-de Vries (KdV) theory than the first-order KdV model. These results indicate that the northwestern South China Sea (SCS) is rich in highly nonlinear ISWs that are an indispensable part of the energy budget of the internal waves in the northern South China Sea.     

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.     

Effects of tidal currents on nonlinear internal solitary waves in the South China Sea

The propagation and fission process of internal solitary waves (ISWs) with amplitudes of about 170 m are simulated in the northeast of the South China Sea (NSCS) by using the generalized Korteweg-de Vries (KdV) equation under continuous stratification. More attention is paid to the effects of the ebb and flood background currents on the fission process of ISWs. This kind of background current is provided by the composed results simulated in terms of monthly mean baroclinic circulation and barotropic tidal current. It is found that the obtained relation of the number of fission solitons to the water depth and stratification is roughly in accordance with the fission law derived by Djordjevic and Redekopp in 1978; however, there exists obvious difference between the effects of the ebb and flood background currents on the wave-lengths of fission solitons (defined as the distance between two neighboring peaks of ISWs). The difference in nonlinearity coefficient α between the ebb and flood background currents is a main cause for the different wave-lengths of fission solitons.     

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.     

Characteristics of nonlinear internal waves observed in the northern South China Sea

The South China Sea (SCS) is one of the most active areas of internal waves. We undertook a program of physical oceanography in the northern South China Sea from June to July of 2009, and conducted a 1-day observation from 15:40 of June 24 to 16:40 of June 25 using a chain of instruments, including temperature sensors, pressure sensors and temperature-pressure meters at a site (117.5°E, 21°N) northeast of the Dongsha Islands. We measured fluctuating tidal and subtidal properties with the thermistor-chain and a ship-mounted Acoustic Doppler Current Profiler, and observed a large-amplitude nonlinear internal wave passing the site followed by a number of small ones. To further investigate this phenomenon, we collected the tidal constituents from the TPXO7.1 dataset to evaluate the tidal characteristics at and around the recording site, from which we knew that the amplitude of the nonlinear internal wave was about 120 m and the period about 20 min. The horizontal and vertical velocities induced by the soliton were approximately 2 m/s and 0.5 m/s, respectively. This soliton occurred 2–3 days after a spring tide.     

Internal solitary waves on the southwest shelf of Dongsha Island observed from mooring ADCP

Internal solitary waves(ISWs) are frequently observed in the area between Dongsha Island(DI) and Taiwan Island. However, there have been few in-situ observations southwest of DI. To improve our knowledge of ISWs in this area, we observed the ISWs over the continental shelf(115.4°E, 20.3°N) from Aug. 29 to Oct. 10, 2011 with temperature sensors and an acoustic Doppler current profiler(ADCP). The observations showed that the a fully developed ISW produced a current whose maximum westward velocity was 0.92 m/s and maximum northward velocity was 0.47 m/s. During the 41-day observation period the ISWs appeared for three periods with about 7-day gaps between each period. During each day, two types of ISWs were observed. The first type of wave arrived regularly diurnally at the same time each day, with a similar pattern to that of the type- a wave identified by Ramp et al.(2004). The second type arrived about 12 h after the first type and was delayed about 1 hour each day; this wave type was related to the type- b wave. Thus, our observations confirmed that both type- a and type- b waves can reach the area southwest of the DI. Moreover, the waves observed by the mooring propagated toward the directions of 270°–315° clockwise from true north, indicating obvious refraction from uneven topography around DI.     

Study on internal waves generated by tidal flow over critical topography

Resonance due to critical slope makes the internal wave generation more effectively than that due to supercritical or subcritical slopes(Zhang et al., 2008). Submarine ridges make a greater contribution to ocean mixing than continental margins in global oceans(Müller, 1977; Bell, 1975; Baines, 1982; Morozov, 1995). In this paper, internal wave generation driven by tidal flow over critical topography is examined in laboratory using Particle Image Velocimetry(PIV) and synthetic schlieren methods in synchrony. Non-tidal baroclinic velocities and vertical isopycnal displacements are observed in three representative regions, i.e., critical, outward-propagating, and reflection regions. Temporal and spatial distributions of internal wave rays are analyzed using the time variations of baroclinic velocities and vertical isopycnal displacement, and the results are consistent with those by the linear internal wave theory. Besides, the width of wave beam changes with the outward propagation of internal waves. Finally, through monitoring the uniformly-spaced 14 vertical profiles in the x-z plane, the internal wave fields of density and velocity fields are constructed. Thus, available potential energy, kinetic energy and energy fluxes are determined quantitatively. The distributions of baroclinic energy and energy fluxes are confined along the internal wave rays. The total depth averaged energy and energy flux of vertical profiles away from a ridge are both larger than those near the ridge.     

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.     

Radial tidal current field in a semi-enclosed rectangular basin: formation and evolution

The radial tidal current field accounts for the formation of the radial sand ridges in the South Yellow Sea. Understanding the formation and evolution of this radial tidal current field is vital to assessing the morphodynamic features in the area. A semi-enclosed rectangular basin with and without a coastal barrier was schematized from the topography of the Bohai Sea and Yellow Sea. The 2D tidal current field in this basin was simulated using the DELFT3D-FLOW model. The concept of tidal wave refraction, which highlights the effect of the sloped or stepped submarine topography on the propagation of the tidal waves, was introduced to explain the formation of the radial tidal current field. Under the effect of tidal wave refraction, co-phase lines of the counterclockwise rotating tidal wave and incident tidal wave are transformed into clockwise and counterclockwise deflections, respectively, leading to the convergence and divergence of the flow field. Regardless of whether a coastal barrier exists or not, the outer radial tidal current field might emerge over certain topography. The responses of the radial tidal current field in this basin to the environmental variations such as coastline changes and bottom erosions were discussed. Results show that local protrusion near the focal point of the radial tidal current field will have limited effects on the location of the tidal system. However, a remarkable shift of the amphidromic point toward the entrance and central axis of this basin and a movement of the focal point of the radial tidal current field toward the entrance could be caused by the significant seaward coastline advance and submarine slope erosion.     

Propagation of internal waves up continental slope and shelf

In a two-dimensional and linear framework, a transformation was developed to derive eigensolutions of internal waves over a subcritical hyperbolic slope and to approximate the continental slope and shelf. The transformation converts a hyperbolic slope in physical space into a flat bottom in transform space while the governing equations of internal waves remain hyperbolic. The eigensolutions are further used to study the evolution of linear internal waves as it propagates to subcritical continental slope and shelf. The stream function, velocity, and vertical shear of velocity induced by internal wave at the hyperbolic slope are analytically expressed by superposition of the obtained eigensolutions. The velocity and velocity shear increase as the internal wave propagates to a hyperbolic slope. They become very large especially when the slope of internal wave rays approaches the topographic slope, which is consistent with the previous studies.     

The suspended sediment concentration distribution in the Bohai Sea, Yellow Sea and East China Sea

The distribution of the suspended sediment concentration (SSC) in the Bohai Sea, Yellow Sea and East China Sea (BYECS) is studied based on the observed turbidity data and model simulation results. The observed turbidity results show that (i) the highest SSC is found in the coastal areas while in the outer shelf sea areas turbid water is much more difficult to observe, (ii) the surface layer SSC is much lower than the bottom layer SSC and (iii) the winter SSC is higher than the summer SSC. The Regional Ocean Modeling System (ROMS) is used to simulate the SSC distribution in the BYECS. A comparison between the modeled SSC and the observed SSC in the BYECS shows that the modeled SSC can reproduce the principal features of the SSC distribution in the BYECS. The dynamic mechanisms of the sediment erosion and transport processes are studied based on the modeled results. The horizontal distribution of the SSC in the BYECS is mainly determined by the current-wave induced bottom stress and the fine-grain sediment distribution. The current-induced bottom stress is much higher than the wave-induced bottom stress, which means the tidal currents play a more significant role in the sediment resuspension than the wind waves. The vertical mixing strength is studied based on the mixed layer depth and the turbulent kinetic energy distribution in the BYECS. The strong winter time vertical mixing, which is mainly caused by the strong wind stress and surface cooling, leads to high surface layer SSC in winter. High surface layer SSC in summer is restricted in the coastal areas.     

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.     

Energy dissipation through wind-generated breaking waves

Wave breaking is an important process that controls turbulence properties and fluxes of heat and mass in the upper oceanic layer.A model is described for energy dissipation per unit area at the ocean surface attributed to wind-generated breaking waves,in terms of ratio of energy dissipation to energy input,windgenerated wave spectrum,and wave growth rate.Also advanced is a vertical distribution model of turbulent kinetic energy,based on an exponential distribution method.The result shows that energy dissipation rate depends heavily on wind speed and sea state.Our results agree well with predictions of previous works.     

The sensitivity of numerical simulation to vertical mixing parameterization schemes: a case study for the Yellow Sea Cold Water Mass

The vertical mixing parameterization scheme,by providing the effects of some explicitly missed physical processes and more importantly closing the energy budgets,is a critical model component and therefore imposes significant impacts on model performance.The Yellow Sea Cold Water Mass(YSCWM),as the most striking and unique phenomenon in the Yellow Sea during summer,is dramatically affected by vertical mixing process during its each stage and therefore seriously sensitive to the proper choice of parameterization scheme.In this paper,a hindcast of YSCWM in winter of 2006 was implemented by using the Regional Ocean Modeling System(ROMS).Three popular parameterization scheme s,including the level2.5 Mellor-Yamada clo sure(M-Y 2.5),Generic Length Scale clo sure(GL S) and K-Profile Parameterization(KPP),were tested and compared with each other by conducting a series of sensitivity model experiments.The influence of different parameterization scheme s on modeling the YSCWM was then carefully examined and assessed based on these model experiments.Although reasonable thermal structure and its seasonal variation were well reproduced by all schemes,considerable differences could still be found among all experiments.A warmer and spatially smaller simulation of YSCWM,with very strong the rmocline,appeared in M-Y 2.5 experiment,while a spatially larger YSCWM with shallow mixed layer was found in GLS and KPP schemes.Among all the experiments,the discrepancy,indicated by core temperature,appeared since spring,and grew gradually by the end of November.Additional experiments also confirmed that the increase of background diffusivity could effectively weaken the YSCWM,in either strength or coverage.Surface wave,another contributor in upper layer,was found responsible for the shrinkage of YSCWM coverage.The treatment of wave effect as an additional turbulence production term in progno stic equation was shown to be more superior to the strategy of directly increasing diffusivity for a coastal region.     

Wave breaking on turbulent energy budget in the ocean surface mixed layer

As an important physical process at the air-sea interface, wave movement and breaking have a significant effect on the ocean surface mixed layer （OSML）. When breaking waves occur at the ocean surface, turbulent kinetic energy （TKE） is input downwards, and a sublayer is formed near the surface and turbulence vertical mixing is intensively enhanced. A one-dimensional ocean model including the Mellor-Yamada level 2.5 turbulence closure equations was employed in our research on variations in turbulent energy budget within OSML. The influence of wave breaking could be introduced into the model by modifying an existing surface boundary condition of the TKE equation and specifying its input. The vertical diffusion and dissipation of TKE were effectively enhanced in the sublayer when wave breaking was considered. Turbulent energy dissipated in the sublayer was about 92.0% of the total depth-integrated dissipated TKE, which is twice higher than that of non-wave breaking. The shear production of TKE decreased by 3.5% because the mean flow fields tended to be uniform due to wave-enhanced turbulent mixing. As a result, a new local equilibrium between diffusion and dissipation of TKE was reached in the wave-enhanced layer. Below the sublayer, the local equilibrium between shear production and dissipation of TKE agreed with the conclusion drawn from the classical law-of-the-wall （Craig and Banner, 1994）.     

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 .     

Tidal Effects on the Bottom Thermal Front of North Yellow Sea Cold Water Mass near Zhangzi Island in Summer 2009

Three seabed-mounted TD/CTD chains and two upward-looking acoustic Doppler current profilers(ADCPs) in the southwest of Zhangzi Island are used and a simultaneous cruise observation in the northern North Yellow Sea(NYS) is conducted to study temperature variation in the bottom thermal front zone of the NYS Cold Water Mass(NYSCWM) during the summer of 2009. In the flood-ebb tidal cycles, the bottom temperature decreases(increases) during flood(ebb) tides, which are dominated by the tidal-current induced horizontal advection. The ebb tide-induced temperature increase is larger than the flood tide-induced temperature decrease due to seasonal warming. In the spring-neap tidal cycles, the temperature and the vertical temperature structure show notable fortnightly variation from 16 July to 25 August. The bottom temperature increases from neap to spring tides and decreases from spring to neap. The Richardson number demonstrates strengthened vertical mixing during spring tides but enhanced stratification during neap tides. The spring-neap variation in vertical shear caused by tidal current is the dominant factor that induces the fortnightly variation in vertical mixing and thus bottom temperature.     

Nonlinear modulation of the short internal waves in the weakly stratified ocean

A nonlinear evolution equation of 2-D short internal waves under condition of weak stratification—cubic Schrödinger equation—is derived by using the reductive perturbation method. Because αβ<0 in the Schrödinger equation, in the linear system the sideband perturbation for the harmonic wave modulation is neutrally stable. At the same time, there is also a sort of wave packet.—KdV envelope soliton. In the nonlinear system the dark soliton is obtained under condition of weak stratification. It is shown that the vertical perturbation of the Brunt-Väìsälä frequency plays a role in forming the KdV envelope soliton and dark soliton.     

Numerical simulation and preliminary analysis of typhoon waves during three typhoons in the Yellow Sea and East China Sea

In this study, typhoon waves generated during three typhoons(Damrey(1210), Fung-wong(1416), and Chan-hom(1509)) in the Yellow Sea and East China Sea were simulated in a simulating waves nearshore(SWAN) model, and the wind forcing was constructed by combining reanalyzed wind data with a Holland typhoon wind model. Various parameters, such as the Holland fitting parameter(B) and the maximum wind radius(R), were investigated in sensitivity experiments in the Holland model that affect the wind field construction. Six different formulations were considered and the parameters determined by comparing the simulated wind results with in-situ wind measurements. The key factors affecting wave growth and dissipation processes from deep to shallow waters were studied, including wind input, whitecapping, and bottom friction. Comparison with in-situ wave measurements suggested that the KOMEN scheme(wind input exponential growth and whitecapping energy dissipation) and the JONSWAP scheme(dissipation of bottom friction) resulted in good reproduction of the significant wave height of typhoon waves. A preliminary analysis of the wave characteristics in terms of wind-sea and swell wave revealed that swell waves dominated with the distance of R to the eye of the typhoon, while wind-sea prevailed in the outer region up to six to eight times the R values despite a clear misalignment between wind and waves. The results support the hypothesis that nonlinear wave-wave interactions may play a key role in the formation of wave characteristics.