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.     

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     

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.     

Distribution of vertical turbulent mixing parameter caused by internal tidal waves and solitary waves in the South Yellow Sea

Many observations show that in the Yellow Sea internal tidal waves (ITWs) possess the remarkable characteristics of internal Kelvin wave, and in the South Yellow Sea (SYS) the nonlinear evolution of internal tidal waves is one of the mechanisms producing internal solitary waves (ISWs), which is different from the generation mechanism in the case where the semidiurnal tidal current flows over topographic drops. In this paper, the model of internal Kelvin wave with continuous stratification is given, and an elementary numerical study of nonlinear evolution of ITWs is made for the SYS, using the generalized KdV model (GKdV model for short) for a continuous stratified ocean, in which the different effects of background barotropic ebb and flood currents are considered. Moreover, the parameterization of vertical turbulent mixing caused by ITWs and ISWs in the SYS is studied, using a parameterization scheme which was applied to numerical experiments on the breaking of ISWs by Vlasenko and Hutter in 2002. It is found that the vertical turbulent mixing caused by internal waves is very strong within the upper layer with depth less than about 30m, and the vertical turbulent mixing caused by ISWs is stronger than that by ITWs.     

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

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

INTERNAL TIDES, SOLITARY WAVES AND BORES IN SHALLOW SEAS

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

Estimates of global M_2 internal tide energy fluxes using TOPEX/POSEIDON altimeter data

TOPEX/POSEIDON altimeter data from October 1992 to June 2002 are used to calculate the global barotropic M2 tidal currents using long-term tidal harmonic analysis. The tides calculated agree well with ADCP data obtained from the South China Sea (SCS). The maximum tide velocities along the semi-major axis and semi-minor axis can be computed from the tidal ellipse. The global distribution of M2 internal tide vertical energy flux from the sea bottom is calculated based on a linear internal wave generation model. The global vertical energy flux of M2 internal tide is 0.96 TW, with 0.36 TW in the Pacific, 0.31 TW in the Atlantic and 0.29 TW in the Indian Ocean, obtained in this study. The total horizontal energy flux of M2 internal tide radiating into the open ocean from the lateral boundaries is 0.13 TW, with 0.06 TW in the Pacific, 0.04TW in the Atlantic, and 0.03 TW in the Indian Ocean. The result shows that the principal lunar semi-diurnal tide M2 provides enough energy to maintain the large-scale thermohaline circulation of the ocean.     

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 K1 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.     

A LAYERED NUMERICAL MODEL FOR SIMULATING THE GENERATION AND PROPAGATION OF INTERNAL TIDES OVER CONTINENTAL SLOPE I. MODEL DESIGN

A layered three-dimensional nonlinear numerical model was constructed to simulate the generation and propagation of internal tides over the continental slope. The simulation was split into external mode computation (EMC) and internal mode computation (IMC) to minimize the computational load. IMC was carried out once after EMC was implemented N times. As to EMC, a semi-implicit numerical scheme was applied in such a way that the pressure gradient terms and the velocity divergence terms were discretized semi-implicitly, but the other terms were discretized explicitly. Eulerian-Lagrangian explicit discretization was applied to the convective terms simultaneously. As a result, the stability of EMC did not depend on the wave celerity and time step was not limited by the CFL condition. More than that, use of the conjugate gradient accelerated Jacobi method further improved the computational efficiency of the model.     

A layered numerical model for simulating the generation and propagation of internal tides over continental slope

A layered three-dimensional nonlinear numerical model was constructed to simulate the generation and propagation of internal tides over the continental slope. The simulation was split into external mode computation (EMC) and internal mode computation (IMC) to minimize the computational load. IMC was carried out once after EMC was implemented N times. As to EMC, a semi-implicit numerical scheme was applied in such a way that the pressure gradient terms and the velocity divergence terms were discretized semi-implicitly, but the other terms were discretized explicitly. Eulerian-Lagrangian explicit discretization was applied to the convective terms simultaneously. As a result, the stability of EMC did not depend on the wave celerity and time step was not limited by the CFL condition. More than that, use of the conjugate gradient accelerated Jacobi method further improved the computational efficiency of the model. Contribution No. 3588 from the Institute of Oceanology, Chinese Academy of Sciences. Project 49676275 supported by NSFC and National Special Research Program 97-925-05-02.     

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.     

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.     

INTERNAL WAVE EIGENMODES AND THEIR WEAK NONLINEAR RESONANT INTERACTION IN A NONLINEARLY STRATIFIED FLUID- A PRELIMINARY THEORETICAL AND EXPERIMENTAL STUDY

A preliminary theoretical and experimental study was conducted on internal wave modes and their weak nonlinear resonant interaction in a nonlinearly stratified fluid . An asymptotical solution of the modes and a dispersion relation of internal waves in a stratified fluid with density profile similar to that in our experiment were obtained theoretically . The resonant-interaction mechanism to 2nd order approximation is also discussed . The resonant interaction of the 3rd and 4th mode internal waves excited by the unstable 1st mode wave is analyzed on the basis of data obtained by conductivity probes. The resonant-interaction condition, , is examined . It is shown that the resonant instability increases with pycnocline thickness and wave maker driving frequency .     

AN EXACT SOLUTION OF SUB-INERTIAL FREQUENCY BAROCLINIC WAVES

By using a coordinate transformation, an exact solution of internal tides with sub-inertial frequency isobtained when the bottom slope is linear and the Vaisala frequency is constant. Accordingly thedispersion relations of free waves are presented. This solution is suitable for general coastal low-frequencybaroclinic waves with zero alongshore wavenumber.     

A VERTICAL COORDINATE TRANSFORMATION FOR 3-D NUMERICAL MODELLING OF OCEAN CIRCULATION

A so called sine-sigma vertical coordinate transformation is proposed. A vertical implicit scheme is de-rived by using cubic-spline representation of vertical current profiles. The derived 3-D nurmericalmodel has been applied to simulate the water leved field and the vertical structures of wind-induced cur-rents in an enclosed rectangular region, and the tides in the Bohai Sea. The model is believed to besatisfactory after comparing its results with an analytical soclution and observed data from tidal staions.     

AN EXACT SOLUTION OF INTERNAL TIDES GENERATED AT CONTINENTAL SLOPE

By using a coordinate transformation,an exact solution of internal tides is obtained when the bot- tom slope is linear and the V(?)is(?)la frequency is constant.Consequently the dispersion relations of free waves are presented.Compared with Baines solution,the solution derived here is more consistent with experiment     

中国台湾地区海洋负荷潮汐对重力、位移、倾斜和应变固体潮观测的影响

利用最新的由卫星测高数据解算获得的Csr4.0全球海潮模型，中国近海海潮资料和标准地球模型负荷格林函数，采用积分格林函数方法研究了台湾地区10个台站的重力，位移，倾斜和应变固体潮观测中的海潮负荷效应。给出了4个主要潮波（O1，K1，M2，S2）的负荷振幅和相位，研究了负荷应变花分布特征，构制了台北站的负荷时变特征，数值结果说明，台湾地区各台站受海潮影响十分明显，因此在实施重力，位移，倾斜和应变固体潮观测中心必须考虑海潮负荷效应。     

A LAYERED NUMERICAL MODEL FOR SIMULATING THE GENERATION AND PROPAGAYION OF INTERNAL TIDES OVER CONTINENTAL SLOPE Ⅰ.MODEL DESIGN

mODUCnONSinceRattw(lwn)develoPedthefirstthcoreticalm0dl0ninternaltides,Inandifferentmodlshavebeenpresented.Theearlym0dlssuchastheonescreatedbyCoxandSandstorm(l962),Baines(l973,l982),etal.wereInainlylinear.Itwasnottmtilthe1980'sthatmodelsforstUdvingthenonlinearclertersofintemaltidesbegant0bedeveloPed.ThempicaloneswerethoseProposedorusedbyPinpeeetal.(1984),Maze(l987),WllmottandEdnds(l987),~(l994),andGerkema(l996).klthoughthesemodlscontribuegnailytoourundrstandingofthegenerationandproPag…     

Internal Tide Generation and Dissipation by Small Periodic Topography in Deep Ocean

Internal tides generated by a rough sea floor are an important source of mixing in the abyssal ocean. Two linear models are employed to evaluate the conversion rate from barotropic tides to internal tides and the energy distribution in each mode. Considering the periodicity of internal tides, the topography is represented by periodically distributed knife edges and sinusoidal ridges within one wavelength of mode-1 internal tides. The knife edges generate greater internal tides than the sinusoidal ridges due to their sharp shape, which approximates an extremely supercritical condition. Energy flux concentrates in modes whose numbers are multiples of the knife edge or ridge number. Then, a fully nonlinear model that integrates viscosity and diffusion is implemented, and its results are compared with those of the linear model. Internal wave rays generated in the nonlinear model show a distribution similar to the linear models' prediction. High dissipation rates coincide with the rays, suggesting that nonlinear wave-wave interaction is a dominant mechanism for internal tide dissipation in the abyssal ocean.     

Estimates of global M 2 internal tide energy fluxes using TOPEX/POSEIDON altimeter data

TOPEX/POSEIDON altimeter data from October 1992 to June 2002 are used to calculate the global barotropic M ₂ tidal currents using long-term tidal harmonic analysis. The tides calculated agree well with ADCP data obtained from the South China Sea (SCS). The maximum tide velocities along the semi-major axis and semi-minor axis can be computed from the tidal ellipse. The global distribution of M ₂ internal tide vertical energy flux from the sea bottom is calculated based on a linear internal wave generation model. The global vertical energy flux of M ₂ internal tide is 0.96 TW, with 0.36 TW in the Pacific, 0.31 TW in the Atlantic and 0.29 TW in the Indian Ocean, obtained in this study. The total horizontal energy flux of M ₂ internal tide radiating into the open ocean from the lateral boundaries is 0.13 TW, with 0.06 TW in the Pacific, 0.04TW in the Atlantic, and 0.03 TW in the Indian Ocean. The result shows that the principal lunar semi-diurnal tide M ₂ provides enough energy to maintain the large-scale thermohaline circulation of the ocean. Supported by the National Basic Research Program of China (973 Program, No. 2005CB422303), the International Cooperation Program (No. 2004DFB02700), and the National Natural Science Foundation of China (No. 40552002). The TOPEX/POSEIDON data are provided by Physical Oceanography Distributed Active Archive Center (PO DACC)