NLS EQUATION OF INTERNAL WAVES IN WEAKLY STRATIFIED OCEAN

The NLS (Non-Linear Schr(?)dinger) equation of internal waves in a wekly stratified ocean is der-ived in phase coordnates in terms of the RPM (Reductive Perturbation Method). It was shown thatwhen AB>0 there exist modulation forms of envelope soliton and dn, and tha when AB<0 there arethree modulation forms dark soliton, sn and cn. Only if K~2>B/A(?) . the side-band perturbation is stable,otherwise unstable. For the stable side-band perturbation there ekisis a modulation form of MdV soliton.     

Theoretical and experimental investigation on nonlinear interaction among wave groups

Wave group is important in ocean wave theory and applications. In the past, nonlinear interaction among wave groups has been studied on the basis of the nonlinear Schr?dinger equation. Using this theoretical approach, we found that the nonlinear interaction among wave groups causes asymmetry in the shape of the wave envelope (steeper in the front of the curve of the envelope). An important consequence of this asymmetry is that the highest wave in a wave group appears one individual wave length ahead of the center of the wave group. Further results show that the degree of envelope asymmetry increases with increasing spectral width and the wave steepness. This theoretical analysis has been supplemented by a systematic experimental study of wind waves. Laboratory and some open sea wave data were analyzed. The results show that the shape of the wind wave envelope of wind waves has the same asymmetry predicted by the theoretical approach. The observed degree of deformation of the envelope also increases with increasing spectral width and the wave steepness as predicted by theory. These conclusions have important ramifications for practical applications of ocean wave theory.     

振荡型Rossby孤立波与大气阻塞

从正压涡度方程出发,在弱非线性和弱基流切变条件下,导得了描述非线性大气长波活动的推广的Ｋｄｖ方程,并得到了方程的孤立波解及其色散关系。取近似于实际大气运动的物理参数作数值计算,得到了振荡型Ｒｏｓｂｙ孤立波的水平结构和移动特征,其结果较之寻常的Ｋｄｖ孤立波更接近于实际大气中的阻塞流型。     

具有任意阶非线性薛定谔方程的新行波解

对具有任意阶非线性薛定谔方程的行波解进行了研究。给出具有任意阶非线性薛定谔方程的精确解。利用行波变换和辅助函数法把具有任意阶非线性薛定谔方程最终转化为一个非线性常微分方程的解,通过对这个微分方程的研究可以得到具有任意阶非线性薛定谔方程的行波解。具有任意阶非线性薛定谔方程存在的孤立波解、三角孤立波解、扭孤立波解、Jacobi椭圆函数解。得到了具有任意阶非线性薛定谔方程新的Jacobi椭圆函数解。     

非线性Rossby波所满足的三阶Zakharov方程与低频振荡

本文在基本气流具有水平切变的情况下,利用摄动法导出了非线性Rossby波所满足的三阶Zakharov方程,然后,考虑了基流具有弱切变的情况,通过使用三阶Zakharov方程研究了Rossby波列的第一类不稳定性问题。结果表明:通过非线性作用,大气中的Rossby波列可产生调制不稳定。同时,本文对这种不稳定的区域,增长率和周期进行了详细的计算,并讨论了波振幅、波数、纬度和基流切变对它们的影响,指出Rossby波列的调制不稳定可以激发30～60天的低频振荡。     

热源强迫的非线性惯性重力内波及其应用

利用动力学分析中的相平面方法,由z坐标系下的非绝热大气运动方程组导出了与非线性惯性重力内波有关的KdV方程,然后利用直接积分法得到两类有天气意义的孤立波解.初步建立了孤立波解与高原低涡的联系,进一步从理论上论证了高原低涡具有与热带气旋类低涡类似的涡眼和暖心结构的特征.     

大气中非线性Rossby波包的传播

本文研究了纬向基本气流具有弱切变而不是缓变的情况下的正压非线性Rossby波包,在仅考虑纬向波数k是tx的缓变函数时,可以得到一个描述非线性Rossby波包的推广的非线性Schrodinger方程,并指出,(1)当纬向波数k是t,x的一次缓变(即Z,X的函数)时,非线性Rossby波的波作用密度和能量密度是守恒的。(2)而当纬向波数k是t,x的二次缓变(即Τ,ξ的函数)时,非线性Rossby波包的波作用密度和能量密度并不是守恒的,而且我们还指出在纬向波数k不变的情况下,其波包振幅就变为典型的非线性Schrodinger方程,其流场具有阻塞结构。     

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.     

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.     

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.     

NONLINEAR INERTIA—GRAVITY INTERNAL WAVE IN STRATIFIED FLUID

Based on the fundamental equations of geophysical fluid dynamics and on the consequence of verticaldensity stratification,travelling wave coordinates are used in this work to study the geometric topologicalstructures of nonlinear permanent wave in phase plane.Rigorous mathematical mechanics demonstratethat the solution of permanent solitary wave does not exist.Hamilton functions and "action-angle" varia-bles are used to express the travelling wave system in the simplest form and the analytic solution of the nonlinear inertia-gravity internal wave is obtained.     

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.     

A water movement study in Lianzhou Bay,Guangxi Province,China

This study investigates the physical conditions (water depth, current speed, salinity, temperature) in Lianzhou Bay, a shallow coastal bay in southern China, during two expeditions in the dry and wet seasons of 2011. Based on these expedition data, basic hydrodynamic parameters like Brunt-Väisälä Frequency, Richardson Number, Rossby radius, and Resonance Period are calculated. The results show that Lianzhou Bay is characterized by comparatively small quantity of freshwater input and weak stratification. Strong tides, which are spatially uniform within the bay, cause turbulent mixing. Residence time of the water is shorter in winter due to a stronger coastal current in that season. Consideration of the water movement may help to reduce the harmful ecological impact of aquaculture waste water discharge.     

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.     

非线性惯性重力内波的特征及天气意义

对大气非线性惯笥重力内波方程组,利用相平面分析法导出了相应的ＫｄＶ方程。采用直接积分法求出两类有意义的孤立波解,讨论了波解的基本特征,并着重分析了一类奇异孤立波与某些天气系统（如青藏高原５００ｈＰａ低涡）的可能联系。     

摄动Wadati-Segur-Ablowitz方程的精确行波解

利用G′/G展开方法求解摄动的Wadati-Segur-Ablowitz（WSA）方程的解,并得到该方程推广形式的行波解,这几组行波解对Schrdinger方程的适定性的研究、可变为Lienard方程形式的一类非线性偏微分方程行波解的求解都有重要意义.为了更好的理解这几组行波解,给出了解的数值模拟图,通过数值模拟图可以直观的了解WSA方程中摄动项对方程波幅的影响.     

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 .     

A New Multigrid 3D-VAR Optimization Method for Bottom Friction Using HF Radar Current Observation

This paper proposes a new method for data assimilation of the surface radial current observed by High Frequency ground wave radar and optimization of the bottom friction coefficient. In this method, the shallow water wave equation is introduced into the cost function of the multigrid three-dimensional variation data assimilation method as the weak constraint term, the surface current and the bottom friction coefficient are defined as the analytical variables, and the high spatiotemporal resolution surface radial flow observed by the high-frequency ground wave radar is used to optimize the surface current and bottom friction coefficient. This method can effectively consider the spatiotemporal correlation of radar data and extract multiscale information from surface radial flow data from long waves to short waves. Introducing the shallow water wave equation into the cost function as a weak constraint condition can adjust both the momentum and mass fields simultaneously to obtain more reasonable analysis information. The optimized bottom friction coefficient is introduced into the regional ocean numerical model to carry out numerical experiments. The test results show that the bottom friction coefficient obtained by this method can effectively improve the accuracy of the numerical simulation of sea surface height in the offshore area and reduce the simulation error.     

Rossby waves with linear topography in barotropic fluids

Rossby waves are the most important waves in the atmosphere and ocean, and are parts of a large-scale system in fluid. The theory and observation show that, they satisfy quasi-geostrophic and quasi-static equilibrium approximations. In this paper, solitary Rossby waves induced by linear topography in barotropic fluids with a shear flow are studied. In order to simplify the problem, the topography is taken as a linear function of latitude variable y, then employing a weakly nonlinear method and a perturbation method, a KdV （Korteweg-de Vries） equation describing evolution of the amplitude of solitary Rossby waves induced by linear topography is derived. The results show that the variation of linear topography can induce the solitary Rossby waves in barotropic fluids with a shear flow, and extend the classical geophysical theory of fluid dynamics.     

Full waveform inversion based on initial model built from envelope inversion

Full waveform inversion is a fitting process based on full seismic wave field simulation data using the full waveform information in seismic records and theoretically it is the ultimate goal of seismic inversion.Howev-er, there are many problems to be solved in practical application.Firstly, it is the strong nonlinear problem be-tween the seismic wave field and inversion parameters;secondly, the lack of low-frequency information in seis-mic records.In this study, the envelope is used as objective function inversion to provide the inversion result for the multi-scale full waveform inversion as the initial model, solving the lack of low-frequency information in seismic records.Taking the envelope of seismic records as the objective function in combination of multi-scale full waveform inversion became a new inversion strategy, which naturally achieved the compensation of shortage of low-frequency information and inversion from low frequency to high frequency, reducing the non-linearity in the inversion process.The comparison of the result of full waveform inversion of the initial model built through envelope inversion with the result of the conventional multi-scale full waveform inversion indicates the effective-ness of envelope inversion for the recovery of low-frequency information in seismic records.