地球流体中有限振幅波解的一般形式

从地球流体中非线性波动所的方程经行波变换所得的平面自治动力系统出发，利用微分方程几何理论，揭示了地球流体中几种非线性波动均具有周期解，而不存在孤波解的普遍性质，采用在平面自治系统的平衡点附近作Ｔａｙｌｏｒ展开方法，论述了分式简谐函数是有限振幅波解的一般形式的结论。     

层结流体中的非线性惯性重力内波

根据地球流体力学基本方程组,在密度垂直层结的情况下,引进行波坐标,研究非线性定形波在相平面上的几何拓扑结构。严格论证了不存在定形孤立波,并通过Ｈａｍｉｌｔｏｎ函数及其角作用变把行波系统化成最简形式,由此而得到非线性惯性重力内波的解析解。     

正压海洋地形拦截波的不稳定

从描述f平面上的正压地形拦截波的非线性动力方程出发,利用常微分方程定性理论研究了海底地形坡度和海底摩擦对线性和非线性地形拦截波的动力不稳定性的影响,分析了不稳定的性质,找出了不稳定的判据。还在特定的海底地形坡度和海底摩擦条件下,建立了线性和非线性波的频散关系,并比较了两者的差别。     

深水波中进动共振的数值模拟研究

进动(precession)共振是一种非线性共振相互作用,2016年才有学者对这一现象进行研究。采用非静压二维自由表面流模型模拟了深水条件下重力波的进动共振现象。通过边界造波的方法产生双色波,分析了触发进动共振的初始条件;探讨了进动共振在小振幅前提条件下发生的简化初始条件。数值模拟分析两组对称测点,对不同测点的波面、能量谱进行对比分析。数值结果表明:非静压二维自由表面流模型可以模拟进动共振现象,并且可以采用双色波作为条件来研究深水五波进动共振现象,进动共振需要一定的能量转化时间,进动共振发生的条件是三波组合的进动频率等于一个系统存在的非线性频率。     

深水有限振幅重力波的一种解法

采用变量代换的方法,处理水波的自由边界,获得了新的水波控制方程和边界条件。以摄动法解非线性偏微分方程的近似解析解,求得了与三阶斯托克斯波略有差别的非线性波面和包含振幅的非线性水波色散关系,并且得出了二阶以上的波动势函数在深水情况下不为零的结论。     

岬间海湾滨面带波浪结构和外观统计特征

对中等波能条件下收集的粤东两个岬间海湾滨面带4个站点的波浪数据作了滨面带波面、波包和长重力波的基本特征的分析，得到如下主要结果：（1）滨面带波谱由多峰频构成，从海向岸波高增大，波周期减小，谱宽度加大，谱尖度减小；（2）入射波群性较强，表征入射波群性的相对均方根群高与谱宽度无关；（3）长波振幅与波浪能量增大，其形成主要与组成波间的非线性相互作用有关。     

混合Rossby惯性重力波致Lagrange余流

基于在一个连续层化条件下热带海洋波动的弱非线性动力学系统中建立的最低阶Ｌａｇｒａｎｇｅ余流协力学模型及由此导出的赤道波致Ｌａｇｒａｎｇｅ余流的一般解,导出了混合Ｒｏｓｓｂｙ惯性重力波第一斜压模态导致的最低阶Ｌａｇｒａｎｇｅ余流的表达式。从中发现,该波可产生纬向、经向和铅垂方向的Ｌａｇｒａｎｇｅ余流,其中水平分量与赤道中、东太平洋表层流速的年平均值（约５ｃｍ／ｓ）同量级;纬向和铅垂向余流关于赤道正对     

长重力波形成机制研究进展

简要介绍了长重力波的概念和它在近岸过程的重要性,概述和评析了长重力波形成的Munk与Tucker模式,BLW,Unoki和非线性作用模式,BFLW模式以及BLW和BFLW联合作用等6种模式,展望了长重力波综合研究的内容和必要性.     

非线性freak波分析及模拟理论探讨

概述了国内外学者对freak波的认识，并从各种观测资料分析总结了freak波的特征。引入完全非线性控制方程Schroedinger方程的1＋1模式，对freak波进行模拟，为在实验室造波或计算研究提供一种方法。     

长重力波运动与近岸过程研究综述

简要介绍了长重力波的概念和作用,概述了近岸长重力波的运动形式、类型、分布和波能变化,分析了近岸长重力波与泥沙运动、海岸侵蚀、近岸环流系统、海滩碎波带地貌形态和潮汐等的关系,提出了进一步研究的几点建议。     

New periodic wave solutions of a time fractional integrable shallow water equation

In this paper, author employed Jacobi elliptic function expansion method to build the new wave solutions of time fractional modified Camassa–Holm equation which is completely integrable dispersive shallow-water equation. In ocean engineering, Camassa–Holm equation is generally used as a tool in computer simulation of the water waves in shallow sees, coastal and harbors. The obtained solutions show that the Jacobi elliptic function expansion method (JEFEM) which based on Jacobi elliptic functions is an efficient, reliable, applicable and accurate tool for analytic approximation of a wide variety of nonlinear conformable time fractional partial differential equations.     

缓变风场驱动下正压环流中的多涡结构

利用正压涡度方程，研究了缓变风场驱动下水平尺度1000km平底方形海盆中海洋环流的响应。结果表明，缓变风场驱动下海洋环流的响应是多涡型的，线性情形下多涡结构表现为共振受迫Rossby波；非线性情形下受迫Rossby波被扭曲，多涡结构是由受迫Rossby波和次海盆尺度的惯性再循环共同构成。无论是稳定风场还是缓变风场，非线性作用越强，环流越趋于不稳定；非线性作用强且水平耗散作用弱时，非线性不稳定过程可能完全掩盖了变化的风旋度向海盆涡度输人的影响，此时风的变化对环流型式不再重要。     

非线性弱色散波内部流场的重构

基于势流理论和级数直接求逆方法,本文建立了基于Ｂｏｕｓｉｎｅｓｑ方程或Ｇｒｅｅｎ－Ｎａｇｈｄｉ方程给出的水深平均流速或某特征流速及波面信息重构非线性弱色散波内部流场的算法。以Ｂｏｕｓｉｎｅｓｑ方程的孤立波解为例,用本反演方法计算了孤立波的表面水平流速及底部水平流速。结果表明本算法是有效的。本反演算法可用于获取非线性弱色散波的内部流场的详细信息。     

Generation of a double Kelvin wave resulting from the reflection of the Rossby wave by the jump layer

This paper considers the evolution of a spatially-localized divergent Rossby wave field near the depth jump. If the jump magnitude is comparable to the depth, Rossby waves are fully reflected and a double Kelvin wave is then generated. The Rossby waves and the double Kelvin wave are described by the first- and zero-approximation fields of the asymptotic expansion, respectively. Over the characteristic Rossby wave period, the level elevation produced by the double Kelvin wave spreads over an extensive area, theraby making up for the change in the total fluid mass of the Rossby waves.Translated by Vladimir A. Puchkin.     

Does the Ulleung eddy owe its existence to β and nonlinearities?

A nonlinear theory for the generation of the Ulleung Warm Eddy (UWE) is proposed. Using the nonlinear reduced gravity (shallow water) equations, it is shown analytically that the eddy is established in order to balance the northward momentum flux (i.e., the flow force) exerted by the separating western boundary current (WBC). In this scenario, the presence of β produces a southward (eddy) force balancing the northward momentum flux imparted by the separating East Korean Warm Current (EKWC).It is found that, for a high Rossby number EKWC (i.e., highly nonlinear current), the eddy radius is roughly 2R_d/ε^1/6 (here ε≡βR_d/f₀, where R_d is the Rossby radius), implying that the UWE has a scale larger than that of most eddies (R_d). This solution suggests that, in contrast to the familiar idea attributing the formation of eddies to instabilities (i.e., the breakdown of a known steady solution), the UWE is an integral part of the steady stable solution. The solution also suggests that a weak WBC does not produce an eddy (due to the absence of nonlinearity).A reduced gravity numerical model is used to further analyze the relationship between β, nonlinearity and the eddy formation. First, we show that a high Rossby number WBC which is forced to separate from the wall on an f plane does not produce an eddy near the separation. To balance the northward momentum force imparted by the nonlinear boundary current, the f plane system moves constantly offshore, producing a southward Coriolis force. We then show that, as β is introduced to the problem, an anticyclonic eddy is formed. The numerical balance of forces shows that, as suggested by the analytical reasoning, the southward force produced by the eddy balances the northward flow force imparted by the boundary current. We also found that the observed eddy scale in the Japan/East Sea agrees with the analytical estimate for a nonlinear current.     

A proof and applications of the expansion theorem for the Rossby normal modes in a closed rectangular basin

An expansion theorem is derived for Rossby normal modes in a closed rectangular basin and the set of Rossby normal modes is proved to be complete. This theorem provides a general linear solution to the initial value problem as well as to the response problem. In particular, the Green's function is obtained for the instantaneous localized torque anywhere in the basin. Weakly nonlinear versions are solved also by the combination of the general linear solution with the asymptotic expansion in terms of small amplitude. Further, an application is suggested to the spectral method of numerical simulation based on Rossby normal modes relevant to the more nonlinear evolution equation on a-plane, instead ofsin functions or Chebyshev polynomials, which have been employed conventionally for this purpose.     

Asymptotic analysis of transition to turbulence and chaotic advection in shear zonal flows on a beta-plane

The generation of narrow-band Rossby wave packets and the modulated vortex chains induced by them in a weakly-dissipative zonal flow on the beta-plane with a velocity profile in the form of a shear layer is studied. The analysis is performed within the framework of the asymptotic approach based on the distinguishing a thin critical layer inside of which the vortex chains are formed. The evolution equations, describing the simultaneous development of a wave packet envelope and vorticity perturbations in a nonlinear critical layer, are derived for a weakly supercritical flow. A transition to the complex dynamics of a wave packet (low-mode turbulence) is studied within the framework of a numerical solution of the derived equations and its mechanism is revealed. The onset of chaotic advection and anomalous diffusion of passive scalar in the critical layer is considered, and the exponent of the diffusion law is calculated.     

A coupled-mode system with application to nonlinear water waves propagating in finite water depth and in variable bathymetry regions

A non-linear coupled-mode system of horizontal equations is presented, modelling the evolution of nonlinear water waves in finite depth over a general bottom topography. The vertical structure of the wave field is represented by means of a local-mode series expansion of the wave potential. This series contains the usual propagating and evanescent modes, plus two additional terms, the free-surface mode and the sloping-bottom mode, enabling to consistently treat the non-vertical end-conditions at the free-surface and the bottom boundaries. The present coupled-mode system fully accounts for the effects of non-linearity and dispersion, and the local-mode series exhibits fast convergence. Thus, a small number of modes (up to 5–6) are usually enough for precise numerical solution. In the present work, the coupled-mode system is applied to the numerical investigation of families of steady travelling wave solutions in constant depth, corresponding to a wide range of water depths, ranging from intermediate depth to shallow-water wave conditions, and its results are compared vs. Stokes and cnoidal wave theories, as well as with fully nonlinear Fourier methods. Furthermore, numerical results are presented for waves propagating over variable bathymetry regions and compared with nonlinear methods based on boundary integral formulation and experimental data, showing good agreement.     

Narrow banded wave propagation from very deep waters to the shore

A fully nonlinear Boussinessq-type model with several free coefficients is considered as a departure point. The model is monolayer and low order so as to simplify numerical solvability. The coefficients of the model are here considered functions of the local water depth. In doing so, we allow to improve the dispersive and shoaling properties for narrow banded wave trains in very deep waters. In particular, for monochromatic waves the dispersion and shoaling errors are bounded by ~ 2.8% up to kh = 100, being k the wave number and h the water depth. The proposed model is fully nonlinear in weakly dispersive conditions, so that nonlinear wave decomposition in shallower waters is well reproduced. The model equations are numerically solved using a fourth order scheme and tested against analytical solutions and experimental data.