完整Coriolis力作用下带有外源强迫的非线性KdV方程

利用摄动方法,从描写既有Coriolis力垂直分量又含有水平分量的位涡方程出发,给出了近赤道非线性Rossby波所满足的具有外源强迫的非线性KdV方程,并利用Jacobi椭圆函数展开法,求解了改进后的非线性KdV方程的行波解及孤立波解.通过分析KdV方程的行波解,指出Coriolis力的水平分量和外源对Rossby波动的影响.     

完整Coriolis力作用下的非线性Rossby波

在正压流体中,利用摄动方法从描写既有Coriolis参数的垂直分量又含有水平分量的位涡方程出发,推导了近赤道非线性Rossby波振幅演变所满足的非线性mKdV方程,并利用Jacobi椭圆函数展开法,求解了推广后的非线性mKdV方程的行波解及孤立波解.通过分析其方程的行波解及孤立波,表明地球旋转的水平分量对Rossby波动产生一定的影响.     

强阻尼非线性波方程的近似惯性流形

本文研究一类强阻尼非线性波方程．通过交换的方法，我们构造了方程的近似惯性流形序列，并得到了对于方程的整体吸引子的逼近估计．     

完整Coriolis力与弱地形作用下的非齐次mKdV-Burgers方程

本文研究了中高纬度含有完整Coriolis力的准地转位涡方程问题.利用时空伸缩变换方法,获得了描述Rossby波的振幅形态满足非齐次mKdV-Burgers方程的结论.方程的近似解表明,弱地形效应对Rossby波的振幅产生强迫作用,并推广了文献[12]中的结果.     

完整Coriolis力作用下带有外源强迫的非线性ZK方程

在正压流体中,从包含完整Coriolis参数的准地转位涡方程出发,在弱非线性长波近似下,采用多时空尺度和摄动方法,推导出大气非线性Rossby波振幅演变满足带有外源强迫的二维Zakharov-Kuznetsov(ZK)方程.然后利用Jacobi椭圆函数展开法,求解了ZK方程的椭圆正弦波解和孤立波解.分析结果表明,Coriolis参数的水平分量将影响二维Rossby波传播的频率特征,而外源不仅对二维Rossby波动的传播的频率有影响,对振幅也产生一个调制作用.     

一类非线性时滞波方程的惯性流形

在假设时滞时间足够小的情况下,本文得到一类非线性时滞波动方程的惯性流形的存在性.     

一类完整Coriolis力作用下的高阶非线性Schr?dinger方程的推导

在正压流体中,从含有完整Coriolis力的准地转位涡方程出发,采用摄动展开的方法推导了,一类新的高阶非线性Schr?dinger方程,用于描述地球流体力学中的非线性调制Rossby波.从方程中,讨论了调制波列.结果表明,完整Coriolis力下的水平分量和地形会影响均匀Rossby波调制不稳定,并且不稳定.区域也会随着改变.此外,均匀基本流也是影响Rossby孤立波调制不稳定性的的重要因素.     

三阶非线性KdV方程的交替分段显-隐差分格式

对三阶非线性KdV方程给出了一组非对称的差分公式,用这些差分公式与显、隐差分公式组合,构造了一类具有本性并行的交替分段显-隐格式A·D2证明了格式的线性绝对稳定性．对1个孤立波解、2个孤立波解的情况分别进行了数值试验．数值结果显示,交替分段显-隐格式稳定,有较高的精确度．     

非线性波方程准确孤立波解的符号计算

该文将机械化数学方法应用于偏微分方程领域，建立了构造一类非线性发展方程孤立波解的一种统一算法，并在计算机数学系统上加以实现，推导出了一批非线性发展方程的精确孤立波解．算法的基本原理是利用非线性发展方程孤立波解的局部性特点，将孤立波表示为双曲正切函数的多项式．从而将非线性发展方程（组）的求解问题转化为非线性代数方程组的求解问题．利用吴文俊消元法在计算机代数系统上求解非线性代数方程组，最终获得非线性发展方程（组）的准确孤立波解.     

基于时滞惯性流形的非线性Galerkin算法

针对Marion-Temam型非线性Galerkin方法可行性强烈依赖于最小解题规模的不足,利用时滞惯性流形的新思想,以二维Navier-Stokes方程为例,给出了该类非线性Galerkin方法的一种改进形式,并证明了改进后的方法在保持原方法优越性的同时,其可行性条件得到了很大的改善,从而,给出的是一种可行的高效稳定算法。     

On Nonlinear Kelvin-Helmholtz Waves Near Direct Resonance

The evolution equation for the nonlinear Kelvin-Helmholtz wave envelope with its carrier wavenumber near direct resonance is formulated directly by using the nonlinear dispersion relation. The stability of a wavetrain is examined, and the long-time evolution for an arbitrary initial condition is studied through inverse scattering transforms.     

波浪上方飞行二维地效翼的非线性分析

针对二维波浪上方飞行的非定常二维地效翼进行了非线性分析．通过对二维奇点在规则波上方运动的Green函数的推导,利用离散涡方法解决了二维波浪上方飞行的非定常地效翼的升力问题．针对不同的几何参数和波浪参数对升力系数进行了研究．通过与定常情况的对比,验证了方法的有效性.     

Long Nonlinear Water Waves in a Channel Near a Cut-off Frequency

A theoretical study is made of the free-surface flow induced by a wavemaker, performing torsional oscillations about a vertical axis, in a shallow rectangular channel near a cut-off frequency. Exactly at cut-off, linearized water-wave theory predicts a temporally unbounded response due to a resonance phenomenon. It is shown, through a perturbation analysis using characteristic variables, that the nonlinear response is governed by a forced Kadomtsev—Petviashvili (KP) equation with periodic boundary conditions across the channel. This nonlinear initial-boundary-value problem is investigated analytically and numerically. When surface-tension effects are negligible, the nonlinear response reaches a steady state and exhibits jump phenomena. On the other hand, in the high-surface-tension regime, no steady state is obtained. These results are discussed in connection with similar forced wave phenomena studied previously in a deepwater channel and related laboratory experiments.     

变化底部对非线性表面波的影响

考虑表面张力的作用,研究了不可压缩、无粘性流体流过变化壁面时的共振流动,分析了不同的底部壁面变化对非线性表面波的影响．在导出非线性表面波遵循的fKdV方程后,利用拟谱方法进行数值模拟,用Matlab软件绘制瀑布图,由此得出结论:上凸底部上的波可以看成是向前凸台阶和向后凸台阶分别向前后散射发展的结果,二者不发生相互作用;下凹壁面的波形是向前凹台阶和向后凹台阶相互作用的结果;某些组合式底部的波形是上凸和下凹相互作用的结果．     

On the Modelling of Shallow-Water Waves with the Coriolis Effect

Journal of Nonlinear Science - Consideration herein is a rotation-Camassa–Holm-type equation, which can be derived as an asymptotic model for the propagation of long-crested shallow-water...     

Nonlinear Waves of Vorticity

This is a review of solutions of the vorticity equation for two-dimensional flow of an inviscid incompressible fluid that represent nonlinear waves. Geophysical applications are emphasized. Some of the solutions are valid in the beta-plane of Rossby. Some are related to weakly nonlinear perturbations of basic parallel flows and axisymmetric flows, to initial-value problems of hydrodynamic instability and to variational principles of minimal enstrophy or maximal entropy. Some have been found by exploiting well-known ideas of the theory of solitons. In addition to listing known solutions and presenting a synthesis of their relationship to other fluid dynamic results, we report a few new ideas and new solutions for strongly nonlinear waves.     

Scattering of Inertial Waves by Smooth Convex Cylinders

A general method of solution of the hyperbolic partial differential equation governing the scattering of inertial waves in a rotating fluid is presented for the case of cylindrical scatterers with smooth convex cross-sections. The specific case of a parabolic cylinder is discussed in some detail.     

Scattering of Inertial Waves in a Rotating Fluid

The scattering of plane inertial waves by both a flat strip and a circular cylinder whose generators are perpendicular to the rotation vector is examined. The properties of the reflected and diffracted fields, viz. spatial decay, propagation, structure, etc....are contrasted with those of the classical scattering fields in the limit where the wave length is small compared to the size of the scatterer.     

The Evolution of Waves Near Direct-Resonance Conditions

An analytical and numerical study is made of the propagation of waves whose wavenumbers are close to conditions for direct resonance. These waves emerge from the linear initial value problem as the dominant far field signal. The nonlinear evolution characteristics are investigated. It is found that weakly nonlinear waves at direct resonance may rapidly amplify and tend to become fully nonlinear in a finite time.